Work and Wages (dk;Z vkSj etnwjh)

(CLASSROOM SHEET)
1. Tina alone can do a piece of work in 12 days (a) 5500 (b) 6600
and Meena alone can do the same work in
15 days. If Tina and Meena undertook to do (c) 6400 (d) 7200
this work for Rs. 18,000, then how much 4. A and B worked together and received a
amount will Meena get, if they work total of Rs 18,000 for 15 days. A's
together? efficiency in the work was 5 times that
Vhuk vdsys fdlh dk;Z dks 12 fnuksa esa dj ldrh gS vkSj
of B's. The daily wage of A (in Rs) was:
ehuk vdsys mlh dk;Z dks 15 fnuksa esa dj ldrh gSA ;fn A vkSjB us ,d lkFk dke fd;k vkSj 15 fnuksa ds
Vhuk vkSj ehuk `dks
18]000 esa bl dk;Z dks djus dh
fy, dqy 18]000 #i;s çkIr fd,A dk;Z esaA dh
ftEesnkjh lkSaih tkrh gS rks ehuk dks fdruh /ujkf'k izkIr

r
dq'kyrkB dh dq'kyrk dh 5 xquk FkhA
A dk nSfud
gksxh] ;fn nksuksa lkFk feydj dke djsa\
etnwjh (#i;s esa) fdruh Fkh\

si
SSC CHSL 09/03/2023 (Shift-01)
(a) ` 10,000 (b) ` 6,000 SSC CGL MAINS 03/02/2022
(c) ` 12,000
an by (d) ` 8,000 (a) 800 (b) 600
2. Mohit and Rohit undertook a work for `

n
(c) 1200 (d) 1000
4400. Mohit alone can do that work in 10
days and Rohit alone can do the same work 5. P and Q completed a work together and
ja
in 15 days. If they work together, then what were paid Rs 1,080 and Rs 1,440,
R s

will be the difference in the amount they respectively. If P can do the entire work
in 20 days, how many days did they take
a th

receive?
eksfgr vkSj jksfgr`us
4400 esa ,d dke gkFk esa fy;kA to complete the work together?
eksfgr vdsys ml dke dks 10 fnuksa esa dj ldrk gS vkSj P vkSj Q us ,d lkFk ,d dke iwjk fd;k vkSj
jksfgr vdsys mlh dke dks 15 fnuksa esa dj ldrk gSA ;fn mUgsa Øe'k% #- 1]080 vkSj #- 1]440 dk Hkqxrk
ty a

os ,d lkFk dk;Z djrs gSa] rks mUgsa izkIr gksus okyh jkf'k esax;kA ;fn P iwjs dk;Z dks 20 fnuksa esa dj
fd;k
fdruk varj gksxk\ ldrk gS] rks mUgksaus ,d lkFk feydj dk;Z dks iwjk
di M

SSC CHSL 09/03/2023 (Shift-04) djus esa fdrus fnu dk le; fy;k\
(a) ` 800 (b) ` 1050
SSC CGL 20/04/2022 (Shift- 02)
(c) ` 900 (d) ` 880
3. A can complete a task in 18 days and B 3
can complete the same task in 32 days. (a) 8
7
They start working together but B works
only for 8 days. There after the work is 4
completed by A. If they received Rs.8,800 (b) 8
7
after completion of the work, then what
is A's share (in Rs.)? 3
(c) 6
,d dk;Z dks 18 fnuksa esa iwjk dj ldrk gS vkSj
A

A 7
B mlh dk;Z dks 32 fnuksa esa iwjk dj ldrk gSA os
4
,d lkFk dk;Z djuk 'kq: djrs gSa ysfduB dsoy (d) 6
7
8 fnuksa ds fy, dk;Z djrk gSA blds cknA }kjk
6. Sachin alone can complete a piece of work
dk;Z lekIr fd;k tkrk gSA ;fn dk;Z iwjk djus ds
1
ckn mUgsa 8]800 #i;s feyrs gSa]A'srks
dk fgLlk for Rs 8500 in 8 days. But with the help
2
(#i;s esa) D;k gS\
of Vishnu, the work is completed in 6 days.
SSC Phase X 04/08/2022 (Shift- 02) The share to be paid to Vishnu is:

[1]
 vdsys lfpu] #i;s 8]500 ds fy, fdlh dk;Z dks 10. Ashok and Anil undertake to do a piece of
work for Rs. 4,500. Ashok alone could do the
1
8
2
fnu esa iwjk dj ldrk gSA ysfdu fo".kq dh work in the 8 days and Anil in 12 days. With
the assistance of Amar, they finished the
enn ls] dk;Z 6 fnu esa iwjk gks tkrk gSA fo".kq dks
work in 4 days. What is the share of Amar?
Hkqxrku fd;k tkus okyk fgLlk Kkr djsaA v'kksd vkSj vfuy ,d dke dks Rs. 4]500 esa djus dk
SSC CHSL 05/08/2021 (Shift- 03) Bsdk ysrs gSaA v'kksd vdsys ml dke dks 8 fnu esa vkS
(a) Rs 2500 (b) Rs 2400 vfuy vdsys ml dke dks 12 fnu esa iwjk dj ldrk gSA
vej dh lgk;rk ls mUgksaus 4 fnu esa dke iwjk fd;kA bl
(c) Rs 2000 (d) Rs 3200
jkf'k esa vej dk fgLlk fdruk gksxk\
7. A, B and C can do a work in 8, 10 and 12
SSC CGL (PRE) 27/07/2023 (Shift-1)
days, respectively. After completing the
work together, they received Rs. 5,550. (a) Rs. 1,500 (b) Rs 750
What is the share of B (in Rs.) in the (c) Rs. 2,250 (d) 2, 500
amount received? 11. A can do a work in 20 days, while B can do
the same work in 25 days. They started the
A, B vkSjC ,d dke dks Øe'k% 8] 10 vkSj 12

r
work jointly. Few days later C also joined
fnuksa esa dj ldrs gSaA ,d lkFk feydj dke iwjk them and thus all the them completed the

si
djus ds ckn] mUgsa
Rs.5]550 izkIr gq,A izkIr jkf'k whole work in 10 days. All of the were paid a
an by
esaB dk fgLlk (Rs. esa) fdruk gS\ total of Rs.700. What is the share of C?

SSC CGL 12/04/2022 ( Shift- 01)

A fdlh dk;Z dks 20 rFkk B mlh dk;Z dks25

n
fnuksa eas lekIr dj ldrk gSA mUgksaus ,d lkFk dk;
(a) 1500 (b) Rs.1850
izkjEHk fd;k] dqN fnuksa ds i'pkr~
C Hkh muds lkFk
(c) 1800
ja (d) 1696
dk;Z esa 'kkfey gks x;k bl izdkj lEiw.kZ10 dk;Z
R s

8. A, B and C can do a work in 10 days, 15 fnuksa esa lekIr gqvkA lHkh dks dqy 700 feykdj
a th

days, and 20 days, respectively. They

finished that work together and got `2,600 #i;s dk Hkqxrku fd;k x;kA
C dk fgLlk Kkr dhft,A
as wages. Find C's wage. SSC CPO 16/03/2019 (Shift- 03)
A, B vkSj C ,d dke dks Øe'k% 10 fnu] 15 fnu (a) 55 (b) 65
ty a

vkSj 20 fnu esa iwjk dj ldrs gSaA mUgksaus ml dke dks

(c) 75 (d) 70
,d lkFk feydj iwjk fd;k vkSj etnwjh ds :i esa 12. A and B undertake a contract of a task
di M

`2,600 çkIr fd,A C dh etnwjh Kkr djsaA for Rs. 7,500. A can do complete the task
all alone in 50 days and B can complete
SSC CGL TIER I 20/07/2023 (Shift-02) the same task all by himself in 60 days.
(a) `550 (b) `600 However, to finish the work early, they
take C’s help and complete the entire work
(c) `575 (d) `625
in 20 days. What is the difference (in Rs.)
9. Rani can do a work in 10 days, Priya can do between B’s and C’s share for their
the same work in 15 days and Guddu can do contribution in completing the task?
the same work in 12 days. If they do that
work together and they are paid ` 9000, then vkSjB ,d dke dks Bsdk 7500 :i;s esa ysrs gSaA
A
what is the share of Priya? vdsys dke dks 50 fnu esa iwjk dj ldrk gS
A
jkuh ,d dke dks 10 fnu esa dj ldrh gS] fç;k mlh vkSj B mlh dke dks vdsys 60 fnu esa iwjk dj
A

dke dks 15 fnu esa dj ldrh gS vkSj xqM~Mw mlh dke dksldrk gSA gkykafd] dke dks tYnh lekIr djus ds
12 fnu esa dj ldrk gSA vxj os ml dke dks ,d lkFk fy,] os C dh enn ysrs gSa vkSj iwjs dke dks 20
djrs gSa vkSj mUgsa
` 9000 dk Hkqxrku fd;k tkrk gS] rks fnu esa iwjk djrs gSaA dke dks iwjk djus esa mu
fiz;k dk fgLlk fdruk gS\ ;ksxnku ds fy, B vkSjC dks izkIr fgLls ds chp
dk varj (:- esa) Kkr djsa\
SSC CHSL 17/03/2023 (Shift-01)
DP Head Constable 14/10/2022 (Shift- 03)
(a) ` 2400 (b) ` 3000
(a) 2,000 (b) 250
(c) ` 3500 (d) ` 3600
(c) 500 (d) 1500

[2]
13. Samir and Puneet can complete the same (a) Rs.300, Rs.250, Rs.300
work in 10 days and 15 days respectively. (b) Rs.600, Rs.400, Rs.500
The work was assigned for Rs. 4500. After
working together for 3 days Samir and (c) Rs.200, Rs.300, Rs.400
Puneet involved Ashok. The work was (d) None of these
completed in total 5 days. What amount 16. X, Y and Z have undertaken to complete
(in Rs.) was paid to Ashok? a piece of work for ` 4,800. All the three
lehj vkSj iquhr ,d dk;Z dks Øe'k% 10 fnu vkSj 3
15 fnu esa iwjk dj ldrs gSaA bl dk;Z ds fy, together can complete the work in 8
4
4500 #i;s dh /ujkf'k vkoafVr dh xbZ FkhA lehj
days. Y and Z together can complete the
vkSj iquhr us 3 fnu rd ,d lkFk feydj dk;Z
djus ds ckn] v'kksd dks dk;Z esa 'kkfey dj fy;kA 5
work in 15 days. X and Z together can
dk;Z dqy 5 fnu esa iwjk gqvkA v'kksd dks Hkqxrku 9
dh xbZ jkf'k (:i;s esa) Kkr djsaA
8
SSC CGL 16/08/2021(Shift 03) complete the work in 12 days. Find

r
11
(a) 750 (b) 1500

si
the difference between the shares of X and Z.
(c) 1071 (d) 800
X, Y vkSj Z us fdlh dk;Z dks` 4]800 esa djus
14.
an by
A can do a piece of work in 8 days while
B alone can do it in 12 days. They work 3
gsrq fy;kA os rhuksa ,d lkFk dk;Z8 dksfnuksa

n
together for 4 days and the remaining work
4
is completed by C alone in 2 days. They
esa lekIr dj ldrs gSaA
Y vkSj Z ,d lkFk dk;Z
ja
are paid Rs 7,200 for the completion of
R s
the entire work. The earnings of A, B and
5
C, respectively, are: dks 15 fnuksa esa lekIr dj ledrs gSaA
X vkSj
a th

9
A ,d dk;Z dks 8 fnuksa esa dj ldrk gS tcfdB
vdsyk mls 12 fnuksa esa dj ldrk gSA os 4 fnuksa ds 8
Z ,d lkFk dk;Z dks 12 fnuksa esa lekIr dj
fy, ,d lkFk dk;Z djrs gSa vkSj 'ks"k dk;Z vdsys
ty a

11
C }kjk 2 fnuksa esa iwjk fd;k tkrk gSA mUgsa iwjsldrs
dkegSaAX rFkk Z dks feyus okys fgLls esa varj
dks iwjk djus ds fy, 7]200 #i;s dk Hkqxrku fd;k
di M

Kkr dhft,A
tkrk gSA Øe'k%A, B vkSjC dh dekbZ gS%
(a) Rs.1200 (b) Rs.1500
SSC MTS (Shift- II) 18/10/2021
(c) Rs.900 (d) Rs.600
(a) Rs 2400, Rs 2400 Rs 2400 17. An expert, an average and a lazy labor work
(b) Rs 4000, Rs 2400 Rs 800 for 7, 8 and 10 days respectively and they
together get Rs.369 as labor charge. If the
(c) Rs 3600, Rs 2400 Rs 1200 ratio of their work done in one day is
(d) Rs 3000, Rs 3000 Rs 1200 1 1 1
: :
then how much the expert
15. A and B can do a work in 10 days, and 3 4 6
15 days respectively. A and B work labor gets?
together for 5 days and remaining work ,d fo'ks"kK] ,d vkSlr vkSj ,d vkylh Jfed
A

is done by C in two days. If they are paid Øe'k% 7] 8 vkSj 10 fnu dj;Z djrk gS vkSj mUgsa
` 6000 for this work, then find daily ,d lkFk esa 369 #i;s dk Jfed ewY; feyrk gSA
income of each? ;fn muds }kjk ,d fnu esa fd, x, dk;Z dk
A vkSj B ,d dk;Z dks 10 fnu vkSj 15 fnu esa 1 1 1
djrs gSaAA rFkkB nksuksa ,d lkFk 5 fnu rd dke vuqikr : : gks] rks fo'ks"kK] Jfed dks
3 4 6
djrs gSa vkSj ckadh dk;ZC, 2 fnu esa iwjk djrk gSA fdruh /ujkf'k izkIr gqbZ\
;fn mudks bl dk;Z dks djus ds fy, 6000 #i;s (a) Rs.120 (b) Rs.102.50
fn;k tk, rks izR;sd dh 1 fnu dh dekbZ fdruh gksxh\ (c) Rs.200 (d) Rs.143.50

[3]
 13 21. 5 men and 3 boys can complete a work
18. A and B have to do of a work, working in 7 days while 9 men and 5 boys can do
15
the work in 4 days. If total amount of
11
together, B and C have to do of the `6000 is given to 6 men and 4 boys for
20 doing work in 6 days. Then how much a
same work. If the difference between the
boy has been paid in one day?
wages of A and C is Rs.7600 then find the
wages of A , B and C together? 5 vkneh vkSj 3 yM+ds ,d dk;Z dks 7 fnuk esa
13 iwjk dj ldrs gSa tcfd 9 vkneh vkSj 5 yM+ds
A rFkk B dks ,d lkFk feydj Hkkx dk;Z
15 ml dke dks 4 fnu esa dj ldrs gSaA ;fn 6 vkneh
11 vkSj 4 yM+dksa dks 6 fnu dds dk;Z dk osru 6]000 #i;s
djuk gS vkSjB rFkkC dks feydj Hkkx dk;Z
20 fn;k x;k rc ,d yM+ds dk ,d fnu dk osru D;k gS\
djuk gSA ;fnA vkSj B dh etnwjh dk varj #i;s
(a) ` 100
7600 gS] rks
A, B rFkkC dh dqy etnwjh gS &
(a) Rs.24,000 (b) Rs.18,000 (b) ` 300

r
(c) Rs.36,000 (d) Rs.56,000 (c) ` 200

si
19. The labourers A, B, C were given a (d) ` 400
contract of Rs.750 for doing a certain
an by
piece of work. All the three together can
22. A can do a piece of work in 60 days, B in
f inish the work in 8 days. A and C 40 days, and C in 12 days. They work for

n
together can do it in 12 days, while A and a day each in turn, that is, first day A does
it alone, second day B does it alone, and
1 third day C does it alone. After that. the
ja
B together can do it in 13 days. they
R s
3 cycle is repeated till the work is finished.
money will be divided in the ratio They get ` 270 for this job If the wages
a th

rhu JfedksaA, B, C dks Bsds ij #i;s 750 ij are divided in proportion to the work each
fdlh dk;Z dks iwjk djus ds fy, yxk;k x;kA ;s had done, find the amount A will get?
rhuksa feydj bl dk;Z dks 8 fnuksa esa lekIr dj A ,d dk;Z dks 60 fnu esa djrk gS]B 40 fnu esa
ty a

ldrs gSaA
A vkSj C nksuksa feydj bls
12 fnuksa] esa djrk gS rFkkC 12 fnu esa djrk gSA izR;sd O;fDr
ckjh&ckjh ls ,d fnu ds fy, bl izdkj dk;Z djrs
di M

1
tcfd A vkSj B nksuksa feydj bls
13 fnuksa eas
3 gSa fdA igys fnu dk;Z djrk gS] B nwljs fnu
iwjk dj ldrs gSaA esgurkus dh jde dks fdl vuqikr dk;Z djrk gS vkSjC rhljs fnu dk;Z djrk gS vkSj
eas foHkkftr fd;k tk,xk\ blh izdkj tc rd dk;Z lekIr ugha gks tkrk os
(a) 4 : 5 : 6 (b) 4 : 7 : 5 dke djrs jgrs gSaA mudks bl dk;Z ds `fy,270
(c) 5 : 7 : 4 (d) 5 : 6 : 8 fn;s tkrs gSaA dk;Z ds vuqlkj ;fn mudks #i;s fn,
20. 4 women and 7 men earn a total of Rs. 11,480 tk, rks A dks fdrus :i;s feys\
in 7 days, while 10 women and 17 men earn a
(a) ` 14 (b) ` 36
total of Rs. 36,360 in 9 days. How much will
11 women and 9 men together earn (in Rs.) in (c) ` 24 (d) ` 27
A

13 days?
23. A can do a piece of work in 90 days, B in
4 efgyk,a vkSj 7 iq#"k 7 fnu esa oqQy 11480 dekrs gSa]40 days and C in 12 days. They work for
tcfd 10 efgyk,a vkSj 17 iq#"k 9 fnu esa oqQy 36360 a day each in turn i.e., first day A does
#i;s dekrs gSaA 11 efgyk,a vkSj 9 iq#"k feydj 13 fnu it alone, B does it the second day and C
esa fdruk (#- esa) dek,axs \ they third day. After that A does it for
another day, and so no, after finishing the
SSC CGL PRE, 24/07/2023 (Shift-3)
work they get Rs. 240. If the wages are
(a) 42770 (b) 42640 divided in Proportion to the work done by
(c) 42510 (d) 42900 them, find what each will get.

[4]
 A fdlh dke dks 90 fnu esa]B 40 fnu esa vkSj24. S, T and U can complete a work in 40, 48
C 12 fnu esa dj ldrk gSA os izR;sd ,d&,d fnu and 60 days respectively They received Rs.
10800 to complete the work. They begin
dke djrs gSA igys fnuA vdsys dke djrk gSA
the work together but T left 2 days before
nwljs fnuB vdsys rFkk rhljs fnuC vdsys dke the completion of the work and U left 5
djrk gSA blh rjg dke iwjk gksus rd pØ nksgjk;k days before the completion of th work. S has
tkrk gSA mUgsa ml dke ds 240 fy, #i;s feyrs completed the remaining work alone. What
gSA ;fn etnwjh izR;sd ds dke ds vuqikr esa foHkkftr is the share of S (in Rs.) from total money?

dh tkrh gSA rks jkf'k Kkr djs Atks

dks feysxhA S, T rFkk U ,d dk;Z Øe'k% 40, 48 rFkk 60
(a) A Rs.24, B Rs.54 and C Rs.162 fnu esa iwjk djrs gSaA dk;Z dks iwjk djus ds fy,
(b) A Rs.22, B Rs.50 and C Rs.132 mUgsa 10800 #i;s feyrs gSaA mUgksaus dk;Z dk
(c) A Rs.26, B Rs.52 and C Rs.142 lkFk izkjaHk fd;k] ijUrq
T dk;Z iwjk gksus2 ls
fnu
(d) A Rs.20, B Rs.44 and C Rs.185 igys rFkkU dk;Z iwjk gksus5 lsfnu igys dk;Z
dks NksM+dj pyk tkrk SgSA'ks"k dk;Z dks vdsyk
iw.kZ djrk gsA fuèkkZfjr jkf'kS esa
Hkkx
ls (#i;s

r
eas) fdruk gSA

si
(a) 4000 (b) 4320
an by (c) 4500 (d) 4860

n
ja Answer Key
R s

1. (d) 2.(d) 3. (b) 4. (d) 5. (b) 6. (a) 7. (c) 8. (b) 9. (a) 10. (b)
a th

11.(a) 12.(c) 13.(a) 14.(c) 15.(b) 16.(c) 17.(d) 18.(a) 19.(a) 20.(b)
ty a

21.(a) 22.(b) 23.(a) 24.(d)

di M
A

[5]
Join Telegram- Maths by Aditya Ranjan Work & Wages

Work & Wages @dk;Z vkSj etnwjh

(Practice Sheet With Solution)
1. The income of A, B, and C together in one day P, Q vkSjR ,d dk;Z dks Øe'k% 16 fnu] 24 fnu vkSj
isRs. 1275 to do a piece of work. Efficiency of
A and B is 17:21 respectively. If A earns more
12 fnu esa iwjk dj ldrs gSaA mUgksaus 2 fnuksa rd ,d lk
than C which is the same as B earns more than dk;Z fd;k] vkSj fiQjP us dk;Z NksM+ fn;kA mldsQ ckn]
A, then, find the amount of money earned by vkSjR us 1 fnu dk;Z fd;k vkSj fiQjQ us dk;Z NksM+
A and C together in 7 days to do the same
fn;kA vkSj 'ks"k dk;Z
R }kjk fd;k x;kA ;fn mUgsa iwjs dk;Z
piece of work.
,d fnu eas A, B vkSjC dh ,d lkFk ,d dke djus ds ds fy, 3420 :i;s feys] rks R dk fgLlk Kkr dhft,A

r
fy, vk; 1275 :i;s gSA A vkSjB dh n{krk Øe'k% 17 % (a) Rs 2565 (b) Rs 2385

si
21 gSA ;fnA, C ls vf/d dekrk gS tks fd B ds leku (c) Rs 2370 (d) Rs 2470
A ls vf/d dekrk gSA rks leku dk;Z dks djus ds fy,
A 4. If M had worked alone, he would have taken

an by
vkSjC }kjk ,d lkFk 7 fnuksa esa vftZr dh xbZ jkf'k Kkr 32 hours to do the task. What is M’s share, if
M and N worked together on a task and
dhft,A

n
finished it in 18 hours and they get paid of
(a) Rs 5020 (b) Rs 3582
(c) Rs 2948 (d) Rs 5250 Rs.2976 for it?

ja
;fn vdsyk M dk;Z djrk] rks mls dk;Z djus esa 32 ?kaVs
2.
R s
Three friends P, Q and R started work. P alone
can finish a work in ‘a' days and Q alone can yxrs gSaA
M dk fgLlk D;k gS] ;fn ,d lkFk M vkSjN
a th
finish work in ‘a + 15’ days and R alone can
finish work in ‘a + 30’ days. Three friends started
,d dk;Z ij dke djrs gSa vkSj bls 18 ?kaVs esa iwjk djrs gS
work after ‘b' days P left the job and after ‘b + 5’ vkSj mUgsa blds fy, 2976 :i;s dk Hkqxrku feyrk gS\
days Q also left the job and the remaining work (a) Rs 1590 (b) Rs 1654
ty a

will be finished by R in the next b +10 days. Work (c) Rs 1689 (d) Rs 1674
done by P in 4 days is equal to work done by Q
5. 46 women earned Rs 172500 by working 25
di M

in 6 days. If the total wages for their work is Rs

5400 and they are paid according to their work days. How many men must work for 24 days
then find the share of Q? to receive Rs 230400 provided the daily wages
rhu nksLrP, Q vkSjR us dke 'kq: fd;kAP vdsyk ,d of a man is twice that of a woman?
dke dks 'a' fnuksa esa iwjk dj ldrk gS Q
vkSj
vdsyk 'a + 46 efgykvksa us 25 fnu dke djds 172500 #i;s dek,A
15' fnuksa esa dke [kRe dj ldrk gS vkSjR vdsyk 'a + 230400 #i;s çkIr djus ds fy, fdrus iq#"kksa dks 24 fnuksa
30' fnuksa esa dke [kRe dj ldrk gSA rhu nksLrksa 'b' us rd dke djuk gksxk] c'krZs ,d iq#"k dh nSfud etnwjh
fnuksa ds ckn dke 'kq: fd;k]p us ukSdjh NksM+ nh 'b vkSj ,d efgyk dh rqyuk esa nksxquh gks\
+ 5' fnuksa ds cknQ us Hkh ukSdjh NksM+ nh vkSj 'ks"k (a) dke30 men (b) 32 men
vxys b + 10 fnuksa R esa}kjk iwjk fd;k tk,xkA
P }kjk 4 (c) 28 men (d) 34 men
fnuksa esa fd;k x;k dk;Z
Q }kjk6 fnuksa esa fd, x, dk;Z6. A alone complete the work in 24 days and B
A

ds cjkcj gSA ;fn muds dke dh dqy etnwjh 5400 :i;s alone complete the work in 40 days and A, B
gS vksj mUgsa muds dke ds vuqlkj Hkqxrku fd;k tkrk gSand
rks C together can complete the work in 10
Q dk fgLlk Kkr dhft,\ days. If they earned the total wages Rs 1680,
(a) Rs 2000 (b) Rs 2400 what is the share of C?
(c) Rs 1500 (d) 1800 A vdsys dke dks 24 fnuksa esa iwjk djrk gS B vdsys
vkSj
3. P, Q and R can do a piece of work in 16 days,
24 days and 12 days respectively. They worked dke dks 40 fnuksa esa iwjk djrk gS
A] vkSj
B vkSjC feydj
together for 2 days, and then P left the work. dke dks 10 fnuksa esa iwjk dj ldrs gSaA ;fn mUgksaus
After that, Q and R worked for 1 day and then etnwjh 1680 #i;s vftZr dh] rksC dk fgLlk D;k gS\
Q left the work. And the remaining work was
(a) Rs 520 (b) Rs 560
done by R. If they got Rs.3420 for the whole
work, then find the share of R. (c) Rs 600 (d) Rs 480

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7. A alone completes the work in 30 days and B 11. A can do the piece of work in 15 days and the
alone completes the work in 20 days. A and B ratio of the efficiency of A and B is 4 : 1. A, B
gets the wages of Rs 6000. With the help of C and C together can complete the half of the
they finish the work in 10 days. How much work in 4 days. If they are gets the total wages
money will C be paid? is 5400, then what is the wage of C?
A ,d dke dks 15 fnuksa esa iwjk dj ldrk gS vkSj
A vkSj
A vdsys dke dks 30 fnuksa esa iwjk djrk gS B vdsys
vkSj
B dh n{krk dk vuqikr 4%1 gSA A] B vkSj C feydj
dke dks 20 fnuksa esa iwjk djrk A vkSj
gSA B dks 6000
dke dk vk/k fgLlk 4 fnuksa esa iwjk dj ldrs gSaA ;fn
#i;s dh etnwjh feyrh gSAC dh enn ls os 10 fnuksa esa
mudk dqy osru 5400 gS] rks
C dk osru D;k gS\
dke iwjk djrs gSaA
C dks fdruk iSlk fn;k tk,xk\ (a) Rs 1200 (b) Rs 1500
(a) Rs 800 (b) Rs 1000 (c) Rs 1800 (d) Rs 2000
(c) Rs 1200 (d) Rs 600 12. A, B and C can complete the work in 16 days,
8. A alone completes the work in 30 days and the 20 days and 24 days respectively. The total
efficiency of A is 300% more than the wage is Rs 1850. If they work together to
efficiency of B. If A, B and C together can complete the work, what is A’s wage?

r
complete the work in 16 days and they are get A] B vkSj C Øe'k% 16 fnu] 20 fnu vkSj 24 fnu esa

si
the total wages of Rs 27000, then what is the dke iwjk dj ldrs gSaA dqy etnwjh 1850 #i;s gSA ;fn os
wages of C? dke iwjk djus ds fy, ,d lkFk dke djrs gSa] rks
A dh

an by
A vdsys dke dks 30 fnuksa esa iwjk djrk gSA vkSj
dh etnwjh D;k gS\
n{krkB dh n{krk ls 300» vf/d gSA ;fn A] B vkSjC (a) Rs 500 (b) Rs 750

n
feydj dke dks 16 fnuksa esa iwjk dj ldrs gSa vkSj mUgsa
(c) Rs 650 (d) Rs 850
13. A alone can finish a job in 12 days and B alone
dqy etnwjh 27000 #i;s feyrh gS] rks D;k
C dk osru

ja
can do It in 20 days. If they work together and
D;k gS\
R s finish it, then the share of A in total wages of
(a) Rs 9000 (b) Rs 12000 Rs100 is.
a th
(c) Rs 10000 (d) Rs 6000 A vdsys ,d dke dks 12 fnuksa esa iwjk dj ldrk gS vkSj
9. A can complete 60% of the work in 9 days and B vdsyk mlh dke dks 20 fnuksa esa dj ldrk gSA ;fn os
A and B together can complete half of the work ,d lkFk dk;Z djrs gSa vkSj mls iwjk djrs gSa] rks dqy
ty a

in 4.5 days. If A, B and C together can etnwjh 100 :i;s esa lsA dk fgLlk gSA
complete 40% of the work in 3 days and they (a) Rs.56.25 (b) Rs.67.50
di M

are gets the total wages is 1200, then what is (c) Rs.62.50 (d) Rs.50
the wage of B?
1
A 60» dke 9 fnuksa esa iwjk dj ldrk gS vkSj
A vkSj B 14. If A can do of a work in 3 days and B can
4
feydj dke dk vk/k fgLlk 4-5 fnuksa esa iwjk dj ldrs
1
gSaA ;fnA] B vkSj C feydj 3 fnuksa esa 40» dke iwjk do of the same work in 4 days, how much
6
dj ldrs gSa vkSj mUgsa dqy etnwjh 1200 feyrh BgS] rks
will A get if both work together and are paid
dh etnwjh D;k gS\ Rs 180 in all?
(a) Rs 200 (b) Rs 360
1
(c) Rs 280 (d) Rs 400 ;fn A fdlh dk;Z dk Hkkx 3 fnuksa esa dj ldrk gS
4
10. A can complete a piece of work in 18 days , B
is 25% less efficient than A. B started the work 1
A

vkSjB mlh dk;Z dk Hkkx 4 fnuksa esa dj ldrk gS] rks

and worked for 6 days and left and remaining 6
part of the work is completed by A. What is the A dks fdruk çkIr gksxk ;fn nksuksa ,d lkFk dk;Z djrs gSa
share of B if the total wages is Rs.3000? vkSj mUgsa dqy 180 #i;s dk Hkqxrku fd;k tkrk gS\
A ,d dke dks 18 fnuksa esa iwjk dj ldrk gS]
B] A ls (a) Rs. 60 (b) Rs. 120
25» de dq'ky gSAB us dke 'kq: fd;k vkSj 6 fnuksa rd (c) Rs. 90 (d) Rs. 180
dke fd;k vkSj NksM+ fn;k vkSj dke dk 'ks"k A Hkkx
}kjk 15. Amit , Ajay and sachin take up a task to finish
for Rs 876. Amit completes his assignment in
iwjk fd;k x;kA
B dk fgLlk D;k gS ;fn dqy etnwjh 3000
4 days, ajay does it in 8 days and Sachin takes
#i;s gS\ 12 days to finish it. They complete the work
(a) Rs 2250 (b) Rs 750 with the help of there mother Nirupama in 2
(c) Rs 600 (d) Rs 2400 days. What does Nirupama get?

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vfer] vt; vkSj lfpu 876 #i;s esa ,d dk;Z iwjk djus 18. If a man earns Rs 2000 for his first 50 hours
ds fy, gkFk esa ysrs gSaA vfer viuk dk;Z 4 fnuksa esa iwjk
of work in a week and is then paid one and half
times his regular hourly rate, then hours he
djrk gS] vt; bls 8 fnuksa esa iwjk djrk gS vkSj lfpu bls must work to make Rs 2300 in a week is.
iwjk djus esa 12 fnu ysrk gSA os viuh eka fu#iek dh
;fn ,d vkneh ,d lIrkg esa vius igys 50 ?kaVksa ds dke
enn ls 2 fnuksa esa dke iwjk djrs gSaA fu#iek dks D;k
ds fy, 2000 #i;s dekrk gS vkSj mlds ckn fu;fer ?kaVs
feyrk gS\
dh nj ls Ms<+ xquk Hkqxrku fd;k tkrk gS] rks ,d lIrkg esa
(a) Rs. 307 (b) Rs. 73
2300 #i;s dekus ds fy, fdrus ?kaVs dke djuk gksxkA
(c) Rs. 75 (d) Rs. 267
(a) 6 hours (b) 4 hours
16. A and B undertake a project worth Rs. 54000.
A alone can do the work in 10 days. They work (c) 5 hours (d) 7 hours
together for 3 days. After 3 days, B works alone 19. A, B and C can complete a piece of work
for 3 days and A completes the remaining work separately in 10, 20 and 40 days, respectively.
in 3 more days. What is the share of B in the In how many days will the work be completed
earnings? if A is assisted by both B and C every third

r
day?
A vkSjB 54000 #i;s dh ,d ifj;kstuk 'kq: djrs gSaA A
vdsyk ml dke dks 10 fnuksa esa dj ldrk gSA os 3 fnuksaA, B vkSjC ,d dk;Z dks vyx&vyx Øe'k% 10, 20

si
rd ,d lkFk dke djrs gSaA 3 fnuksa ds ckn] B vdsys 3
vkSj40 fnu esa iwjk dj ldrs gSaA ;fnA dks izR;sd

an by
fnuksa ds fy, dk;Z djrk gS vkSj
A 'ks"k dk;Z dks 3 vkSj
rhljs fnu B vkSj C nksuksa }kjk lgk;rk iznku dh tk,
fnuksa esa iwjk djrk gSABvk;
dkesa
fgLlk fdruk gS\ rks dk;Z fdrus fnu esa iwjk gksxk\

n
(a) Rs. 21600 (b) Rs. 33400 SSC CGL 01/12/2022 (Shift- 02)

ja
(c) Rs. 27800 (d) Rs. 35780 2
R s
17. A company assigned a job to three employees
(a) 8
7
(b) 9
P, Q and R for Rs 529. P and Q together do
a th
2
19 (c) 10 (d) 6
part of the work and Q and R together do 3
23
20. 5 men and 8 women can complete a work in
ty a

8 12 days working together, while 3 men and

part of the work. Then find what amount
23 7 women together can complete the same work
di M

should be paid to P? in 15 days. In how many days will 11 women

complete the same work?
,d daiuh }kjk P] Q vkSj R rhu deZpkfj;ksa dks 529
#i;s ds fy, ,d dke lkSaik x;k P vkSjQ feydj dke 5 iq#"k vkSj 8 efgyk,¡ ,d lkFk dke djrs gq, ,d
dke dks 12 fnu esa iwjk dj ldrs gSa] tcfd 3 iq#"k
19 8 vkSj 7 efgyk,a feydj mlh dke dks 15 fnu esa iwjk
dk vkSj Q vkSj R feydj dke dk Hkkx iqjk
23 23 dj ldrs gSaA 11 efgyk,¡ mlh dke dks fdrus fnu esa
djrs gSA rc Kkr dhft, P dks fdruh jkf'k dk Hkqxrku iwjk djsaxh\
fd;k tkuk pkfg,\ SSC CGL 03/12/2022 (Shift- 03)
(a) Rs. 315 (b) Rs. 345 (a) 12 (b) 8
(c) Rs. 355 (d) Rs. 375 (c) 6 (d) 16
A

Answer Key
1.(d) 2.(d) 3.(a) 4.(d) 5.(b) 6.(b) 7.(b) 8.(a) 9.(d) 10.(b)

11.(c) 12.(b) 13.(c) 14.(b) 15.(b) 16.(a) 17.(b) 18.(b) 19.(c) 20.(a)

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Pipe and Cistern (uy vkSj Vadh)

(CLASSROOM SHEET)
1. Pipe A can fill an empty tank in 18 hours 4. A pipe can fill a tank in 30 hours. Due to
and pipe B can fill the same empty tank in a leakage at the bottom, it is filled in 50
24 hours. If both the pipes are opened hours. How much time will the leakage
simultaneously, how much time (in hours) take to empty the completely filled tank?
will they take to fill the empty tank? ,d ikbi fdlh Vadh dks 30 ?kaVs esa Hkj ldrk gSA ryh esa
ikbi A ,d •kyh VSad dks 18 ?kaVs esa Hkj ldrk gS vkSjfjlko gksus ds dkj.k ;g50 ?kaVs esa Hkjrh gS A iwjh rjg ls
ikbi B mlh •kyh VSad dks 24 ?kaVs esa Hkj ldrk gSA ;fn Hkjh Vadh dks •kyh djus esa fjlko dks fdruk le;
nksuksa ikbiksa dks ,d lkFk •ksy fn;k tk,] rks •kyh VSadyxsxk\

r
dks Hkjus esa mUgsa fdruk le; (?kaVs esa) yxsxk\ SSC CGL (PRE) 24/07/2023 (Shift-2)

si
(a) 60 hours (b) 85 hours
CGL PRE, 14/07/2023 (Shift-4)
(c) 70 hours (d) 75 hours
an by
3 1 5. A pipe can fill a tank in 15 hours. Due to
(a) 11 (b) 10
7 7 leakage in the bottom it is filled in 20

n
hours. If the tank is full, and the pipe is
2 2
(c) 10 (d) 11 closed, how much time will the leak take
7 7
ja
to empty the entire tank?
R s

2. A tap can fill a tank in 4 hours. Another

tap can fill the same tank in 6 hours. If ,d ikbi ls ,d VSad dks 15 ?kaVs esa Hkjk tk ldrk
a th

both the taps are opened at the same time, gSA iassnh esa fjlko ds dkj.k ;g 25 ?kaVs eas Hkjrk
then in how much time will the empty ;fn VSad iwjk Hkj x;k gS vkSj ikbi cn gS] rks fjlko
tank be filled completely? ds }kjk bls [kkyh gksus esa fdruk le; yxsxk\
ty a

,d uy] fdlh Vadh dks 4 ?kaVs esa Hkj ldrk gSA nwljk SSC CHSL 02/06/2022 (Shift- 2)
uy] mlh Vadh dks 6 ?kaVs esa Hkj ldrk gSA ;fn nksuksa
di M

(a) 60 hrs (b) 50 hrs

uy ,d lkFk [kksys tkrs gSa] rks [kkyh Vadh dks iwjh
(c) 40 hrs (d) 30 hrs
rjg ls Hkjus esa fdruk le; yxsxk\
1
SSC CHSL 12/08/2021 (Shift- 1) 6. A tap can fill a tank in 5 hours. Because
2
(a) 3 h (b) 2 h 25 min
1
(c) 2 h 30 min (d) 2 h of a leak, it took 8
hours to fill the tank.
4
3. Pipe A can fill 50% of the tank in 6 hours
In how much time (in hours) will the leak
and pipe B can completely fill the same
tank in 18 hours. If both the pipes are alone empty 30% of the tank?
opened at the same time, in how much 1
time (in minutes) will the empty tank be ,d uy ,d Vadh dks 5 ?kaVs esa Hkj ldrk gSA ,d
A

2
completely filled?
ikbi A] 6 ?kaVs esa VSad
50 »dk
Hkkx Hkj ldrk gS vkSj 1
fjlko ds dkj.k Vadh dks Hkjus8esa?kaVs dk le;
4
ikbi B mlh VSad dks
18 ?kaVs esa iwjh rjg ls Hkj ldrk
gSA ;fn nksuksa ikbiksa dks ,d gh le; ij •ksy fn;k yxkA fdrus le; esa (?kaVksa esa) fjlko ls VSad dk 30»
tk,] rks •kyh VSad fdrus le; esa (fefuV esa) iw.kZr% fgLlk [kkyh gks tk,xk\
Hkj tk,xk\ SSC CGL MAINS 29/01/2022

SSC CGL (PRE) 26/07/2023 (Shift-2) 99 5

(a) (b)
20 2
(a) 420 (b) 425
9 17
(c) 432 (d) 435 (c) (d)
2 2

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7. An inlet pipe can fill a tank in 10 hours and 11. Pipes A, B and C can fill a tank in 30 h,
an other pipe can empty the completely filled 40 h and 60 h respectively. Pipes A, B and
tank in 20 hours. Both the pipes are opened C are opened at 7 a.m., 8 a.m. and 10 a.m.
at 6.30 a.m. When will the tank get filled? respectively on the same day. When will
,d varxZr ikbi fdlh Vadh dks 10 ?kaVs esa Hkj ldrk the tank be full?
gS tcfd ,d cfgxZe ikbi iwjh rjg ls Hkjh gqbZ Vadh ikbi A, B vkSj C fdlh Vadh dks Øe'k% 30] 40
dks 20 ?kaVksa esa [kkyh dj ldrk gSA nksuksa ikbiksavkSj dks
60 ?kaVksa esa Hkj ldrs gSaA
A, B vkSj
ikbiC dks
lqcg 6%30 cts pkyw fd;k tkrk gSA Vadh dc Hkj tk,xh\ ,d gh fnu Øe'k% lqcg 7] 8 vkSj 10 cts pkyw
SSC CHSL 03/07/2019 (Shift- 02)
fd;k tkrk gSA Vadh fdl le; Hkj tk,xh\
(a) 2 : 30 a.m. next day
(b) 2 a.m. next day SSC CGL TIER-II 11/09/2019
(c) 1 a.m. next day (a) 10.00 p.m. (b) 10.20 p.m.
(d) 12:00 midnight (c) 9.20 p.m. (d) 9.40 p.m.
8. P can fill a tank in 5 hours. Q can fill the 12. Pipes A and B can fill a tank in one hour
and two hours respectively while pipe C

r
same tank in 10 hours. R can empty the
same tank in 20 hours. How much time will can empty the filled up tank in one hour

si
all the three take together to fill the tank? and fifteen minutes. A and C are turned on
P ,d Vadh dks 5 ?kaVs esa Hkj ldrk
Q mlh
gSAVadh dks together at 9 a.m. After 2 hours, only A is
an by
closed and B is turned on. When will the
10 ?kaVs esa Hkj ldrk
R gSA
mlh Vadh dks 20 ?kaVs esa [kkyhtank be emptied?
dj ldrk gSA rhuksa feydj mlh Vadh dks Hkjus esa fdrukikbi A vkSj B fdlh Vadh dks Øe'k% ,d ?kaVs vkSj
le; ysxkA

n
SSC CHSL 13/03/2023 (Shift-02)
nks ?kaVs esa Hkj ldrs gSa ysfdu C Hkjh
ikbi gqbZ Vadh
dks ,d ?kaVs 15 feuV esa [kkyh dj ldrkAgSA vkSj
ja
R s

(a) 10 hours (b) 4 hours

C dks ,d lkFk lqcg 9 cts pkyw fd;k tkrk gSA 2
(c) 6 hours (d) 5 hours
?kaVs ckn dsoy A dks can fd;k tkrk gS vkSj B dks
a th

9. Pipe A can fill a tank in 12 minutes; pipe B

can fill it in 18 minutes, while pipe C can pkyw fd;k tkrk gSA Vadh dc [kkyh gks tk,xh\
empty the full tank in 36 minutes. If all SSC CGL 06/06/2019 (Shift- 01)
the pipes are opened simultaneously, how (a) 12:10 p.m. (b) 11:30 a.m.
ty a

much time will it take to fill the empty tank (c) 10:30 a.m. (d) 12:20 p.m.
completely? 13. Pipe A and B can fill a tank in 16 hours
di M

ikbi A ,d Vadh dks 12 feuV esa Hkj ldrk gS_ and 24 hours respectively, and pipe C
ikbi B bls 18 feuV esa Hkj ldrk gS] tcfd ikbi alone can empty the full tank in x hours.
C iwjh Hkjh gqbZ Vadh dks 36 feuV esa •kyh dj ldrk All the pipes were opened together at
gSA ;fn lHkh ikbiksa dks ,d lkFk •ksy fn;k tk,] rks 10.30 a.m., but C was closed at 2.30 p.m.
•kyh Vadh dks iwjh rjg Hkjus esa fdruk le; yxsxk\ If the tank was full at 8.30 p.m. on the
SSC CGL TIER I 20/07/2023 (Shift-04) same day, then what is the value of x?
(a) 7 minutes 30 seconds ikbi A vkSjB fdlh Vadh dks Øe'k% 16 vkSj 24 ?kaVs
(b) 10 minutes esa Hkj ldrs gSa rFkk C ikbi
vdsyk Hkjh gqbZ Vadh dks
(c) 9 minutes
(d) 6 minutes x ?kaVs esa [kkyh dj ldrk gSA lHkh ikbiksa dks lqc
10. Pipes A, B and C can fill a tank in 15, 30 10%30 cts ,d lkFk pkyw fd;k x;k ysfdu 2%30p.m.
A

and 40 hours, respectively. Pipes A, B and esaC dks can dj fn;k x;kA ;fn Vadh mlh fnu 8%30
C are opened at 6 a.m., 8 a.m. and 10 a.m.,
p.m. esa Hkj xbZ]xrks
dk eku Kkr djsaA
respectively, on the same day. When will
the tank be full? SSC CGL TIER-II 12/09/2019
ikbi A, B vkSj C fdlh Vadh dks Øe'k% 15, 30 (a) 64 (b) 48
vkSj40 ?kaVksa esa Hkj ldrs gSaA ,d gh fnu A, ikbi (c) 45 (d) 96
B vkSjC dks Øe'k%6, 8 vkSj10 cts [kksyk tkrk 14. Pipe A and B can fill a tank in 12 minutes
and 15 minutes, respectively. The tank
gSA Vadh fdrus cts Hkj tk,xh\ when full can be emptied by pipe C in x
SSC CPO 24/11/2020 (Shift-2) minutes. When all the three pipes are
(a) 3:20 p.m. (b) 11:20 p.m. opened simultaneously, the tank is full in
(c) 7:20 p.m. (d) 5:20 p.m. 10 minutes. The value of x is :

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ikbi A vkSj B Øe'k% 12 feuV vksj 15 feuV esa nks ikbiA vkSj ikbi B fdlh Vadh dks Øe'k% 16
,d VSad Hkj ldrs gSaA tc VSad Hkjh gks C rks ikbi vkSj 20 ?kaVs esa Hkj ldrs gSaA
A ls 'kq:vkr
ikbi djrs
}kjkx feuV esa [kkyh fd;k tk ldrk gSA tc rhuksa gq, mUgsa 1 ?kaVs ds fy, ,d ds ckn ,d djds [kksyk
ikbi ,d lkFk [kksys tkrs gSa] rks VSad 10 feuV esa Hkj
tkrk gSA [kkyh Vdh fdrus ?kaVksa esa Hkj tk,xh\
tkrk gSA x dk eku gS & SSC CPO 13/03/2019 (Shift- 03)
CGL TIER-II 16/10/2019 3 1
(a) 17 hours (b) 17 hours
(a) 18 (b) 15 5 5
(c) 20 (d) 24 1 3
(c) 17 hours (d) 17
hours
15. Pipe A and B can empty a filled tank in 20 4 4
hours and 15 hours respectively, while pipe 18. Two pipes A and B can fill an empty tank
C alone can fill the same tank in x hours.
in 10 hours and 16 hours respectively.
The three pipes have been opened
They are opened alternately for 1 hour
simultaneously and they took 40 minutes

r
1 each starting with pipe A first. In how
to finish the (one-eighteenth) part of many hours, the empty tank will be filled?

si
18
the tank. The value of x is : nks ikbiA vkSj B fdlh [kkyh Vadh dks Øe'k% 10
ikbi A vkSjB ,d Hkjs VSad dks Øe'k% 20 ?kaVs vkSjvkSj 16 ?kaVs esa Hkj nsrs AgSaA
ls 'kq:vkr
ikbi djrs
an by
15 ?kaVs esa [kkyh dj ldrs gSa] tcfd mlh VSad dksgq, mUgsa ,d&,d djds 1 ?kaVs ds fy, [kksyk tkrk gSA

n
ikbi C vdsyk x ?kaVksa esa Hkj ldrk gS rhuksa ikbi
fdrus ?kaVksa esa [kkyh Vadh Hkj tk,xh\
1 SSC CGL 06/06/2019 (Shift- 01)
,d lkFk [kksy fn, x, gSa vkSj mUgksaus VSad ds
ja
R s

18
Hkkx dks [kkyh djus esa 40 feuV dk le; fy;kA
x 1 1
(a) 12 hours (b) 12 hours
a th

dk eku gS & 3 8
SSC MTS 21/08/2019 (Shift- 03)
1 1
(a) 21 (b) 30 (c) 12 hours (d) 12 hours
ty a

4 6
(c) 26 (d) 24 19. A monkey climbs a 100 meter high pole.
di M

16. Two pipes A and B can fill an empty tank It climbs 6 meters in the first minute and
in 8 hours and 12 hours respectively. They slides 4 meters in the second minute. Find
are opened alternately for 1 hour each out in how much time will the monkey
starting with pipe A first. In how many climb the pole?
hours will the empty tank be filled?
,d cUnj 100 ehVj Åaps [kEHks ij p<+rk gSA ;g
nks ikbiA vkSj B fdlh [kkyh Vadh dks Øe'k% 8 igyh feuV esa 6 ehVj p<+rk gS vkSj nwljh feuV esa
vkSj 12 ?kaVs esa Hkj nsrs AgSaA
ls 'kq:vkr
ikbi djrs
4 feuV fiQly tkrk gSA Kkr djksa fdrus le; esa
gq, mUgsa ,d&,d djds 1 ?kaVs ds fy, [kksyk tkrk gSA
cUnj [kEHks ij p<+ tk;sxk\
fdrus ?kaVksa esa ;g [kkyh Vadh Hkj tk,xh\
(a) 90 min (b) 95 min
SSC CPO 12/03/2019 (Shift- 03) (c) 100 min (d) 120 min
A

1 20. A monkey climbs a 60 meter high pole. It

(a) 9 hours (b) 9 hours climbs 5 meters in 1st 18 minutes and slides
3
4 meters in 2nd minutes. Find out how much
time will it take to climb the pole?
1 1
(c) 9 hours (d) 9 hours ,d cUnj 60 ehVj Åaps [kEHks ij p<+rk gSA
1st ;g
2 4
18 feUkV essa 5 ehVj p<+rk gS
2ndvkSj
feUkV esa 4
17. Two pipes A and B can fill a tank in 16
ehVj fiQly tkrk gSA Kkr djks fd fdrus le; esa
hours and 20 hours respectively. They are
opened alternatively for 1 hour each, [kEHks ij p<+ tk;sxk\
starting with pipe A first. In how many (a) 111 min (b) 108 min
hours with the empty tank be filled? (c) 115 min (d) None of these

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21. Three pipes A, B, C are connected to a tank. 1

A and B can fill it in 20 and 30 minutes
nks ikbiA vkSj B Øe'k% 12 ?kaVs vkSj 25 ?kaVs esa
2
respectively while C can empty it in 15 ,d Vadh Hkj ldrs gSaA ikbi ,d lkFk [kksys tkrs gSa vkSj
minutes. If all three are opened one by one ;g ik;k tkrk gs fd ,d uhps fNnz ds dkj.k
for 1 minute each, find the time taken to 1 ?kaVs vkSj 40 feuV vf/d le; yxkA tc Vadh Hkj
fill the tank. tkrh gS] rks Vadh dks fNnz fdrus le; esa [kkyh dj nsxk\
rhu ikbi A, B, C, fdlh VSad ds lkFk tksM+s x, gS SSC CPO 25/11/2020 (Shift- 03)
A vkSjB bls Øe'k% 20 vkSj 30 feuV esa Hkj ldrs
(a) 42 hours (b) 48 hours
gS tcfd C bls 15 feuV esa [kkyh dj ldrk gSA
(c) 45 hours (d) 50 hours
vxj rhuksa dks ckjh ls 1&1 feuV ds fy, [kksyk
25. Pipe A can fill a tank in 12 hours and pipe
tk, rks VSad dks Hkjus esa yxk le; Kkr djsaA B takes 18 hours to fill it. Both pipes were
(a) 167 min (b) 160 min opened together and a leak was spotted
(c) 165 min (d) None of these which increased the filling-up time by 48

r
minutes. Find how many hours will it take
22. A and B can fill a tank in 10 and 12 hours
for the leak to empty a full tank.

si
respectively while C can empty it in 12
hours. If all three taps are opened one by ikbi A ,d VSad dks 12 ?kaVs esa Hkj ldrk gS vkSj
ikbi B bls Hkjus esa 18 ?kaVs ysrk gSA nksuksa ikb
an by
one for 1 hour, how much time will it take
to fill the tank? ,d lkFk •ksyk x;k vkSj ,d fjlko ns•k x;k ftlls
A vkSj B fdlh Vadh dks Øe'k%10 vkSj 12 ?k.Vs esa Hkjus dk le; 48 feuV c<+ x;kA Kkr dhft, fd

n
Hkj ldrs gS tcfd C bls 12 ?k.Vs esa [kkyh dj ,d Hkjs gq, VSad dks fjlko }kjk •kyh djus esa fdrus
ja
ldrk gSA vxj rhuksa uyksa dks ckjh ls 1&1 ?k.Vk?kaVs yxsaxsA
R s

[kksyk tk, rks Vadh dks Hkjus esa fdruk le; yxsxkA CRPF HCM 27/02/2023 (Shift - 02)
a th

(a) 60 (b) 68
(a) 60 min (b) 65 min
(c) 72 (d) 64
(c) 72 min (d) None of these
26. Pipes A and B can fill a tank in 16 hours
23. A pipe can fill a tank in 4 hours and a leak
ty a

and 24 hours, respectively, whereas pipe

at the bottom can empty that full tank in
C can empty the full tank in 40 hours. All
6 hours. If after the tank is 1/3 full, the
di M

three pipes are opened together, but pipe

leak is completely closed, How much time
A is closed after 10 hours. After how many
from beginning will it take for the tank to
hours will the remaining part of the tank
get filled completely?
be filled?
,d ikbi fdlh Vadh dks 4 ?kaVs esa Hkj ldrk gS rFkk ry
ikbi A vkSjB fdlh Vadh dks Øe'k% 16 vkSj24
ij ekStwn ,d fNnz bl Hkjh gqbZ Vadh dks 6 ?kaVs esa [kkyh
?kaVs eas Hkj ldrs gSa] tcfdCikbi
Hkjh gqbZ Vadh dks
dj ldrk gSA ;fn Vadh ds 1@3 Hkkx Hkj tkus ds ckn
40 ?kaVs esa [kkyh dj ldrk gSA rhuksa ikbi ,d lkFk
bl ns dks iwjh rjg ls can dj fn;k tkrk gS] rks Vadh dks
[kksys tkrs gSa] ysfdu
10 ?kaVs ckn ikbi A dks can
iw.kZr% Hkjus esa 'kq: ls dqy fdruk le; yxsxk\
SSC CPO 16/03/2019 (Shift- 02)
dj fn;k tkrk gSA Vadh dk 'ks"k Hkkx fdrus ?kaVs ck
(a) 12 hours (b) 4 hours Hkjsxk\
A

20 SSC CPO 23/11/2020 (Shift-1)

(c) 9 hours (d) hours
3
1 1
1 (a) 15 (b) 12
24. Two pipe A and B can fill a cistern in 12 2 2
2 (c) 20 (d) 10
hours and 25 hours respectively. The pipes
27. Pipe A can fill a tank in 16 minutes and
are opened simultaneously and it is found
that due to a leakage in the bottom, it took pipe B empties it in 24 minutes. If both
1 hour and 40 minutes more to fill the the pipes are opened together after how
cistern. When the cistern is full, in how many minutes should B be closed, so that
much time will the leak empty the cistern? the tank is filled in 30 minutes?

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ikbi A fdlh Vadh dks 16 feuV esa Hkj ldrk gS rFkk

30. Pipe A and B fill a tank in 43.2 minutes
and 108 minutes respectively, Pipe C can
ikbi B bls 24 feuV esa [kkyh dj ldrk gSA ;fn bu
empty it at 3 litres/minutes. When all the
nksuksa ikbi dks ,d lkFk pkyw fd;k x;k gS]
B dks
rks three pipes are opened together, they will
fdrus feuV ckn can djuk gksxk rkfd Vadh 30 feuV fill the tank in 54 minutes. The capacity
esa Hkj tk,\ (in litres) of the tank is:

SSC CPO 16/03/2019 (Shift- 03) ikbi A vkSjB Øe'k% 43-2 feuV vkSj 108 feuV esa ,d
VSad Hkjrs gSaA C bls
ikbi3 yhVj@feuV ij [kkyh dj
(a) 21 min (b) 20 min
ldrk gSA tc rhuksa ikbi ,d lkFk [kksys tk,axs] rks os 54
(c) 18 min (d) 15 min
feuV esa VSad dks Hkj nsaxsA VSad dh {kerk (yhVj esa)
28. Pipe A and B are filling pipes while C is an
SSC CGL TIE R-II 15/10/2020
emptying pipe. A and B can fill a tank in
72 and 90 minutes respectively. When all (a) 160 (b) 180
the three pipes are opened together, the (c) 216 (d) 200

r
tank gets filled in 2 hours. A and B are
31. When operated separately, pipe A taks 5
opened together for 12 minutes, then closed

si
hours less than pipe B to fill a cistern and
and C is opened. The tank will be empty after when both pipe are operated together, the
ikbi A vkSjB Hkjus okys ikbi gSa tcfd ikbi
C [kkyh
an by
cistern get filled in 6 hours. In how much
djus okyk ikbi gSAA vkSjB fdlh Vadh dks Øe'k% 72 time (in hours) will pipe B fill the cistern,
if oprated?

n
vkSj 90 feuV esa Hkj ldrs gSaA tcfd bu rhuksa ikbi dks
,d lkFk pkyw dj fn;k tkrk gS rks Vadh 2 ?kaVs esa Hkjuy A, tc vyx ls lapkfyr fd;k tkrk gS rks Vadh
ja
tkrh gSA A vkSj B dks 12 feuV rd ,d lkFk pkyw dks Hkjus ds fy, ikbiB ls 5 ?kaVs de ysrk gS vkSj
R s

fd;k tkrk gS] fiQj can djdsC dks pkyw fd;k tkrk gSA tc nksuksa ikbi ,d lkFk lapkfyr gksrs gSa rks Vadh 6
a th

Vadh fdrus le; ckn [kkyh gks tk,xk\ ?kaVs esa Hkj tkrk gSA lapkfyr gksus ij fdrus ?kaVs
es) ikbi B Vadh dks Hkj nsxk\
SSC CGL TIER-II 13/09/2019
SSC CPO 23/11/2020 (Shift- 03)
ty a

(a) 15 minutes (b) 18 minutes

(c) 12 minutes (d) 16 minutes (a) 9 (b) 18
di M

29. Pipes A and B can fill a tank in 15 hours (c) 10 (d) 15

and 20 hours, respectively. Pipe C is an 32. Pipe A and B can fill a tank in 10 hours and
emptying pipe. A and B are opened 40 hours, respectively. C is an outlet pipe
together for 4 hours, and then only A is attached to the tank. If all the three pipes
1 are opened simultaneously, it takes 80
closed and C opened. It took 19 hours minutes more time than what A and B
5
together take to fill the tank. A and B are
more to fill the tank. Pipe C alone can kept open for 7 hours and then closed and
empty the full tank in: C is opened. C will now empty the tank in :
ikbi A vkSjB ,d VSad dks Øe'k% 15 ?kaVs vkSj 20 ikbi A rFkkB fdlh Vadh dks Øe'k% 10 ?kaVs rFkk 40
?kaVs esa Hkj ldrs gSaAC ,dikbi
•kyh djus okyk ?kaVs esa Hkj ldrs C ,d
gSaA
fudkl ikbi gS tks Vadh ls
A

ikbi gSA
A vkSjB dks ,d lkFk 4 ?kaVs ds fy, •ksyk tqM+k gqvk gSA ;fn lHkh rhu ikbiksa dks ,d lkFk pk
tkrk gS vkSj mlds ckn dsoyA dks can fd;k tkrk dj fn;k tk, rks Vadh dks Hkjus Aesa vkSjB ds }kjk
1 ,d lkFk fy, x, le; dh rqyuk esa 80 feuV vf/d
gS vkSj
C dks •ksyk tkrk gSA Vadh dks Hkjus
19 ?kaVs
5
esa yxrs gSaAA vkSjB dks 7 ?kaVksa rd pkyw NksM+k tkrk
vkSj yxsA ikbi rFkk
C vdsys Hkjs gq, VSad dks fdrus fnuksa fiQj can djds ikbiC dks pkyw fd;k tkrk gSA
C bl Vadh dks fdrus le; esa [kkyh djsxk\
esa •kyh dj ldrk gS%
CRPF HCM 28/02/2023 (Shift - 03) SSC CGL 06/06/2019 (Shift- 01)

(a) 42 hours (b) 48 hours (a) 45.5 hours (b) 38.5 hours
(c) 45 hours (d) 40 hours (c) 42 hours (d) 49 hours

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ANSWER KEY

1. (c) 2.(b) 3. (c) 4. (d) 5. (a) 6. (a) 7. (a) 8. (b) 9. (c) 10. (a)

11.(c) 12.(d) 13.(d) 14.(c) 15.(b) 16.(c) 17.(d) 18.(c) 19.(b) 20.(a)

21.(a) 22.(d) 23.(d) 24.(d) 25.(c) 26.(b) 27.(a) 28.(b) 29.(c) 30.(c)

31.(d) 32.(d)

r
si
an by
n
ja
R s
a th
ty a
di M
A

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Pipe & Cistern@uy vkSj Vadh

(Practice Sheet With Solution)
1. A pump can fill a tank with water in 2 h. Because 5. A pipe can fill a tank in x hours and another
7 pipe can empty it in y hours. Here y>x. If both
of a leak in the tank, it takes h to fill the tank. the pipes are kept open simultaneously in how
3
many hours will the tank be filled?
The leak can empty the filled tank in ___.
,d ikbi ,d VSad dks x ?kaVs esa Hkj ldrk gS vkSj nw
,d iai fdlh Vadh dks 2 ?kaVs esa ikuh ls Hkj ldrk gSA VSad
7 ikbi bls y ?kaVs esa •kyh dj ldrk gSA y>x
;gk¡ ;fn
esa fjlko ds dkj.k] VSad dks Hkjus ?kaVs
esa yxrs gSaA fjlko
nksuksa ikbiksa dks ,d lkFk •ksy fn;k tk, rks Vadh fd

r
3
Hkjs VSad dks ------------ esa •kyh dj ldrk gSA ?kaVs esa Hkj tk,xh\

si
(a) 8 hours (b) 7 hours
(c) 213 hours (d) 14 hours (a) (x – y) hours (b) (y – x) hours

an by
2. A tank can be filled by a pipe A in 2 h and pipe
 yx   xy 
B in 6 h. At 10 am pipe A was opened. At what (c) 
1 – x  hours (d)   hours

n

time will the tank be filled if pipe B is opened   y – x 
at 11 am?

ja
}kjk 6 6.
,d VSad dks ikbiA }kjk 2 ?kaVs esa vkSjBikbi A water tank has two pipes. the empty tank
R s
filled in 12 min by the first and the full tank
?kaVs esa Hkjk tk ldrk gSA iwokZgu 10A cts
dksikbi
•ksyk
is emptied by the second in 20 min. Calculate
a th

x;kA ;fn ikbi B dks 11 iwokZÉ ij •ksy fn;k tkrk gS] the time required to fill half tank when both
rks VSad fdrus cts Hkjsxk\ the pipes are opened.
(a) 12 : 45 am (b) 5 : 00 pm
,d ikuh dh Vadh esa nks ikbi gSaA igyk ikbi 12 feu
ty a

(c) 11 : 45 am (d) 12 : 00 pm
3. Three pipes A, B and C can fill a tank in 6 esa •kyh Vadh dks Hkj ldrk gS vkSj nwljk ikbi 20 feu
hours. After three pipes worked for 2 hours C esa Hkjh Vadh dks •kyh dj ldrk gSA nksuksa ikbi
di M

is closed. Then A and B filled the remaining

•ksys tkus ij vk/h Vadh dks Hkjus esa yxus okys le; d
part in 7 hours. calculate the number of hours
taken by C alone to fill the tank is? x.kuk dhft,A
rhu ikbi A] B vkSj C ,d Vadh dks 6 ?kaVs esa Hkj ldrs (a) 16 min (b) 15 min
gSaA rhu ikbiksa dks 2 ?kaVs rd dke djusC dscanckn
dj (c) 20 min (d) 30 min
fn;k tkrk gSA fiQj
A vkSjB us 'ks"k Hkkx dks 7 ?kaVs esa Hkj
7. Two pipes A and B can fill a water tank in 12
fn;kA VSad dks Hkjus ds fy, vdsys
C }kjk fy, x, ?kaVksa
min and 24 min respectively. Third pipe C can
dh la[;k dh x.kuk djsa\ empty at the tank at the rate of 7 gallons per
(a) 16 hours (b) 12 hours minute. If A, B and C opened together fill the
(c) 13 hours (d) 14 hours
tank in 15 minutes, the capacity of the tank
4. A tap can fill a tank in 6 hours. When the tank
A

in gallons is _______.
is half filled, three more similar taps are
opened to fill water into the same tank. What nks ikbi A vkSj B ,d ikuh dh Vadh dks Øe'k% 12
is the total time taken to fill the tank feuV vkSj 24 feuV esa Hkj ldrs gSaA rhljkC,ikbi
7
completely by all the four pipes?
,d uy fdlh Vadh dks 6 ?kaVs esa Hkj ldrk gSA tc VSadxSyu çfr feuV dh nj ls VSad dks •kyh dj ldrk gSA
;fn A] B vkSj C ,d lkFk •ksys tk, rks VSad dks 15
vk/k Hkj tkrk gS] rks mlh VSad esa ikuh Hkjus ds fy, blh
rjg ds rhu vkSj uy •ksy fn, tkrs gSaA lHkh pkj ikbiksa feuV esa Hkj tkrk gSa] rks xSyu esa VSad dh {kerk -
}kjk VSad dks iwjh rjg ls Hkjus esa fy;k x;k dqy le; ------- gSA
fdruk gS\ (a) 180 (b) 150
(a) 6 hours (b) 2 hours 4 min
(c) 120 (d) 60
(c) 3 hours 48 Min (d) 3 hours 45 Min

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8. A water tank has three taps A, B and C. A fills nks Hkjus okys ikbiksa dh {kerk dk vuqikr 4 % 5 gS
four buckets in 24 minutes, B fills 8 buckets in
rhljk •kyh djus okyk ikbi gS ftldh n{krk igys nks Hkjus
1 hour and C fills 2 buckets in 20 minutes. If
all the taps are opened together, a full tank is okys ikbiksa dh vkSlr {kerk dh nks frgkbZ gS tks ,d Hk
emptied in 2 hours. If a bucket can hold 5 liters VSad dks 36 feuV esa •kyh dj ldrk gSA •kyh gksus ij nk
of water, what is the capacity of the tank? Hkjus okys ikbi VSad dks fdrus le; esa Hkj ldrs gSa\
,d ikuh dh Vadh esa rhu uyA] B vkSj C gSaA A, 24 (a) 16 min. (b) 12 min.
feuV esa pkj ckfYV;k¡ Hkjrk B, gS]
1 ?kaVs esa 8 ckfYV;k¡
(c) 14 min. (d) 20 min.
Hkjrk gS vkSjC, 20 feuV esa 2 ckfYV;k¡ Hkjrk gSA ;fn
lHkh uy ,d lkFk •ksys tkrs gSa] rks ,d iwjh Vadh 212. Two filling taps P and Q together can fill a tank
?kaVs
with rate of 40 lit/min and 60 lit/min
esa •kyh gks tkrh gSA ;fn ,d ckYVh esa 5 yhVj ikuh vkrespectively in 8 min. If a waste tap can empty
ldrk gS] rks Vadh dh {kerk D;k gS\ the filled tank in 32 min, then what is the rate
(a) 120 litres (b) 240 litres of waste tap?

r
(c) 180 litres (d) 60 litres nks Hkjus okys PuyvkSjQ ,d lkFk ,d VSad dks Øe'k%

si
9. 12 buckets of water fill a tank when the 40 yhVj@feuV vkSj 60 yhVj@feuV dh nj ls 8 feuV es
capacity of each tank is 13.5 liters. How many Hkj ldrs gSaA ;fn ,d csdkj uy Hkjh gqbZ Vadh dks

an by
buckets will be needed to fill the same tank,if
the capacity of each bucket is 9 liters?
feuV esa •kyh dj ldrk gS] rks csdkj uy dh nj D;k gS\

n
(a) 34 lit/min. (b) 25 lit/min.
12 ckYVh ds ikuh ls ,d VSad dks Hkjk tkrk gS çR;sd VSad
dh {kerk 13-5 yhVj gSA mlh VSad dks Hkjus ds fy, fdruh(c) 22 lit/min. (d) 18 lit/min.

ja
R s
ckfYV;ksa dh vko';drk gksxh] ;fn çR;sd ckYVh dh {kerk
13. Pipe A is an inlet pipe that can fill an empty
9 yhVj gS\ cistern in 69 hours. Pipe B can drain the filled
a th

cistern in 46 hours. When the cistern was filled

(a) 8 (b) 15
the two pipes are opened one at a time for an
(c) 16 (d) 18 hour each, starting with Pipe B. how long will
ty a

10. Two pipes A and B can separately fill a cistern it take for the cistern to be empty?
in 10 and 15 minutes respectively. A person
ikbi A ,d çosf'kdk ikbi gS tks ,d •kyh Vadh dks 69
di M

opens both the pipes together when the cistern

should have been was full he finds the waste ?kaVs esa Hkj ldrk gSA B ikbi
Hkjh gqbZ Vadh dks 46 ?ka
pipe open. Then he closes the waste pipe and •kyh dj ldrk gSA tc Vadh Hkj tkrh gS rks nks ikbik
in another 3 minutes the cistern was full. In dks ikbi B ls 'kq: djrs gq, ,d&,d djds ,d ?kaVs ds
what time can the waste pipe empty the
fy, •ksyk tkrk gSA Vadh dks •kyh gksus esa fdruk l
cistern when fill ?
yxsxk\
nks ikbiA vkSj B vyx&vyx ,d Vadh dks Øe'k% 10
(a) 11 days (b) 11 days 7 hours
vkSj 15 feuV esa Hkj ldrs gSaA ,d O;fÙkQ nksuksa ikbiksa dks
,d lkFk •ksyrk gS tc Vadh iwjh Hkj tkuh pkfg, Fkh rks (c) 11 days 12 hours (d) 1 days 13 hours
og vif'k"V ikbi dks •qyk ikrk gSA fiQj og csdkj ikbi14. Two taps X and Y can fill a tank in 15 hours
dks can dj nsrk gS vkSj vxys 3 feuV esa gkSt Hkj tkrk gSA
and 20 hours respectively. If the two taps are
A

Hkjus ij vif'k"V ikbi Vadh dks fdrus le; esa •kyh dj opened at 2 p.m., then at what time (in p.m.)
ldrk gS\ should the tap X be closed to completely fill
the tank at exactly 2 a.m.?
(a) 10 min (b) 13 min
nks uy X vkSj Y ,d Vadh dks Øe'k% 15 ?kaVs vkSj 2
(c) 12 min (d) 17 min
?kaVs esa Hkj ldrs gSaA ;fn nks uy nksigj 2 cts •ksys
11. The ratio of efficiencies of two filling pipes is
4 : 5. There is a third emptying pipe which
gSa] rks Bhd 2 iwokZÉ ij VSad dks iwjh rjg ls Hkjus
efficiency is two third of the average efficiency uy X dks fdl le; (vijkÉ esa) can djuk pkfg,\
of first two filling pipes can empty a filled tank (a) 8 (b) 7
in 36 minutes. In how much time both the
filling pipes can fill the tank when it is empty? (c) 9 (d) 10

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15. One pipe can fill an empty cistern in 4 hours 18. Pipe A could fill an empty cistern in 18 hrs
while another can drain the cistern when full while pipe B can drain a filled cistern in 30 hrs.
in 10 hours. Both the pipes were turned on When the cistern is empty, pipe A is turned on
when the cistern was half-empty. How long will for an hour and then turned off. The pipes were
it take for the cistern to be full? alternately left open for an hour each time till
the cistern was full. How much time did it take
,d ikbi ,d •kyh Vadh dks 4 ?kaVs esa Hkj ldrk gS tcfd for the cistern to be full?
nwljk ikbi Hkjs gq, VSad dks 10 ?kaVs esa •kyh dj ldrk gSA
ikbi A ,d •kyh Vadh dks 18 ?kaVs esa Hkj ldrk gS tcfd
vk/k •kyh gksus ij nksuksa ikbiksa dks pkyw dj fn;k x;kAikbi B Hkjh gqbZ Vadh dks 30 ?kaVs esa •kyh dj ldrk g
gkSt dks Hkjus esa fdruk le; yxsxk\ Vadh •kyh gksrh gS] rksAikbi
dks ,d ?kaVs ds fy, pkyw fd;k
(a) 3 hrs. 20 minutes tkrk gS vkSj fiQj can dj fn;k tkrk gSA gj ckj ,d ?kaVs d
(b) 6 hrs. 40 minutes fy, ikbiksa dks ckjh&ckjh ls •qyk NksM+ fn;k tkrk Fkk tc
(c) 4 hrs. 20 minutes fd gkSt Hkj ugha tkrk FkkA gkSt dks Hkjus esa fdruk le; y
(d) 5 hrs. 30 minutes (a) 90 hrs. (b) 86 hrs. 40

r
(c) 45 hrs. (d) 86 hrs. 48 min.
16. Two pipes A and B can fill an empty cistern in
19. Pipes A, B and C can fill a tank in 30, 60 and
32 and 48 hrs, respectively. Pipe C can drain

si
120 minutes respectively. Pipes B and C are
the entire cistern in 64 hrs when no other pipe
kept open for 10 minutes, and then Pipe B is
is in operation. Initially, when the cistern was

an by
empty Pipe A and Pipe C were turned on. After shut while Pipe A is opened. Pipe C is closed
a few hrs, Pipe A was turned off and Pipe B was 10 minutes before the tank overflows. How

n
turned on instantly. In all it took 112 hrs to long does it take to fill the tank?
fill the cistern. For how many hrs was Pipe B ikbi A] B vkSjC ,d VSad dks Øe'k% 30] 60 vkSj 120
feuV esa Hkj ldrs gSaA Bikbi vkSj C dks 10 feuV ds

ja
turned on?
R s
nks ikbiA vkSjB ,d •kyh Vadh dks Øe'k% 32 vkSj 48 fy, •qyk j•k tkrk gS] vkSj fiQj ikbi B dks can dj
?kaVs esa Hkj ldrs gSaAC iwjs fn;k tkrk gS tcfd ikbi A dks •ksy fn;k tkrk gSA VSad
ikbiVSad dks 64 ?kaVs esa •kyh
a th

dj ldrk gS tc dksbZ vU; ikbi dke ugha dj jgk gksA ds Hkjus ls 10 feuV igys ikbi C dks can dj fn;k tkrk
çkjaHk esa] tc Vadh •kyh Fkh rksA ikbi
vkSj ikbi C dks gSA VSad dks Hkjus esa fdruk le; yxrk gS\
pkyw fd;k x;kA dqN ?kaVksa ds ckn] A dks
ikbican dj (a) 40 minutes (b) 28 minutes
ty a

fn;k x;k vkSj ikbi B dks rqjar pkyw dj fn;k x;kA dqy (c) 30 minutes (d) 36 minutes
20. Two pipes can fill a tank in 12 hrs and 18 hrs
feykdj Vadh dks Hkjus esa 112 ?kaVs yxsA
B dksikbi
fdrus
di M

respectively. Pipes are opened together but due

?kaVs ds fy, pkyw fd;k x;k Fkk\ to a pipe leakage, it takes 48 minutes extra to
(a) 72 (b) 70 fill the tank, If the tank is full, what time will
(c) 77 (d) 84 it take to completely empty due to the leakage.
17. Two pipes A and B can fill an empty cistern in nks ikbi ,d VSad dks Øe'k% 12 ?kaVs vkSj 18 ?kaV
1.8 and 2.7 hours, respectively. Pipe C can ldrs gSaA ikbiksa dks ,d lkFk •ksy fn;k tkrk gS ysfd
drain the entire cistern in 4.5 hours when no ikbi esa fjlko ds dkj.k VSad dks Hkjus esa 48 feuV vfrfj
other pipe is in operation. Initially when the yxrs gSa] ;fn VSad Hkjk gqvk gS] rks fjlko ds dkj.k
cistern was empty Pipe A and Pipe C were
turned on. After a few hours Pipe A was turned iwjh rjg ls •kyh gksus esa fdruk le; yxsxk\
off and Pipe B was turned on instantly. In all it (a) 72 hrs. (b) 84 hrs.
took 5.5 hours to fill the cistern. For how many (c) 96 hrs. (d) 112 hrs.
hours was Pipe B turned on? 21. A tank has an inlet pipe and an outlet pipe. If
A

the outlet pipe is closed then the inlet pipe fills

nks ikbiA vkSj B ,d •kyh Vadh dks Øe'k% 1-8 vkSj the empty tank in 8 hours. If the outlet pipe is
2-7 ?kaVs esa Hkj ldrs gSaA tc dksbZ vU; ikbi dke ugha open
dj then the inlet pipe fills the empty tank in
jgk gks rks ikbiC, 4-5 ?kaVs esa iwjs gkSt dks •kyh dj hours. If only the outlet pipe is open then in
10
ldrk gSA 'kq: esa tc Vadh •kyh Fkh rks Aikbi
vkSj ikbi how many hours the full tank becomes half-full?
C dks pkyw fd;k x;kA dqN ?kaVksa ds ckn A dks
ikbican ,d VSad esa ,d buysV ikbi vkSj ,d vkmVysV ikbi gSA ;fn
dj fn;k x;k vkSj ikbi B dks rqjar pkyw dj fn;k x;kA vkmVysV ikbi can gS rks buysV ikbi •kyh VSad dks 8 ?
Vadh dks Hkjus esa dqy feykdj 5-5 ?kaVs yxsA
B fdrus ikbi Hkjrk gSA ;fn vkmVysV ikbi •qyk gS rks buysV ikbi •
?kaVs ds fy, pkyw jgk\ VSad dks 10 ?kaVs esa Hkjrk gSA ;fn dsoy fudkl ikbi gh
gS rks iwjk Hkjk gqvk VSad fdrus ?kaVs esa vk/k Hkjk j
(a) 5 (b) 4.5
(a) 20 (b) 30
(c) 3 (d) 6 (c) 40 (d) 45

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22. Two pipes P and Q can fill a tank in 20hrs and nks ikbiA vkSj B ,d VSad dks Øe'k% 16 ?kaVs vkSj
25hrs respectively while a third pipe R can ?kaVs esa Hkj ldrs gSaA igys
A lsikbi
'kq: djrs gq,] mUgsa
empty the tank in 30hrs. If all the pipes are çR;sd 1 ?kaVs ds fy, vyx&vyx •ksyk tkrk gSA •kyh
opened together for 10hrs and then pipe R is
Vadh fdrus ?kaVs esa Hkj tk,xh\
closed then in what time the tank can be filled.
nks ikbiP vkSjQ ,d VSad dks Øe'k% 20 ?kaVs vkSj 25 ?kaVs 1
(a) 17 3 (b) 17
5
esa Hkj ldrs gSa tcfd ,d rhljk ikbi R VSad dks 30 ?kaVs esa 5
•kyh dj ldrk gSA ;fn lHkh ikbiksa dks ,d lkFk 10 ?kaVs (c) 1
(d) 17
3
17
ds fy, •ksy fn;k tk, vkSj fiQj ikbi R dks can dj fn;k 4 4
tk,] rks VSad dks fdrus le; esa Hkjk tk ldrk gS\ 26. A pipe can fill a tank in 4 hours and a leak at
the bottom can empty that full tank in 6 hours.
400 400 1
(a) hours (b) hours If after the tank is full, the leak is completely
23 27 3

r
closed, how much time from beginning will it
200 200

si
(c) hours (d) hours take for the tank to get filled completely?
23 27
,d ikbi ,d Vadh dks 4 ?kaVs esa Hkj ldrk gS vkSj ryh e

an by
23. Three pipes A, B, C can fill an empty cistern in 2, ,d fjlko ml Hkjh gqbZ Vadh dks 6 ?kaVs esa •kyh dj ld
3 and 6 hours respectively. They are opened

n
1
together. After what time should B be closed, so gSA ;fn VSad dsHkjus ds ckn fjlko iwjh rjg ls can gks
3
that the cistern gets filled in exactly 1 hr. 15 min?

ja
tkrk gS] rks VSad dks iwjh rjg ls Hkjus esa 'kq: ls f
R s
rhu ikbi A, B vkSjC ,d [kkyh tyk'k; dks Øe'k% 2]
le; yxsxk\
3 vkSj 6 ?kaVsa esa Hkj ldrs gSA rhuksa ikbiksa dks ,d lkFk
a th
(a) 12 hours (b) 4 hours
[kksy fn;k tkrk gSA fdrus le; ds ckn ikbiB dks can
20
dj fn;k tkuk pkfg,] rkfd tyk'k; Bhd 1 ?kaVsa 15 feuV (c) 9 hours (d) hours
3
esa Hkj tk,\
ty a

27. A tank is to be filled completely with water for

(a) 30 min. (b) 15 min. which 8 pipes of the same kind are used. The
di M

(c) 20 min. (d) 45 min. tank gets filled in 1 hour and 40 minutes. If
10 pipes of the same kind, as mentioned above.
24. Three pipes A, B and C can fill a cistern in 12,
are used in how much time (in hours and
18 and 24 minutes, respectively. If all the pipes minutes) will the tank be completely filled?
are opened together for 7 minutes, what will be
,d VSad dks iwjh rjg ls ikuh ls Hkjuk gS ftlds fy, leku
the volume of the water that overflows as the
percentage of the total volume of the cistern?
çdkj ds 8 ikbiksa dk mi;ksx fd;k tkrk gSA Vadh 1 ?kaV
feuV esa Hkj tkrh gSA ;fn ,d gh rjg ds 10 ikbi] tSlk
rhu ikbi A, B vkSj C ,d tyk'k; dks Øe'k% 12] 18 fd Åij crk;k x;k gSA ç;ksx fd;k tkrk gS rks Vadh fdrus
vkSj 24 feuV esa Hkj ldrs gSA ;fn lHkh ikbi 7 feuV ds le; (?kaVksa vkSj feuVksa esa) esa iwjh rjg Hkj tk,xh\
fy, ,d lkFk [kksy fn;s tkrs gSa] rks tyk'k; ds dqy vk;ru (a) 1 hours 30 minutes (b) 1 hours 45 minutes
dk fdrus izfr'kr ty vfrizokg ds :i esa cg tk,xk\ (c) 1 hours 5 minutes (d) 1 hours 20 minutes
A

28. Two pipes can fill a tank with water in 15 and

7 1 12 hours respectively, and a third pipe can
(a) 26 % (b) 23 %
18 3 empty it in 4 hours. If the pipes be opened in
order, at 8, 9 and 11 a.m. respectively, the
2 5 tank will be emptied at?
(c) 23 % (d) 26 %
3 18 nks ikbi ,d VSad dks Øe'k% 15 vkSj 12 ?kaVs esa ik
25. Two pipes A and B can fill a tank in 16 hours Hkj ldrs gSa] vkSj ,d rhljk ikbi bls 4 ?kaVs esa •kyh d
and 20 hours respectively. They are opened ldrk gSA ;fn ikbiksa dks Øe'k% 8] 9 vkSj 11 iwokZÉ
alliteratively for 1 hour each, starting with •ksy fn;k tk,] rks Vadh fdrus cts •kyh gksxh\
pipe A first. In how many hours will the empty (a) 11 : 40 a.m. (b) 12 : 40 p.m.
tank be filled? (c) 01 : 40 p.m. (d) 2 : 40 p.m.

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29. Two pipes can fill a tank in 8 h. and 12 h. ikbi A vkSjB VSad dks Øe'k% 15 vkSj 18 ?kaVs es
respectively whereas an escape pipe can empty ldrs gSa vksj ikbiC 3 yhVj@feuV dh nj ls VSad ls
it in 6 h. If the three pipes are opened at 1 ikuh [kkyh dj ldrk gSA ;fn lHkh ikbi ,d gh le; esa
pm, 2 pm and 3 pm respectively, at what time [kksys tkrs gSaA rks Vadh 9 ?kaVs esa Hkj tkrh gSA V
will the tank be filled?
Kkr dhft;sA
nks ikbi ,d Vadh dks 8 ?kaVs esa Hkj ldrs gSaA vkSj 12 (a)
?kaVsA
16200 liters (b) 16300 liters
tcfd ,d fudkl ikbi bls 6 ?kaVs esa •kyh dj ldrk gSA (c) 16400 liters (d) 16500 liters
;fn rhuksa ikbiksa dks Øe'k% nksigj 1 cts] nksigj 233.
cts Pipe A can fill half of the tank in 8 hrs 5 min
vkSj 3 cts •ksyk tkrk gS] rks VSad fdrus cts Hkjsxk\ and pipe B can fill the same tank completely
in 16 hrs 5 min. Another pipe C can empty the
(a) 8 am (b) 7 am
full tank in 12 hrs. If all the pipes are opened
(c) 5 am (d) 7.30 am together then in how much time 80% of the
tank is filled (approx.)?

r
30. Pipes A and B can fill a tank in 6 hrs. and 9
hrs respectively and pipe C can empty the full ikbi A VSad dk vk/k fgLlk 8 ?kaVs 5 feuV esa Hkj ld

si
tank in 12 hrs. If all three pipes are opened
gS vkSj ikbiB mlh VSad dks 16 ?kaVs 5 feuV esa iwj
together when a tank is empty, in how many

an by
hours will 35% of the tank be filled?
ls Hkj ldrk gSA ,d vU; ikbi C iwjs VSad dks 12 ?kaV
[kkyh dj ldrk gSA ;fn lHkh ikbiksa dks ,d lkFkk [kks

n
ikbi A vkSj B ,d VSad dks Øe'k% 6 ?kaVs vkSj 9 ?kaVs esa
fn;k tkrk gS] rks VSad dk 80» (yxHkx) fdrus le; esa
Hkj ldrs gSa vkSj ikbi
C iwjh Vadh dks 12 ?kaVs esa •kyh
Hkj tk,xk\

ja
dj ldrk gSA ;fn ,d VSad •kyh gksus ij lHkh rhu ikbiksa
R s
(a) 30.2 hours
dks ,d lkFk •ksy fn;k tkrk gS] rks fdrus ?kaVs esa VSad dk (b) 16.4 hours
a th

35» Hkj tk,xk\ (c) 26.2 hours (d) 19.2 hours

(a) 1.9 (b) 1.5 34. A tank has two inlet pipes A & B and an outlet
pipe C and the efficiency of pipe B is twice the
ty a

(c) 1.6 (d) 1.8

efficiency of pipe A. If pipe B filled the tank
31. One tap filling a tank in 5 hours and a leak can in 7.5 min and pipe C empty the tank in
di M

empty the tank in 7 hours. If the tap and the 30mins. Initially pipe A is opened and after
leak which was half closed, were left open. How 8mins pipe A is closed and pipe C is opened.
long will it take for the tank to fill? After 5mins pipe C closed and pipe A and B is
,d uy fdlh Vadh dks 5 ?kaVs esa Hkjrk gS vkSj ,d fjlko opened to fill the tank. Find the time taken
by pipes A and B to fill the remaining part of
ls Vadh dks 7 ?kaVs esa •kyh fd;k tk ldrk gSA vxj uy the tank.
vkSj fjlko tks vk/k can Fkk] mls •qyk NksM+ fn;k tk,A
Vadh dks Hkjus esa fdruk le; yxsxk\ ,d VSad esa nks buysV A ikbi
vkSjB gSa vkSj ,d vkmVysV
ikbi C gS vkSj ikbiB dh n{krk ikbi A dh n{krk ls
(a) 6 7 hr. (b) 7 7 hr. nksxquh gSA ;fn ikbi
B VSad dks 7-5 feuV esa Hkjrk gS v
9 9 ikbi C VSad dks 30 feuV esa [kkyh djrk gSA izkjaHk
A

A dks [kksyk tkrk gS vkSj 8 feuV ds ckn A ikbi

dks can
8 3
(c) 8 hr. (d) 8 hr. dj fn;k tkrk gS vkSj ikbi C dks [kksy fn;k tkrk gSA 5
9 4
feuV ds ckn ikbi C dks can dj fn;k tkrk gS vkSj VSad
32. Pipes A and B can fill the tank in 15 and 18 dks Hkjus ds fy, ikbiA vkSjB dks [kksy fn;k tkrk gSA
hours respectively and Pipe C can empty the VSad ds 'ks"k Hkkx dks Hkjus ds fy, A vkSj
ikbi B }kjk
water from the tank at the rate of 3 liters/min. fy;k x;k le; Kkr dhft,A
If all pipes are opened at the same time, then
the tank is filled in 9 hours. Find the capacity (a) 2 minutes (b) 3 min 10 sec
of the tank. (c) 3 minutes (d) 2.75 minutes

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35. Two inlet pipes A and B and one outlet pipe C 38. If two pipes A and B filled the tank in 18
are connected to a tank. Pipes A and C minutes and 24 minutes respectively and pipe
together can fill a tank in 22.5 minutes, while C emptied the same tank in 36 minutes.
pipes B and C together can fill the same tank Initially, pipe A opened to fill the tank and
in 90 minutes and ratio of efficiency of pipe A after 3 minutes all three pipes were opened.
to B is 2 : 1 respectively. If pipes A and B works What is the time taken f or filling the
remaining tank?
1 
with 125% and 83 
  % of their efficiencies ;fn nks ikbi A vkSjB VSad dks Øe'k% 18 feuV vkSj 2
3 
feuV esa Hkjrs gSa vksjCikbi mlh VSad dks 36 feuV es
respectively, then in what time pipes A and B
together will fill the tank? [kkyh djrk gSA izkjaHk esa] VSad dks HkjusAdsdksfy, ik
[kksyk x;k vkSj 3 feuV ds ckn rhuksa ikbiksa dks [kks
nks buysV ikbi (Hkjus ds ikbi)
A vkSjB vkSj ,d vkmVysV
ikbi ([kkyh djus ds ikbi) C ,d VSad ls tqM+s gSaA ,d x;kA 'ks"k VSad dks Hkjus esa fdruk le; yxrk gS\
lkFk ikbi A vkSjC ,d VSad dks 22-5 feuV esa Hkj ldrs (a) 17 min (b) 23 min

r
gSa] tcfd ,d lkFk ikbi B vkSjC mlh VSad dks 90 feuV (c) 14 min (d) 12 min

si
esa Hkj ldrs gSa vkSj ikbi
A ls B dh n{krk dk vuqikr 39. Pipe P can fill a tank in 40 hours; pipe Q can
fill the same tank in x hours while pipe R can
Øe'k% 2 % 1 gSA ;fn ikbi A vkSjB viuh n{krk ds

an by
empty the filled tank in 24 hours. If all three
Øe'k% 125» vkSj83  1  % ds lkFk dke djrs gSa] rks
 
taps are opened simultaneously then the tank

n
3  is filled in 36 hours. Find the time taken by
,d lkFk ikbi A vkSjB VSad dks fdrus le; esa Hkjsaxs\ pipe Q to fill an empty tank?

ja
ikbi P ,d VSad dks 40 ?kaVs esa Hkj ldrk gS_ Q mlh
ikbi
R s
(a) 12 min (b) 6 min
(c) 15 min (d) 9 min VSad dksx ?kaVs esa Hkj ldrk gS tcfd ikbi
R Hkjs gq, VSad
a th

36. Pipe A and B together can fill the tank in dks 24 ?kaVs esa [kkyh dj ldrk gSA ;fn rhuksa uyksa
2  lkFk [kksy fn;k tk, rks VSad 36 ?kaVs esa Hkj tkrh
Q gSA
22   hours. If pipe B is increased its
9 }kjk ,d [kkyh VSad dks Hkjus esa fy;k x;k le; Kkr dhft,\
ty a

efficiency by 25%, then both can fill the tank (a) 24.5 hours (b) 22.5 hours
in 20 hours, in how many hours pipe A to fill
di M

the tank at the half of its efficiency? (c) 26.5 hours (d) 17.5 hours
40. Pipe P start filling tank A and at the same time
2 
,d lkFk ikbi A vkSjB VSad dks 22   ?kaVs es Hkj pipe Q start filling tank B, they alone can fill
9 the tank at 8 pm and 6 pm respectively. If at
ldrs gSaA ;fn ikbiB dh n{krk esa 25» dh o`f¼ dh tkrh 4 pm pipe P is closed, then pipe Q is opened
gS] rks nksuksa ikbi VSad dks 20 ?kaVs esa HkjA ldrs gSa]
forikbi
tank A, and then tank is filled in 3 hours
viuh vk/h n{krk ds lkFk VSad dks fdrus ?kaVs esa Hkjsxk\12 minutes. If Pipe P opened for tank B (at 5
(a) 80 (b) 60 am) then find at what time it will fill the tank
alone, if capacity of both tanks are same?
(c) 90 (d) 100
37. Pipe A, B and C can fill the tank in 30 hours, ikbi P VSad A dks Hkjuk 'kq: djrk gS vkSj mlh le;
10 hours and 15 hours respectively. If Pipe A ikbi Q VSad B dks Hkjuk 'kq: djrk gS] os vdsys VSa
A

and C opened together. After y hours, pipe A

closed and pipe B opened. If pipes B and C dks Øe'k% jkr 8 cts vkSj 'kke 6 cts Hkj ldrs gSaA ;fn
together fill the remaining tank in 3 hours, 4 cts ikbi P dks can dj fn;k tkrk gS] rks ikbiQ dks
then find the value of y? VSad A ds fy, [kksy fn;k tkrk gS] vkSj fiQj VSad 3 ?k
ikbi A, B vkSjC Vadh dks Øe'k% 30 ?kaVs] 10 ?kaVs vkSj
12 feuV esa Hkj tkrk gSA ;fn ikbi
P VSad B ds fy,
15 ?kaVs esa Hkj ldrs gSaA ;fn ikbi ,dAlkFk vkSjC (lqcg 5 cts) [kksyk tkrk gS rks Kkr dhft, fd ;g
[kqyrs gSaA
y ?kaVs ds ckn] ikbi
A can gks tkrk gS vkSj ikbi
vdsys VSad dks fdrus le; esa Hkjsxk] ;fn nksuksa VS
B [kqy tkrk gSA ;fn ,d lkFk ikbiB vkSjC 'ks"k VSad dks
{kerk leku gS\
3 ?kaVs esa HkjrsygSa]
dk eku
rks Kkr dhft,\
(a) 6 hours (b) 8 hours (a) 4 pm (b) 2 pm
(c) 3.75 hours (d) 9 hours (c) 1 pm (d) 3 pm

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41. There are 3 taps A, B, and C in a tank. These 44. Three taps A, B and C together can fill a tank
can fill the tank in 10 hours, 20 hours and 25 in 6 hours. Tap C alone can fill the tank in
hours, respectively. At first, all three taps are 12 hours. To fill the tank, when it is empty,
opened simultaneously. After 2 hours, tap C is all the three taps are started together. After
closed and A and B keep running. After 4 hours
working t hours, tap C is closed and the tank
from the beginning, tap B is also closed. The
remaining tank is filled by tap A alone. Find is filled in 8 more hours. What is t equal to ?
the percentage of work done by tap A itself. rhu uy A, B vkSjC ,d lkFk ,d Vadh dks 6 ?akVs esa
,d VSad eas 3 uyA, B vkSj C gSaA ;s VSad dks Øe'k%Hkj ldrs gSaA uy C vdsyk bl Vadh dks 12 ?kaVs esa H
10 ?kaVs] 20 ?kaVs vkSj 25 ?kaVs eas Hkj ldrs gSaA lcls
ldrk gSA Vadh dks Hkjus ds fy,] tc ;g [kkyh gksrh g
igys rhuksa uy ,d lkFk [kksys tkrs gSaA 2 ?kaVs ds ckn]
uy C can gks tkrk gS vkSj A vkSj B pyrs jgrs gSaA rks rhuksa uy ,d lkFk [kksy fn, tkrs tgSaA
?kaVs ds ckn]
izkjaHk ls 4 ?kaVs ckn B uy
Hkh can gks tkrk gSA 'ks"kuy C dks can dj fn;k tkrk gS vkSj Vadh dks Hkjus
VSad dks vdsys uy A ls Hkjk tkrk gSA uyA Lo;a ds 8 ?kaVs vkSj yxrst gSaA
fdlds cjkcj gS\
}kjk fd, x, dk;Z dk izfr'kr Kkr dhft,A

r
UPSC CDS 2023 (1)
(a) 32% (b) 75%
(a) 1 (b) 2

si
(c) 52% (d) 72%
(c) 4 (d) 6
42. There are three taps of diameter 2 cm, 3 cm

an by
and 4 cm, respectively. The ratio of the water 45. In a water tank there are two outlets. It takes
20 minutes to empty the tank if both the
flowing through them is equal to the ratio of

n
outlets are opened. If the first outlet is opened,
the square of their diameters. The biggest tap the tank is emptied in 30 minutes. What is the
can fill an empty tank alone in 81 min. If all time taken to empty the tank by second outlet?

ja
R s
the taps are opened simultaneously, then how
,d ikuh dh Vadh esa nks vkmVysV gksrs gSaA ;fn nksuk
long will the tank take (in min) to be filled?
•ksys tk,a rks VSad dks •kyh djus esa 20 feuV dk le;
a th

Øe'k%2 lseh] 3 lsehvkSj 4 lseh O;kl ds rhu uy gSaA yxrk gSA ;fn igyk vkmVysV •ksyk tkrk gS] rks VSad
muds ek/;e ls izokfgr ty dk vuqikr muds O;kl ds feuV esa •kyh gks tkrk gSA nwljs vkmVysV }kjk V
oxZ ds vuqikr ds cjkcj gSA lcls cM+k uy vdsys ,d •kyh djus esa fdruk le; yxsxk\
ty a

[kkyh Vadh dks 81 feuV esa Hkj ldrk gSA ;fn lHkh uyksa dks CDS 2020 (Shift-01)
di M

,d lkFk [kksy fn;k tk,] rks Vadh dks Hkjus esa fdruk le; (a) 30 minutes (b) 40 minutes
(feuV esa) yxsxk\ (c) 50 minutes (d) 60 minutes
20 20 46. P can fill a tank in 5 hours. Q can fill the same
(a) 31 (b) 60
29 29 tank in 10 hours. R can empty the same tank in
20 hours. How much time will all the three take
20 20 together to fill the tank?
(c) 54 (d) 44
29 29
P ,d Vadh dks 5 ?kaVs esa Hkj ldrk
Q mlh
gSAVadh dks 10 ?kaV
43. There are two inlets A and B connected to a esa Hkj ldrk gSA
R mlh Vadh dks 20 ?kaVs esa [kkyh dj ld
tank. A and B can fill the tank in 32 h and 28
gSA rhuksa feydj mlh Vadh dks Hkjus esa fdruk le; ysa
h, respectively. If both the pipes are opened
SSC CHSL 13/03/2023 (Shift-02)
A

alternately for 1 h, starting with A, then in how

much time (in hours, to nearest integer) will (a) 10 hours (b) 4 hours
the tank be filled? (c) 6 hours (d) 5 hours
,d VSad ls nks buysV A vkSj B tqM+s gq, A gSaA
vkSj B 47. 15 taps can fill a tank in 36 minutes. How many
VSad dks Øe'k% 32 h vkSj 28 h esa Hkj ldrs gSaA ;fn taps will be required to fill the tank in one hour?
nksuksa ikbiksa
A lsdks
'kq: djrs gq,] ckjh&ckjh ls]
1 h ds 15 uy ,d Vadh dks 36 feuV esa Hkj ldrs gSA Vadh dks 1 ?
esa Hkjus ds fy, fdrus uy dh vko';drk gksxh\
fy, •ksyk tkrk gS] rks VSad fdrus le; (?kaVksa esa] fudVre
iw.kkZad) esa Hkj tk,xk\ SSC CHSL 15/03/2023 (Shift-02)
(a) 22 (b) 30 (a) 12 (b) 9
(c) 36 (d) 24 (c) 8 (d) 6

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48. An inlet pipe can fill an empty tank in 140 hours 1

while an outlet pipe drains a completely-filled tank 51. An inlet pipe can fill an empty tank in 4
hours
2
in 63 hours. If 8 inlet pipes and y outlet pipes are
while an outlet pipe drains a completely filled
opened simultaneously, when the tank is empty,
then the tank gets completely filled in 105 hours. 1
tank in 7 hours. The tank is initially empty,
Find the value of y. 5
,d buysV ikbi ,d •kyh VSad dks 140 ?kaVs esa Hkj ldrk gS]and the two pipes are alternately opened for an
hour each, till the tank is completely filled,
tcfd ,d vkmVysV ikbi iwjh rjg ls Hkjs VSad dks 63 ?kaVs esa
starting with the inlet pipe. In how many hours
•kyh dj nsrk gSA ;fn 8 buysV ikbi vkSj
y vkmVysV ikbi will the tank be completely filled?
,d lkFk •ksys tkrs gSa] tc VSad •kyh gksrk gS] rks VSad 105
1
?kaVs esa iwjh rjg ls Hkj tkrk
y dk
gSA
eku Kkr dhft,A ,d buysV ikbi ,d •kyh VSad dks 4 ?kaVs esa Hkj ldrk
2
CGL PRE, 14/07/2023 (Shift-3)
gS] tcfd ,d vkmVysV ikbi iwjh rjg ls Hkjs VSad dk
(a) 1 (b) 4

r
1
(c) 2 (d) 3 7 ?kaVs esa •kyh dj nsrk gSA VSad 'kq: esa •kyh
5

si
49. Inlet Pipes A and B can together fill an empty buysV ikbi ls 'kq: djrs gq, nksuksa ikbi ckjh&ckjh ls ,d&,d
tank in 1.5 hours. Outlet Pipe C, when opened
?kaVs ds fy, •ksys tkrs gSa] tc rd fd VSad iwjh rjg ls H

an by
alone, can empty the completely filled tank, in
4.5 hours. When only Pipes A and C are opened
u tk,A Vsad fdrus ?kaVs esa iwjh Hkj tk,xh\

n
together, the empty tank is filled in 6 hours. SSC CGL TIER I 21/07/2023 (Shift-02)
Find the time taken by Pipe B, when opened
1

ja
alone, to fill the empty tank. (a) 24 (b) 20
R s
4
buysV ikbiA vkSjB feydj ,d •kyh VSad dks 1-5 ?kaVs
a th

esa Hkj ldrs gSaA tc vkmVysVCikbivdsyk •ksyk tkrk gS] (c) 20

3
(d) 22
3
rks iwjh rjg ls Hkjs VSad dks 4-5 ?kaVs esa •kyh dj ldrk gSA 4 8
tc dsoy ikbi A vkSjC dks ,d lkFk •ksy fn;k tkrk gS] 52. A pipe can fill a tank in 30 hours. Due to a
ty a

rks •kyh VSad 6 ?kaVs esa Hkj tkrk gSAdks •kyh

Hkjus
VSad
ds leakage at the bottom, it is filled in 50 hours.
How much time will the leakage take to empty
fy, vdsys ikbi B }kjk fy;k x;k le; Kkr djsaA
di M

the completely filled tank?

SSC CGL TIER I 19/07/2023 (Shift-02) ,d ikbi fdlh Vadh dks 30 ?kaVs esa Hkj ldrk gSA ryh esa fj
(a) 3 hours 30 minutes gksus ds dkj.k ;g 50 ?kaVs esa Hkjrh gS A iwjh rjg ls H
(b) 3 hours 36 minutes dks •kyh djus esa fjlko dks fdruk le; yxsxk\
(c) 3 hours 32 minutes SSC CGL (PRE) 24/07/2023 (Shift-2)
(d) 3 hours 40 minutes (a) 60 hours (b) 85 hours
50. An inlet pipe can fill an empty tank in 120 (c) 70 hours (d) 75 hours
hours while an outlet pipe drains a completely- 53. Pipe A and pipe B running together can fill a
filled tank in 54 hours. If 8 inlet pipes and 3 cistern in 6 minutes. If B takes 5 minutes more
outlet pipes are opened simultaneously, when than A to fill it, then the time in which A and
the tank is empty, then in how many hours will B will fill that cistern separately will be,
A

the tank get completely filled? respectively,________.

,d buysV ikbi ,d •kyh VSad dks 120 ?kaVs esa Hkj ldrk ikbi A vkSj ikbi B ,d lkFk pkyw gksus ij ,d Vadh dks 6
gS] tcfd ,d vkmVysV ikbi iwjh rjg ls Hkjs VSad dks 54 feuV esa Hkj ldrs gSaAB;fnbls Hkjus esa
A ls 5 feuV vf/d
le; ysrk gS] rksA vkSjB }kjk ml Vadh dks vyx&vyx Hkjus
?kaVs esa •kyh dj nsrk gSA ;fn VSad ds •kyh gksus ij 8
esa fy;k x;k le; Øe'k% gksxkA
buysV ikbi vkSj 3 vkmVysV ikbi ,d lkFk •ksys tkrs gSa]
rks VSad fdrus ?kaVs esa iwjh rjg ls Hkj tk,xk\ SSC CGL (PRE) 26/07/2023 (Shift-2)
(a) 15 min and 10 min
SSC CGL TIER I 20/07/2023 (Shift-01)
(b) 15 min and 20 min
(a) 81 (b) 96 (c) 25 min and 20 min
(c) 72 (d) 90 (d) 10 min and 15 min

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54. Pipes A and B can fill a tank in 10 and 18 hours. SSC MTS 16/06/2023 (SHIFT-01)
Pipe C is a drain pipe. When all the pipes are (a) 2 p.m
4 (b) 1 p.m
opened together for 3 hours, then part of
15 (c) 3 p.m
the the tank can be filled up. Pipe C alone can (d) 12 p.m
empty one-third of the tank in:
57. Pipes A and B can fill a tank in 18 hours and
ikbi A vkSjB ,d VSad dks10 vkSj18 ?kaVs esa Hkj ldrs gSaA
1
ikbi C ,d fudklh ikbi gSA ;fn lHkh ikbiksa dks ,d lkFk 22 hours, respectively. Pipe C is emptying
2
4 pipe. When all the three pipes are opened
3 ?kaVs ds fy, •ksy fn;k tk,] rks VSadfgLlk Hkjk tk together for 3 hour, then 20% of the tank can
15
be filled. A and B together are opened for 4
ldrk gSA ikbiC vdsys ,d frgkbZ VSad •kyh dj ldrk gS% hours, then A is closed and C is opened
instantly with B. In how much total time (in

r
ICAR Mains, 07/07/2023 (Shift-1)
hours) will the whole tank be filled?

si
(a) 3 hours
(b) 6 hours 1
ikbi A vkSjB VSad dks Øe'k% 18 vkSj
?kaVs
22 ?kaVs
esa

an by
2
(c) 5 hours
Hkj ldrs gSaA ikbiC •kyh djus okyk ikbi gSA tc rhuksa

n
(d) 8 hours
ikbiksa dks ,d lkFk 3 ?kaVs ds fy, •ksy fn;k tkrk gS] r
55. Two pipes A and B can fill a tank in 45 minutes Vadh dk 20»Hkj tkrkgSA A vkSjB dks ,d lkFk 4 ?kaVs

ja
and 75 minutes, respectively. A drain pipe C
ds fy, •ksyk tkrk gS] fiQjA dks can dj fn;k tkrk gS
R s
can empty the two-third filled tank in 20
vkSjC dks rqjarB ds lkFk •ksy fn;k tkrk gSA VSad
dqy
a th
minutes. If all three pipes are opened together,
in how much time (in hours) can three-fifth
fdrus le; esa (?kaVksa esa) iwjk Hkj tk,xk\
part of the tank be filled? CRPF HCM 22/02/2023 (Shift - 02)
nks ikbiA vkSjB ,d VSad dks Øe'k%45 feuV vkSj 75
ty a

(a) 57
feuV esa Hkj ldrs gSaA ,d fudkl ikbi
C. Hkjs gq, VSad ds (b) 60
di M

nks&frgkbZ20dksfeuV esa [kkyh dj ldrk gSA ;fn rhuksa (c) 58

3 (d) 52
ikbiksa dks ,d lkFk [kksy fn;k tk,] rks VSad dk
Hkkx
5
58. Pipe A can fill a tank in 12 hours and pipe B
fdrus le; (?kaVksa esa) esa Hkj ldrk gS\ takes 18 hours to fill it. Both pipes were opened
together and a leak was spotted which increased
ICAR Mains, 08/07/2023 (Shift-2)
the filling-up time by 48 minutes. Find how
(a) 5 many hours will it take for the leak to empty a
(b) 4.5 full tank.

(c) 4 ikbi A ,d VSad dks 12 ?kaVs esa Hkj ldrk gS vkSj i

(d) 3.5 B bls Hkjus esa 18 ?kaVs ysrk gSA nksuksa ikbiksa
A

•ksyk x;k vkSj ,d fjlko ns•k x;k ftlls Hkjus dk le;

56. Two taps P and Q can fill a tank alone in 10
hours and 12 hours respectively. If the two taps
48 feuV c<+ x;kA Kkr dhft, fd ,d Hkjs gq, VSad dks
are opened at 9 a.m., then at what time should fjlko }kjk •kyh djus esa fdrus ?kaVs yxsaxsA
the tap P be closed to completely fill the tank CRPF HCM 27/02/2023 (Shift - 02)
at exactly 3 p.m.?
(a) 60
nks uyP vkSjQ vdsys ,d Vadh dks Øe'k% 10 ?kaVs vkSj 12
(b) 68
?kaVs esa Hkj ldrs gSaA ;fn nksuksa uy lqcg 9 cts •ksys tkrs gSa]
(c) 72
rks Bhd 3 cts Vadh dks iwjh rjg Hkjus ds fy,Puydks
(d) 64
fdl le; can fd;k tkuk pkfg,\

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59. Pipes A and B can fill a tank in 15 hours and 60.

There are 3 taps A, B and C in a tank. These
20 hours, respectively. Pipe C is an emptying can fill the tank in 10 h, 20 h and 25 h,
pipe. A and B are opened together for 4 hours, respetively. At first, all three taps are opened
and then only A is closed and C opened. It took simultaneously. After 2 h, tap C is closed and
tap A and B keep running. After 4 h, tap B
1
19 hours more to fill the tank. Pipe C alone is also closed. The remaining tank is filled
5 by tap A alone. Find the percentage of done
can empty the full tank in: by tap A itself.
ikbi A vkSjB ,d VSad dks Øe'k% 15 ?kaVs vkSj 20 ?kaVs,desaVadh esa 3 uyA , B vkSj C yxs gSaA ;s Vadh dk
Hkj ldrs gSaA ikbi
C ,d •kyh djus okyk ikbi gSA A Øe'k% 10 ?kaVs] 20 ?kaVs vkSj 25 ?kaVs es Hkj
vkSjB dks ,d lkFk 4 ?kaVs ds fy, •ksyk tkrk gS vkSj 'kq# esa rhuksa uy ,d lkFk [kksys tkrs gSaA 2 ?k
mlds ckn dsoy A dks can fd;k tkrk gS vkSj
C dks •ksyk uy C dks can dj fn;k tkrk gS vkSjA vkSj B dks
pkyw j[kk tkrk gSA 4 ?kaVs ds ckn B dks
uy Hkh can
1
tkrk gSA Vadh dks Hkjus
19 esa
?kaVs vkSj yxsACikbi
vdsys dj fn;k tkrk gSA 'ks"k Vadh dksAuy
}kjk vdsys Hkjk
5

r
tkrk gSA uyA }kjk vdsys fd, x, dk;Z dk izfr'kr
Hkjs gq, VSad dks fdrus fnuksa esa •kyh dj ldrk gS%
Kkr djsaA

si
CRPF HCM 28/02/2023 (Shift - 03) SSC CPO 10/11/2022 (Shift-02)

an by
(a) 42 hours (b) 48 hours (a) 75% (b) 52%
(c) 72% (d) 32%
(c) 45 hours (d) 40 hours

n
ja
R s
Answer Key
a th

1.(d) 2.(c) 3.(d) 4.(d) 5.(d) 6.(b) 7.(c) 8.(a) 9.(d) 10.(c)

11.(b) 12.(b) 13.(b) 14.(a) 15.(a) 16.(a) 17.(b) 18.(d) 19.(c) 20.(a)
ty a

21.(a) 22.(d) 23.(a) 24.(a) 25.(d) 26.(d) 27.(d) 28.(d) 29.(b) 30.(d)
di M

31.(b) 32.(a) 33.(d) 34.(b) 35.(d) 36.(a) 37.(c) 38.(d) 39.(b) 40.(d)

41.(d) 42.(d) 43.(b) 44.(b) 45.(d) 46.(b) 47.(b) 48.(d) 49.(b) 50.(d)

51.(c) 52.(d) 53.(d) 54.(c) 55.(b) 56.(a) 57.(c) 58.(c) 59.(c) 60.(c)
A

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TIME & DISTANCE (le; vkSj nwjh)

(CLASSROOM SHEET)

Basic Formulae Units of Measurement/eki ds ek=kd

 Time is usually measured in second (sec), min-
Distance njw h utes (min) or hours (hr).
Speed = , pky =
Time le; le; dks lkekU;r% lsdaM] feuV vFkok ?kaVs esa ekirs gS
 Distance is usually measured in meters (m),
Distance njw h kilometer (km) or mile, yards or feet.
, le;

r
Time = =
Speed pky nwjh dks lkekU;r% ehVj] fdyksehVj] ehy vFkok ;kMZ
ekirs gSaA

si
Distance = Speed × Time
 Speed is usually measured in km/h, mile/hr
nwjh
= pky × le; an by or m/sec.
Two frineds left Delhi for Goa at 5 a.m. One friend pky dks lkekU;r% fdeh@?kaVk] ehy@?kaVk vFkok eh@

n
who went by train reached Goa in 24 hours and other ekirs gSaA
friends who went by Aeroplane reached in 3 hours. Conversion of Units/ek=kdksa dk :ikarj.k
ja
R s
nks fe=k fnYyh ls xksok ds fy, iwokZÉ 5 cts fudyrs gSaA1.,d fe=k
1 h = 60 min = 60 × 60 = 3600 sec.
2. 1 km = 1000 m
jsyxkM+h ls 24 ?kaVs esa vkSj nwljk gokbZ tgkt ls 3 ?kaVs esa xksok
a th

3. 1 mile = 1.606 km or 1 km = 0.6214 mile of 5

igq¡prk gSA mile = 8 km
We know that speed of aeroplane is more than train 4. 1 yard = 3 ft
ty a

so time taken by train is more than that of aeroplane. 1000

5. a km/hr = a × m/sec
ge tkurs gSa fd gokbZ tgkt dh pky jsyxkM+h ls vf/d gksrh gSA 60 × 60
di M

blfy, jsyxkM+h }kjk gokbZ tgkt ls vf/d le; fy;k x;kA =a×
5
m/sec
It can be infer from above explanation that 18
60 × 60
1 a m/sec = a × km/hr
Speed  (When distance is constant) 1000
Time
18
=a×
5
EX
km/hr
1
mi;qZDr ls ;g Li"V gS fd pky
 (tgk¡ nwjh fu;r gS)
le; EXERCISE
If two athlete run for constant time then distance 1. Dimple is travelling at a speed of 90 km per
hour on a highway, while Sachin is travelling
covered by the athlete whose speed is more would
A

at a speed of 108 kim per hour. What is the

be more. difference in their speeds, in metres per
;fn nks /kod fu;re le; ds fy, nkSM+s rks ftldh pky vf/d second?
gksxh og vf/d nwjh r; djsxkA fMaiy ,d jktekxZ ij 90km/h dh pky ls ;k=kk dj
It can be infer from above explanation that distance
jgh gS] tcfd lfpu 108km/h dh pky ls ;k=kk dj jgk
 time taken (when speed is constant)
gSA ehVj izfr lsdaM esa] mudh pky esa varj dh x.kuk djsa
SSC CHSL 09/08/2021 (Shift- 1)
mi;qZDr fooj.k ls Li"V gS fd
(a) 5 (b) 6
nwjh fy;s x;s le; (tc pky fu;r gks) (c) 4 (d) 3

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2. A man runs 200 metres in 24 seconds. His speed is:

TYPE-01
,d vkneh 24 sec esa200 m nkSM+rh gSA mldh xfr7.
Kkr A lady walks to her office every day from home
dhft,A and maintains a fixed time for the same. On
SSC CHSL 02/06/2022 (Shift- 3) one day she decreases her speed by 25%. By
what fraction of her usual time will she be late
(a) 30 km/h (b) 32 km/h on that day?
(c) 24 km/h (d) 33 km/h ,d efgyk izfrfnu ?kj ls vius dk;kZy; iSny pydj
3. A car covers a distance of 90 km in 50 min. tkrh gS] ftlds fy, mlus ,d le; fu/kZfjr fd;k gSA
What is its speed (in m/s)? fdlh ,d fnu og viuh pky dks 25» de dj nsrh gSA
,d dkj 50 feuV esa90km dh nwjh r; djrh gSA bldh ml fnu mls vius lkekU; le; ds fdl Hkkx (fraction)
xfr ( m/s esa) D;k gS\ rd nsjh gksxh\
SSC MTS (Shift- II) 12/10/2021
SSC CGL 19/04/2022 (Shift-02)
(a) 1/3 (b) 1/4
(a) 30 (b) 90
(c) 1/6 (d) 2/3
(c) 108 (d) 60

r
8. If Ram covers a certain journey at 60% of his
4. An athlete crosses a distance of 3600 m in 12 usual speed, he reaches the destination late

si
minutes. What is his speed (in km/h)? by 36 min. His usual time (in min) to reach
,d ,FkyhV 12 feuV eas3600 m dh nwjh r; djrk gSA
an by the destination is:
mldh pky (km/h eas
) Kkr djsa\ ;fn jke ,d fuf'pr ;k=kk viuh lkekU; pky dh 60»
pky ls r; djrk gS] rks og 36 feuV dh nsjh ls xarO;

n
SSC CHSL 07/06/2022 (Shift 02)
(a) 15 (b) 17
ij igq¡prk gSA xarO; rd igq¡pus eas mldk lkekU; le;
ja (feuV eas) gSA
R s
(c) 18 (d) 16
SSC CGL 01/12/2022 (Shift- 04)
5. The speed of a train is 108 km/h. The distance
a th

(a) 60 (b) 72
covered by the train in 11 seconds will be: (c) 50 (d) 54
,d Vsªu dh pky 108 km/h gSA Vsªu 11 lsd.M esa fdruh
8. Rajdhani Express leaves, Delhi station one and
half hour late and increases its speed by 10%
nwjh r; djsxh\
ty a

and reached Patna on Scheduled time. Find

SSC CHSL 26/05/2022 (Shift- 2) usual time taken by train to reach Patna from
di M

Delhi.
(a) 620 m (b) 540 m
jkt/kuh ,Dlizsl fnYyh ls iVuk ds fy, 1 ?kaVk 30 feuV nsjh
(c) 440 m (d) 330 m ls fudyrh gS vkSj viuh pky esa 10» dh o`f¼ djds iVuk
6. Which of the following is NOT a correct fu/kZfjr le; ij igq¡prh gSA Vªsu }kjk fnYyh ls iVuk igq¡pus e
statement? fy;k x;k lkekU; le; Kkr dhft,A
fuEufyf[kr eas ls dkSu&lk lgh dFku ugha gS\ (a) 16 hours (b) 16
1
hours
2
SSC CGL 05/12/2022 (Shift- 03) 2 1
(a) The speed of 20 m/s is less than the speed (c) 16 hours (d) 12 hours
3 2
of 85 km/h./20 m/s dh pky 85 km/h dh pky 2
10. A train reduced its speed by of its usual
ls de gksrh gSA 5
speed and reached certain destination 3 hours
A

(b) Time may be calculated by dividing the late. Find present time taken by train to reach
distance by the speed./nwjh dks pky ls foHkkftr destination.
2
djds le; dh x.kuk dh tk ldrh gSA ,d jsyxkM+h viuh lkekU; pky esa dh deh djus ls
5
(c) Covering the same distance in lesser time fdlh fuf'pr xarO; LFkku ij 3 ?kaVs dh nsjh ls igq¡prh gSA
implies a higher speed./de le; esa leku nwjh jsyxkM+h }kjk xarO; LFkku rd igq¡pus esa fy;k x;k orZ
r; djus dk vFkZ gS mPp pkyA le; Kkr dhft,A
(d) The speed of 99 km/h is less than the (a) 7 hours (b) 8 hours
speed of 24 m/s./99 km/h dh pky 24 m/s (c) 6
1
hours (d) 7
1
hours
dh pky ls de gksrh gSA 2 2

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11. Shatabdi Express left Delhi 40 min late. After 1 1

covering half of the distance it increased its (a) 2 (b) 2
1 2 4
usual speed by of original speed and 1 1
6 (c) 3 (d) 3
reached Chandigarh on scheduled time. Find 8 4
usual time taken by Shatabdi Express to cover
complete journey. 16. A takes 2 hours 30 minutes more than B to
'krkCnh ,Dlizsl fnYyh ls 40 feuV dh nsjh ls fudyrh walk 40 km. If A doubles his speed, then he
gSA vk/h nwjh r; djus ds ckn ;g viuh lkekU; pky esa can make it in 1 hour less than B. How much
1 time (in hours) does A require for walking a
dh o`f¼ djrh gS vkSj paMhx<+ fu/kZfjr le; ls igq¡p 40 km distance?
6
tkrh gSA laiw.kZ ;k=kk esa 'krkCnh ,Dlizsl }kjk fy;k x;k
40 km dh nwjh r; djus easA dks B ls 2 ?kaVs 30 feuV
lkekU; le; Kkr dhft,A vf/d yxrs gSaA ;fnA viuh pky nksxquh djrk gS] rks
(a) 560 minutes (b) 520 minutes og bls B ls 1 ?kaVk de le; eas r; dj ldrk gSAA }kjk
(c) 540 minutes (d) 420 minutes 40 km dh nwjh r; djus esa yxus okyk le; (?kaVs esa)
12. A car takes 50 minutes to cover a certain Kkr djsaA

r
distance at a speed of 54 km/h. If the speed is
SSC CPO 23/11/2020 (Shift-1)
increased by 25%, then how long will it take to

si
cover three-fourth of the same distance? (a) 7 (b) 5

dksbZ dkj] an by
54km/h dh pky ls fdlh fuf'pr nwjh dks 50
feuV esa r; djrh gSA ;fn pky esa 25» dh o`f¼ gksrh gS] rks
(c) 6

TYPE-02
(d) 9

n
dkj ml nwjh ds 3@4 Hkkx dks fdrus le; esa r; djsxh\
SSC CHSL 12/08/2021 (Shift- 3) A man go a certain distance with x km/hr and
ja comes back with a speed of y km/hr. If he
R s
(a) 25 minutes (b) 35 minutes takes t hour to go and come back. Find the
(c) 30 minutes (d) 40 minutes distance?
a th

13. If a car increases its speed from 24 km/h to ,d vkneh x fdeh@?kaVk ds lkFk ,d fuf'pr nwjh r;
40 km/h, it would reach certain destination djrk gS vkSjy fdeh@?kaVk dh xfr ls okil vkrk gSA ;fn
1 hours early. Find the distance.
mls tkus vkSj okil vkus esa
t ?kaVk yxrk gSA nwjh Kkr
ty a

;fn dksbZ dkj viuh pky 24 fdeh@?kaVs ls c<+kdj 40 dhft,\

fdeh@?kaVk dj ns rks ;g vius xarO; LFkku ij 1 ?kaVs igys
di M

igq¡p tk,xhA nwjh Kkr dhft,A  xy 

(a) 60 km (b) 48 km
Then distance/nwjh
= x +y×t
 
(c) 72 km (d) 54 km
17. A boy goes to school at 3 km/hr and return
14. If a train reduce its speed from 70 km/hr to
at a speed of 2 km/hr. If he takes 5 hours in
62 km/hr it would reach certain distance 1
all find the distance from his village to school.
hour late. Find the distance covered by train.
,d yM+dk 3 fdeh@?kaVk dh xfr ls Ldwy tkrk gS vkSj 2
;fn dksbZ jsyxkM+h viuh pky 70 fdeh@?kaVs ls ?kVkdj 62
fdeh@?kaVk dj ns rks ;g vius xarO; LFkku ij 1 ?kaVs dhfdeh@?kaVk dh xfr ls okil vkrk gSA ;fn og dqy feykdj
5 ?kaVs ysrk gS rks mlds xk¡o ls Ldwy dh nwjh Kkr dhft
nsjh ls igq¡psxhA jsyxkM+h }kjk r; dh xbZ nwjh Kkr dhft,A
(a) 5 km
(a) 540.5 km (b) 535.5 km
(b) 6 km
(c) 542.5 km (d) 545.5 km
A

(c) 7 km
15. Walking at 60% of his usual speed, a man
reaches his destination 1 hour 40 minutes (d) 8 km
late. His usual time (in hours) to reach the 1
destination is : 18. A student goes to school at a speed of 5 km/
2
viuh lkekU; pky dh rqyuk esa 60» pky ls pyrs gq,
,d O;fDr vius xarO; LFky ij 1 ?kaVs 40 feuV dh nsjh h and returns at a speed of 4 km/h. If he takes
ls igq¡prk gSA xarO; LFky rd igq¡pus esa mls yxus okyk3
4 hours for the entire journey, then the total
lkekU; le; (?kaVs esa) gS % 4
SSC CGL TIER II (13 /09/2019) distance covered by the student (in km) is:

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1 (a) 50 km (b) 55 km
,d Nk=k 5 fdeh@?kaVk dh xfr ls Ldwy tkrk vkSj
gS
2 (c) 45 km (d) 60 km
4 fdeh@?kaVk dh xfr ls okil vkrk gSA ;fn og iwjh ;k=kk
21. esa
If Raman drives his bike at a speed of 24 km/
3 h, he reaches his office 5 minutes late. If he
4 ?kaVs ysrk gS] rks Nk=k }kjk r; dh xbZ dqy nwjh (fdeh
4 drives at a speed of 30 km/h, he reaches his
esa) gS% office 4 minutes early. How much time (in
SSC CGL MAINS 29/01/2022 minutes) will he take to reach his office at a
(a) 11 (b) 22 speed of 27 km/h?
(c) 16 (d) 24
A man go a certain distance with x km/hr and ;fn jeu viuh ckbd 24km/h dh pky ls pykrk gS]
he comes back with a speed of y km/hr. If he rks og vius dk;kZy; esa 5 feuV dh nsjh ls igqaprk gSA
takes t hours more to come back than go. Find ;fn og 30km/h dh pky ls ckbd pykrk gSA rks vius
the distance.
dk;kZy; 4 feuV igys igqap tkrk gSA 27km/h
og dh
,d vkneh x fdeh@?kaVk ds lkFk ,d fuf'pr nwjh r;
pky ls vius dk;kZy; rd igq¡pus esa fdruk le; (feuVksa
djrk gS vkSj ogy fdeh@?kaVk dh xfr ls okil vkrk gSA
esa) ysxk\
;fn og tkus ls okil vkus esat ?kaVs vf/d ysrk gSA nwjh

r
dk irk yxk,aA SSC CGL 20/04/2022 (Shift-02)

si
Then distance/nwjh (a) 40 (b) 55
 xy  an by (c) 50 (d) 45
=   × (difference between time)

x – y  22. A boy when goes to his school by 12 km/hr
speed, reaches 20 mins late and when he

n
 The difference between time can be solved by
the following tricks covers the distance by 16 km/hr, reaches 5
mins late. Find speed by which he may reach
le; ds varj dks fuEufyf•r rjdhcksa ls gy fd;k tk
ja on time and also find distance of his school.
R s
ldrk gS ,d yM+dk tc 12 fdeh@?kaVs dh pky ls vius Ldwy tkrk
a th

Same important cases in speed

gS rks og 20 feuV dh nwjh ls igq¡prk gS vkSj tc og ;gh
Early, early case '–' (subtraction)
Late, Late case '–' (subtraction)
nwjh 16 fdeh@?kaVs dh pky ls r; djrk gS rks 5 feuV dh
Early, Late case '+' (Addition) nsjh ls igq¡prk gSA og pky Kkr dhft, ftlls og lgh
le; ij Ldwy igq¡ps vkSj Ldwy dh nwjh Hkh Kkr dhft,A
ty a

Late, Early case '+' (Addition)

19. A man when goes to his office at the rate of (a) 16 km/hr, 12 km (b) 18 km/hr, 12 km
di M

24 km/hr, reaches 10 mins late and when he (c) 20 km/hr, 10 km (d) 15 km/hr, 10 km
goes by 30 km/hr, he reaches 20 mins early.
Find distance of the office? TYPE-03
,d O;fDr tc vius vkWfiQl 24 fdeh@?kaVs dh pky In ls this variety, changes in speed are given and
tkrk gS rks og 10 feuV nsjh ls igq¡prk gS vkSj tc 30
accordingly changes in time are also given.
fdeh@?kaVs dh pky ls tkrk gS rks og 20 feuV igys bl izdkj ds iz'uksa esa pky esa ifjorZu fn;k gksrk gS vkSj ml
vkWfiQl igq¡p tkrk gSA vkWfiQl dh nwjh Kkr dhft,A vuqlkj le; esa ifjorZu Hkh fn;k gksrk gSA
(a) 60 km (b) 55 km 23. When a person decreases its speed by 6 km/
(c) 50 km (d) 65 km
h, reaches his destination 20 minutes late
20. Ramesh drives from his home at a speed of 40
while when he decreases its speed by 2 km/
km/h and reaches his college 25 minutes late.
h, he reaches 5 minutes late. Find actual speed
A

The next day he increases his speed by 10

of the person?
km/h, yet he is late by 10 minutes. How far
is his college from his home?
tc ,d O;fDr vius pky esa 6 fdeh@?kaVs dh deh djrk
jes'k vius ?kj ls 40 km/h dh pky ls xkM+h pykrk gS rks og vius xarO; LFkku ij 20 feuV dh nsjh ls igq¡prk
gS vkSj 25 feuV nsjh ls vius dkWyst igqprk gSA vxysgS ijarq tc og viuh pky esa 2 fdeh@?kaVk dh deh dj
fnu og viuh xkM+h dh pky10 km/h c<+k nsrk gS] nsrk gS rks og 5 feuV dh nsjh ls igq¡prk gSA O;fDr dh
fiQj Hkh dkWyst igq¡pus esa mls 10 feuV dh nsjh gksOkkLrfod pky Kkr dhft,A
tkrh gSA mldk dkWyst mlds ?kj ls fdruh nwj gS\ (a) 16 km/hr (b) 18 km/hr
SSC CHSL 24/05/2022 (Shift-01) (c) 17 km/hr (d) 20 km/hr

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24. Annu covers certain distance with her own ,d dkj P ls Q rd ,d fLFkj pky ls ;k=kk djrh gSA
speed, but when she reduces her speed by 10 ;fn bldh pky 10 fd-eh@?kaVk c<+k nh tkrh] rks leku
km/hr, her time duration for the journey nwjh dks r; djus esa mls ,d ?kaVk de le; yxrkA ;fn
increases by 40 hr, but when she increases her
bldh pky 10 fd-eh@?kaVk vkSj c<+k nh tkrh rks ;g 45
original speed by 15 km/hr time taken by her
feuV vkSj de le; ysrhAP vkSjQ ds chp dh nwjh Kkr
is 10 hours less than the original time. Find the
distance covered by her.
dhft,A
(a) 540 km (b) 420 km
vuq ,d fuf'pr nwjh viuh ,d fu;r pky ls r; djrh
(c) 600 km (d) 620 km
gS ijarq tc og viuh pky 10 fdeh@?kaVk de djrh gS
rks ;k=kk ds fy, mldh le; vof/ 40 ?kaVs c<+ tkrh gSA TYPE-04
ijarq tc og viuh ewy pky esa 15 fdeh@?kaVs dh o`f¼28. Vikash went to city from his village which is
djrh gS rks mlds }kjk fy;k x;k le; ewy le; ls 10 48 km far by two mode of communi-cation. He
covered some part of distance by cycle and
?kaVs de gksrk gSA mlds }kjk r; dh xbZ nwjh Kkr dhft,Arest part by bus. Average speed of cycle is 16
(a) 300 km/hr (b) 280 km/hr km/h while that of bus is 40 km/h and he

r
(c) 320 km/hr (d) 350 km/hr covered total distance in 2 hrs. Find distance
25. If speed of a train increases by 10 km/hour covered by him going by cycle.

si
then time taken to reach destination decreases fodkl vius xk¡o ls 48 fdeh nwj fLFkr 'kgj ;krk;kr ds
an by
by 1 hour. If speed increases by 10 km/hr nks ekè;eksa ls tkrk gSA og dqy nwjh dk dqN Hkkx lkbZ
further, time again reduces by 45 minutes. Find ls vkSj 'ks"k cl ls r; djrk gSA lkbZfdy dh vkSlr pky
16 fdeh@?kaVk tcfd cl dh 40 fdeh@?kaVk gS vkSj og

n
distance covered by the train.
;fn fdlh jsyxkM+h dh pky esa 10 fdeh@?kaVs dh o`f¼laiw.kZ nwjh 2 ?kaVs esa r; djrk gSA mlds }kjk lkbZfd
gksrh gS rks xarO; LFkku rd igq¡pus esa mlds }kjk fy;s r;
ja x, dh xbZ nwjh Kkr dhft,A
R s
le; esa 1 ?kaVs dh deh vk tkrh gSA ;fn pky esa 10 1
a th

(a) 20 km
fdeh@?kaVs vkSj o`f¼ gksrh gS rks fy;s x;s le; esa 45 feuV 3
dh deh vkrh gSA jsyxkM+h }kjk r; dh xbZ nwjh Kkr dhft,A 1
(a) 420 km (b) 430 km (b) 21 km
3
ty a

(c) 410 km (d) 425 km 1

26. A train covers a certain distance at a certain (c) 24 km
3
di M

speed, if the speed of the train is 6km/hr more,

then to cover the same distance it takes 6 1
hours less. But, if the speed of the train is 6 (d) 25 km
3
km/hr less then it would take 10 hrs more to 29. A person goes to Jaipur from Delhi which is 240
cover the same distance. Find the distance km far. He covers some part of distance by bus
covered by the train. and rest part by train. Time taken by him to
dksbZ jsyxkM+h fdlh fuf'pr pky ls ,d fuf'pr nwjh r; cover complete distance is 6 hours. Average
djrh gS] ;fn jsyxkM+h dh pky 6 fd-eh@?kaVk vf/d gksrh]speed of bus is 30 km/h and that of train is
55 km/h. Find distance covered by the person
rks mlh nwjh dks r; djus ds fy, 6 ?kaVs de yxrsA ysfdu] going by train.
;fn jsyxkM+h dh pky 6 fd-eh@?kaVk de gksrh] rks leku
,d O;fDr fnYyh ls 240 fdeh nwj fLFkr t;iqj tkrk gSA
nwjh r; djus esa 10 ?kaVs vf/d yxrsA jsyxkM+h }kjk r;og ;k=kk dh dqN nwjh cl ls vkSj 'ks"k Hkkx jsyxkM+h ls
A

dh xbZ nwjh Kkr dhft,A djrk gSA mls dqy nwjh r; djus esa 6 ?kaVs dk le; yxrk
(a) 640 km (b) 720 km/h gSA cl dh vkSlr pky 30 fdeh@?kaVk vkSj jsyxkM+h
(c) 540 km/h (d) 680 km/h pky 55 fdeh@?kaVk gSA O;fDr }kjk jsyxkM+h ls r; dh
27. A car travels from P to Q at a constant speed. nwjh Kkr dhft,A
If its speed were increased by 10 km/h, it
(a) 100 km
would have been taken one hour lesser to
(b) 105 km
cover the distance. It would have taken 45
minute lesser if its speed was further increased (c) 110 km
by 10 km/h. The distance between P and Q is (d) 108 km

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TYPE-05 (AVERAGE SPEED) ,d O;fDr fdlh fuf'pr nwjh dks cl }kjk 45 km/h
dh pky ls r; djrk gS vkSj rqjar dkj }kjk80 km/h
Average speed =
Total covered distance dh pky ls izkjafHkd fcUnq ij okil vkrk gSA iwjh ;k=k
Total taken time ds nkSjku mldh vkSlr pky fdruh gS\
dy
q r; dh xbZ njw h SSC CGL 09/12/2022 (Shift- 03)
vkSlr pky = dy
q fy;k x;k le; (a) 57.6 km/h (b) 63.2 km/h
(c) 73.5 km/h (d) 45.5 km/h
Cases for Average Speed 32. Ruksana travelled at 60 km/h while going
vkSlr pky dh fLFkfr;k¡ from point A to point B, and returned via the
1. When distance is constant same route at a different speed. If Ruksana’s
tc nwjh fu;r gks overall average speed during the two-way
2. When time is constant journey was 48 km/h, what was her speed
tc le; fu;r gks while travelling from B to A?
Case-I/fLFkfr&
I #dlkuk us LFkkuA ls LFkku
B rd tkus esa60 km/h
When distance is constant
dh pky ls ;k=kk dh] vkSj ,d fHkUu pky ds lkFk mlh

r
tc nwjh fu;r gks ekxZ ls okil ykSVhA ;fn bl nksrjiQk ;k=kk ds nkSjk
#dlkuk dh dqy vkSlr pky 48 km/h Fkh] rks LFkku

si
D
B ds LFkku A dh vksj ;k=kk djrs le; mldh vkSlr
A S1 B S2 C
an by pky D;k Fkh\
D D SSC CHSL 02/06/2022 (Shift-02)
t1 = S t2 = S

n
1 2
(a) 42 km/ (b) 40 km/h
Average speed/vkSlr pky =
ja (c) 45 km/h (d) 36 km/h
R s
D+D 2D 2S1S2
D D
= = Case-II/fLFkfr&
II
+ 1 1  S1 + S2
When time is constant
a th

D +
S1 S2  S1 S2 
tc le; fu;r gks
From above explanation, it is clear that when S1 S2
distance is constant, average speed is free from
t t
ty a

distance. It means three is no need of distance or D 1 = S1 × t D 2 = S2 × t

question can be solved through any supposed Average speed/vkSlr pky =
distance.
di M

D1 + D 2 S 1t + S 2 t t (S 1 + S 2 ) S1 + S 2
mi;qZDr fooj.k ls ;g Li"V gS fd tc nwjh fu;r gks rks vkSlr pky t +t
=
t +t
=
2t

2
nwjh ls Lora=k gksrh gSA vFkkZr~ nwjh dh dksbZ vko';drk ugha
When gksrh
time is gS
constant, average speed is free from
vFkok iz'u dks gy djus ds fy, nwjh dks dqN eku fy;k tkrk gSAtime. It means when time is constant
30. A car covers a certain distance travelling at tc le; fu;r gks] rks vkSlr pky le; ls Lora=k gksrh gSA vFkkZr
a speed of 60 km/h and returns to the starting tc le; fu;r gks
point at a speed of 40 km/h. The average Average speed/ vkSlr pky =
speed of the car for the entire journey is: Sum of the speed
,d dkj 60 km/h dh xfr ls pyrs gq, ,d fuf'pr Number of speeds / observations
nwjh r; djrh gS vkSj40 km/h dh xfr ls izkjafHkd pkyksa dk ;kxs
fcnq ij okil ykSVrh gSA iwjh ;k=kk ds fy, dkj dh vkSlr pkyka@s i;oZ s{k.kksa dh l[a ;k
A

33. A man travel from A to B at a speed of 29 km/

xfr D;k gS\
hr in 29 minutes and he travel from B to C
SSC CHSL 27/05/2022 (Shift-03) with a speed of 39 km/hr in 29 minutes. Find
(a) 20 km/h (b) 48 km/h the average speed of the whole journey?
(c) 120 km/h (d) 50 km/h ,d vkneh 29 feuV esa 29 fdeh@?kaVk dh xfrA ls ls
31. A person covers a certain distance by bus at B dh ;k=kk djrk gS vkSj og 29 feuV esa 39 fdeh@?kaV
45 km/h and immediately returns to the dh xfr ls B ls C dh ;k=kk djrk gSA iwjh ;k=kk dh vkSlr
starting point by car at a speed of 80 km/h. xfr Kkr dhft;s\
What is his average speed during the whole (a) 34 km/hr (b) 35 km/hr
journey? (c) 36 km/hr (d) 37 km/hr

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34. A car travels with a speed of 21 m/sec in the (a) 56 km/h (b) 60 km/h
first 10 minutes, 9.0 km in the next (c) 62 km/h (d) 58 km/h
10minutes and 10 km in the last 10 minutes
38. A man travels for 4 hours at a speed of 75
of its journey. What is the average speed ofthe
km/h, for next 6 hours at a speed of 65.5 km/
car in km/h during its entire journey?
h and for next 2 hours at a speed of 54 km/
,d dkj viuh ;k=kk ds igys 10 feuV eas 21m/sec h. What is his average speed (in km/h) for the
dh pky ls pyrh gS] vxys 10 feVu esa 9-0km vkSj entire journey?
vafre 10 feuV eas 10km dh ;k=kk djrh gSA viuh iwjh ,d vkneh 75 km/h dh pky ls 4 ?kaVs] 65.5 km/
;k=kk ds nkSjku dkj dh vkSlr pky
km/h eas D;k gS\ h dh pky ls 6 ?kaVs vkSj
54 km/h dh pky nks ?kaVs
SSC CPO 10/11/2022 (Shift- 01) ls ;k=kk djrk gSA iwjh ;k=kk esa mldh vkSlr
(km/pky
(a) 60.0 km/h (b) 63.2 km/h h esa
) D;k gS\
(c) 62.0 km/h (d) 65.3 km/h ICAR Assistant 29/07/2022 (Shift- 02)
35. John drives 250 km at 50 km/h and then he
3 2

r
drives 350km at 70km/h. Find his average speed (a) 64 (b) 64
4 3
for the whole journey in km/h.

si
tkWu250 km dh nwjh50 km/h dh pky ls xkM+h 3 1
(c) 66 (d) 65
pykdj r; djrk gS vkSj fiQj og 350 km dh nwjh
an by 4 3
70 km/h dh pky ls xkM+h pykdj r; djrk gSA iwjh 39. Two-thirds of a certain distance was covered

n
;k=kk ds nkSjku mldh vkSlr pky
( km/h esa
) Kkr dhft,A at the speed of 45 km/h, one-fourth at the
speed of 60 km/h and the rest at the speed
SSC CGL 08/12/2022 (Shift- 02)
ja of 75 km/h. Find the average speed per hour
R s
(a) 55 km/h (b) 60 km/h
for the whole journey. (correct to 2 decimal
a th

(c) 58 km/h (d) 65 km/h places)

36. Prasad goes 96 kilometres on a bike at a speed fdlh fuf'pr nwjh dk nks&frgkbZ Hkkx
45 km/h dh
of 16 km/h, 124 kilometres at 31 km/h in a
car, and 105 kilometres at 7 km/h in a horse
pky ls] ,d&pkSFkkbZ 60Hkkxkm/h dh pky ls vkSj
ty a

cart. Find his average speed for the entire 'ks"k Hkkx
75 km/h dh pky ls r; fd;k x;k A iwjh
distance travelled. ;k=kk ds fy, vkSlr pky izfr ?kaVk (nks n'keyo LFkku
di M

izlkn ,d ckbd ij 16 km/h dh pky ls 96 fdyksehVj rd lgh) Kkr dhft,A

dk eas31 km/h dh pky ls 124 fdyksehVj vkSj SSC CGL 01/12/2022 (Shift- 04)
?kksM+k xkM+h eas dh pky ls 105 fdyksehVj
7 km/h (a) 51.25 km/h (b) 45.75 km/h
tkrk gSA r; dh xbZ iwjh nwjh ds fy, mldh vkSlr (c) 58.25 km/h (d) 49.77 km/h
pky Kkr dhft,A 40. Vikas covered a certain distance by bike. If
SSC CGL 05/12/2022 (Shift- 04) he covers 40% of the distance at 40 km/h,
(a) 16 km/h (b) 13 km/h 50% of the distance at 25 km/h and the
remaining 10% distance at 10 km/h. Find his
(c) 17 km/h (d) 11 km/h
average speed over the whole distance.
37. A person travels in a car at 40 km/h for 3
A

hours, on a bike at 30 km/h for 2 hours, and fodkl us ,d fuf'pr nwjh ckbd ls r; dhA ;fn og
in a train at 80 km/h for 5 hours. What is 40» dks 40 km/h dh pky ls] 50» nwjh25 km/h
the average speed at which he travelled? dh pky ls vksj 'ks"k 10» dh nwjh
10 km/h dh pky
,d O;fDr dkj eas 40 km/h dh pky ls 3 ?kaVs] ckbd ls r; djrk gS] rks iwjh nwjh r; djus eas mldh vkSlr
ij 30 km/h dh pky ls 2 ?kaVs vkSj Vªsu80esa pky Kkr dhft,A
km/h dh pky ls 5 ?kaVs ;k=kk djrk gSA mlds }kjk SSC CGL 03/12/2022 (Shift- 02)
fdl vkSlr pky ls ;k=kk dh xbZ\ (a) 25 km/h (b) 28 km/h
SSC CGL 09/12/2022 (Shift- 02) (c) 26 km/h (d) 30 km/h

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41. In a journey of three unequal laps, a car covers fcuk fdlh Bgjko ds] cl dh pky 54 fd-eh@?kaVk gS
a distance of 200 km in 4 h in the first lap, vkSj Bgjko ds lkFk bldh pky 45 fd-eh@?kaVk gSA cl
while another 162 km at the speed of 15 m/ çfr ?kaVk fdrus feuV ds fy, #drh gS\
s in the second lap. It covered the remaining (a) 9 (b) 10
distance of the final lap in 4 h such that the
(c) 12 (d) 20
average speed of the car for entire journey
was 50 km/h. What was the speed of the car 44. The speed of a bus without stoppages is 40
km/h and with stoppages is 32 km/h. How
in the third lap of the journey?
many minutes per hour does the bus stop?
rhu vleku Hkkxksa dh ;k=kk esa] ,d dkj igys Hkkx dh
200 fdeh dh nwjh 4 ?kaVs esa r; djrh gS] tcfd nwljs ,d cl dh pky fcuk Bgjko ds 40 fdeh@?kaVk rFkk
Hkkx dh 162 fdeh dh nwjh] 15 eh@ls- dh pky ls r; Bgjko ds lkFk pky 32 fdeh@?kaVk gS cl izR;sd ?kaV
esa fdrus feuV ds fy, Bgjrh gS\
djrh gSA blus vafre Hkkx dh 'ks"k nwjh dks 4 ?kaVs esa bl
SSC MTS (Shift- II) 08/10/2021
çdkj r; dj nh fd iwjh ;k=kk ds fy, dkj dh vkSlr

r
(a) dh
pky 50 fdeh@?kaVk gks xbZA ;k=kk ds rhljs Hkkx esa dkj 18 (b) 15

pky D;k Fkh\ (c) 12 (d) 16

si
45. Speed of a car without stoppage is 48 km/h and
SSC CPO 10/11/2022 (Shift-02)

(a) 47 km/h
an by (b) 52 km/h
that of with stoppage is 36 km/h. If car stops
each time for 5 min then find the number of

n
(c) 42 km/h (d) 45 km/h stoppage in 1 hr 20 min.

42. The ratio of the distance between two places ,d dkj dh fcuk Bgjko ds pky 48 fdeh@?kaVk vkSj
ja
A and B to the distance between places B and Bgjko ds lkFk 36 fdeh@?kaVk gSA ;fn dkj izR;sd ckj 5
R s
C is 3 : 5. A man travels from A to B at a speed feuV ds fy, :drh gS rks 1 ?kaVs 20 feuV esa Bgjko dh
a th

of x km/h and from B to C at a speed of 50 la[;k Kkr dhft,A

km/h. If his average speed for the entire (a) 3 times (b) 4 times
journey is 40 km/h, then what is the value of
(c) 5 times (d) 6 times
(x – 10) : (x + 1)?
ty a

LFkkuksa B vkSjC ds 46.

A vkSjB ds chp dh nwjh dk LFkkuksa Speed of a train without stoppage is 80 km/
hr and that at with stoppage is 70 km/hr. If
chp dh nwjh ls vuqikr 3 % 5 gSA ,d O;fDr
A ls B rd]
di M

stoppage time is 3 min then find the number

x fdeh@?kaVk dh pky ls vkSj
B ls C rd 50 fdeh@?kaVk of stoppage in 2 hrs.
dh pky ls ;k=kk djrk gSA ;fn iwjh ;k=kk ds fy, mldh
vkSlr pky 40 fdeh@?kaVk gS] (x rks
–10) : (x + 1) dk
,d jsyxkM+h dh fcuk Bgjko ds pky 80 fdeh@?kaVk vkS
eku D;k gksxk\ Bgjko ds lkFk 70 fdeh@?kaVk gSA ;fn jsyxkM+h izR;s
SSC CGL MAINS 29 Jan 2022
3 feuV ds fy, :drh gS rks 2 ?kaVs esa Bgjko dh la[;k
Kkr dhft,A
(a) 20 : 31 (b) 31 : 20
(c) 11 : 10 (d) 10 : 11 (a) 5 times (b) 6 times
(c) 8 times (d) 4 times
TYPE-6
Question based on Average Speed with Stoppage 47. A train left Delhi station and reached Mumbai
station which is 1600 km far. Average speed
Bgjko ds lkFk vkSlr pky ij vk/kfjr iz'u
A

of the train without stoppage is 100 km/h and

When stoppage time is taken into consideration while there is stoppage of 10 min in every 100 km
calculating average speed, it is said average speed then find total number of stoppages and
with stoppage. average speed of with stoppage.
tc vkSlr pky dh x.kuk djrs gq, Bgjko ds le; dks Hkh 'kkfey ,d jsyxkM+h fnYyh LVs'ku ls 1600 fdeh nwj fLFkr eqE
djrs gSa rks bls Bgjko ds lkFk vkSlr pky ds dgrs gSaA LVs'ku igq¡prh gSA jsyxkM+h dh fcuk Bgjko ds vkSlr p
43. Without any stoppage, speed of the bus is 54
100 fdeh@?kaVk gSA ;fn izR;sd 100 fdeh ij 10 feuV
km/hr and with stoppage its speed is 45 km/
hr. The bus stops for how many minutes per dk Bgjko gks rks dqy Bgjko dh la[;k vkSj Bgjko ds
hour? lkFk vkSlr pky Kkr dhft,A

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3 2 49. A and B started their journeys from X to Y

(a) 15, 9 1 km/h (b) 18, 94 km/h and Y to X, respectively. After crossing each
7 17
other, A and B completed remaining parts of
3 2 1
(c) 15, 94 km/h (d) 16, 94 km/h their journeys in 6 hours and 8 hours,
17 17 8
respectively. If the speed of A is 32 km/h, then
TYPE-7
the speed, in km/h, of B is:
D1 D2 A vkSjB us Øe'k%X ls Y vkSj Y ls X dss fy,
A P B viuh ;k=kk 'kq: dhA ,d&nwljs dks ikj djsu ds
Here, ckn] A vkSjB us viuh ;k=kk ds 'ks"k HkkXk dks Øe'k
S1  Speed of train starting from A 1
( A ls 'kq: gksus okys Vªsu dh xfr)
6 ?kaVs vkSj 8 ?kaVs esa iwjk fd;kAA dh pky
;fn
8
S2  Speed of train starting from B 32 km/h gS] rksB dh pky km/h esa Kke dhft,A
( B ls 'kq: gksus okys Vªsu dh xfr) SSC CGL 12/04/2022 (Shift- 02)
(a) 21 (b) 28
T  Time after which they meet each other.

r
(c) 30 (d) 25
(le; ftlds ckn os ,d&nwljs ls feyrh gS) 50. Suman travels from place X to Y and Rekha

si
T1  Time taken by the train 1 to reach at its travels from Y to X, simultaneously. After
destination after crossing each other. meeting on the way. Suman and Rekha reach

esa fy;k x;k le;)

an by
(Vªsu 1 }kjk ,d&nwljs dks ikj djus ds ckn vius xarO; rd igq¡pus Y and X, in 3 hours 12 minutes and 1 hour 48
minutes, respectively. If the speed of Rekha is

n
T2  Time taken by the train 2 to reach at its 9 km/h. then the speed (in km/h) of Suman is:

ja
destination after crossing each other. ,d gh le; ij lqeu LFkku X ls Y ds fy, pyrh gS
R s
(Vªsu 2 }kjk ,d&nwljs dks ikj djus ds ckn vius xarO; rd igq¡pus vkSj js[kk LFkku
Y ls X ds fy, pyrh gSA jkLrs esa feyus
esa fy;k x;k le;) ds ckn] lqeu vkSj js[kk LFkku Y vkSjX ij Øe'k% 3
a th

D  Total distance form A to B. ?kaVk 12 feuV vkSj ,d ?kaVk 48 feuV esa igqaprh
(A ls B rd dh dqy nwjh
) ;fn js[kk dh pky 9 fdeh@?kaVk gS] rks lqeu dh pky
(fdeh@?kaVk esa) Kkr djsaA
ty a

On this concept three types of questions are asked

in the exams and they are based on the given formula SSC CGL 18/08/2021 (Shift- 02)
below :
di M

1
bl vo/kj.kk ij ijh{kk esa rhu izdkj ds iz'u iwNs tkrs gSa tks uhps (a) 7 (b) 6
2
fn;s x;s lw=kksa ij vk/kfjr gksrs gSaA
3
(a) T= T1  T2 (c) 8 (d) 6
4
S1 T2
(b) S = T 51. Radha walks with the speed of 40 km/h from
2 1
A to meet Shyam and Shyam Walks towards
(c) D = S1T1 + S2T2
her from B. After meeting each other at C they
48. Shyam starts to walk from A towards B at 10 reach at each other's home in 9 hours and 16
a.m. and Radha starts to walk from B towards
hours respectively. Find the distance between
A at 10 a.m. and after meeting at C they both
A and B and speed of Shyam.
reach their destination in 24 and 54 minutes
A

respectively. Find out the time they meet at jk/k] ';ke ls feyus ds fy, A ls 40 fdeh@?kaVk dhxfr
C. ls pyrh gS vkSj ';ke B ls mldh vksj c<+rk gSA
C esa
';ke A ls B dh vksj 10 cts pyuk 'kq: gksrk gS vkSj ,d&nwljs ds feyus ds ckn os Øe'k%
9 ?kaVs vkSj
16 ?kaVs
jk/k B ls A dh vksj lqcg 10 cts pyuk 'kq: djrh gS esa ,d&nwljs ds ?kj igq¡prs gSaA ';ke dh xfr
A vkSj
vkSj
vkSjC ij feyus ds ckn os nksuksa Øe'k% 24 vkSj 54 B ds chp dh nwjh Kkr dhft,A
feuV esa vius xarO; rd igq¡prh C
gSaA
ij feyus dk le; (a) 1120 km, 40 km/hr
Kkr dhft,A (b) 1120 km, 30 km/hr
(a) 10 : 30 a.m. (b) 10 : 36 a.m. (c) 840 km, 30 km/hr
(c) 11 : 00 a.m. (d) 10 : 25 a.m. (d) 840 km, 40 km/hr

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52. A and B start walking towards each-other at 9 TYPE-9 (Relative Speed)

: 00 a.m. from Jaipur and Kanpur respectively.
Speed of A and B are 70 km/hr and 90 km/hr 10 m/s 5 m/s 25 m/s
respectively. They meet at Delhi at a certain
time and have lunch together. At 10 : 39 a.m. A B C
They again start walking towards their 2800 m
destination. If a reached at Kanpur on 12 : 27
p.m., how much time they spent together to do If all of them meet at the same time, find the location
lunch? of that point with respect to A?
A vkSj B lqcg 9 cts Øe'k% t;iqj vkSj dkuiqj ls ;fn os lHkh ,d gh le; ij feyrs gSa rks A ds lanHkZ esa ml fcUnq
,d&nwljs dh vksj pyuk vkjaHk djrs AgSaAvkSj B dh dh LFkku Kkr dhft,\
pky Øe'k%70 fdeh@?kaVk vkSj 90 fdeh@?kaVk gSA 55. jkLrsA thief was noticed by a policeman from a
esa fdlh le; fnYyh esa ;s nksuksa vkil esa feyrs gSa vkSjdistance of 80 metres. The speed of the thief
dqN le; os nksuksa ,d lkFk nksigj dk Hkkstu djrs gSa rFkkis 21 km/h and the policeman is 20 km/h.

r
10 ctdj 39 feuV ij os nksuksa fiQj vius xarO; LFkkuksaWhat is the distance between them after 18

si
seconds?
dh vksj pyuk 'kq: djrs gSaA ;fnA dkuiqj 12 ctdj
an by
27 feuV ij igq¡p tkrk gS] rks nksuksa us fdruk le; ,d
lkFk Hkkstu ij fcrk;k\
,d iqfyldehZ us pksj dks 80 ehVj dh nwjh ls ns[kkA
pksj dh pky 21 km/h gS vkSj iqfyldehZ dh pky

n
(a) 16 min (b) 12 min 20 km/h gSA 18 lsd.M ds ckn muds chp dh nwjh
ja D;k gksxh\
R s
(c) 15 min (d) 20 min
SSC Phase X 01/08/2022 (Shift- 03)
TYPE-8
a th

(a) 70 metres (b) 95 metres

53. I walk a certain distance and ride back taking
(c) 90 metres (d) 85 metres
a total time of 37 minutes. I could walk both
56.A thief is noticed by a policeman from a
ty a

ways in 55 minutes. How long would it take

me to ride both ways? distance of 97 m. The thief starts running and
di M

the policeman chases him. The thief and the

eq>s ,d fuf'pr nwjh iSny tkus vkSj ckbd ls okil vkus policeman run at a speed of 21 m/sec and
esa dqy 37 feuV dk le; yxrk gSA eq>s nksuksa rjiQ iSny23 m/sec respectively. What is the time taken
tkus vkSj vkus esa 55 feuV yxrs gSaA eq>s nksuksa rjiQby
ckbd
the policeman to catch the thief?
ls tkus vkSj okil vkus esa fdruk le; yxsxk\ ,d iqfyldehZ dks 97 m dh nwjh ls ,d pksj fn[kkbZ
(a) 9.5 m (b) 19 min nsrk gSA pksj Hkkxus yxrk gS vkSj iqfyldehZ mldk ih
(c) 18 min (d) 20 min djrk gSA pksj vkSj iqfyldehZ Øe'k%
21 m/sec vkSj
54. A man walks a certain distance by foot and rides 23 m/sec dh pky ls nkSM+rs gSaA pksj idM+us eas iqfyl
back on horse in 4 hr. 30 min. He could ride on dks fdruk le; yxrk gS\
horse both ways in 3hrs. The time required by
A

SSC CGL 02/12/2022 (Shift- 01)

the man to walk by foot both ways is :
(a) 40 sec (b) 45 sec
fdlh O;fÙkQ dks ,d fuf'pr nwjh iSny tkus vkSj ?kksM+s ls
(c) 62.5 sec (d) 48.5 sec
okfil vkus esa dqy 4 ?kaVs 30 feuV yxrs gSA nksuksa rjiQ dh
57. A policeman sees a thief at a distance of 150
nwjh ?kksM+s ls og 3 ?kaVs esa r; dj ldrk gSA nksuksa rjiQ dh
m. He starts chasing the thief who isrunning
nwjh dks iSny pyus esa yxus okyk vko';d le; Kkr djsa% at a speed of 5 m/sec, while the policeman
(a) 4 hrs 30 min (b) 4 hrs 45 min chases with a speed of7m/sec.Find the
distance covered by the thief when he is
(c) 5 hrs (d) 6 hrs caught by the policeman.

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,d iqfyldehZ 150 m dh nwjh ij ,d pkjs dks ns[krk (a) 11 a.m. (b) 10 a.m.
gSA og5 m/sec, dh pky ls Hkkx jgs pkjs dk ihNk (c) 10:45 a.m. (d) 11:30 a.m.
djuk vkjaHk djrk gS] tcfd iqfyldehZ7 m/sec. 61. Two stations are 120 km apart on a straight
dh pky ls ihNk djrk gSA iqfyldehZ }kjk idM+s tkus line. A train starts from station A at 8 a.m.and
ds le; rd pksj }kjk r; dh xbZ nwjh Kkr dhft,A moves towards station B at 20 km/h, and
another train starts from station B at 9a.m.
SSC CPO 09/11/2022 (Shift- 02)
and travels towards station A at a speed of
(a) 285 m (b) 325 m 30 km/h. At what time will they meet?
(c) 375 m (d) 295 m
58. A thief stole jewellery from a shop at 8:15
nks LVs'ku ,d lh/h js[kk 120
esa km dh nwjh ij gSaA
p.m. and left on a bike at a speed of 60 km/ ,d Vsªu LVs'ku A ls lqcg 8 a.m. ij pyuk 'kq:
h. The police were informed at 8:30 p.m. If djrh gS vkSj LVs'ku
B dh vksj 20 km/h dh pky ls
the police want to arrest the thief at 9:00 p.m.,
pyrh gS] vkSj nwljh Vªsu LVs'ku
B ls lqcg 9 a.m. ij
what should be the minimum speed of the
police jeep? pyuk 'kq: djrh gS vkSj LVs'ku
A dh vksj 30 km/h
,d pksj us ,d nqdku ls 8:15 p.m. ij tsoj pqjk, dh pky ls pyrh gSA os fdl le; feysaxh\

r
vkSj60 km/h dh py ij ckbd ls Hkkx x;kA iqfyl SSC CPO 10/11/2022 (Shift- 01)

si
dks8:30 p.m. cts lwpuk nh xbZA ;fn iqfyl pksj dks
(a) 10:30 a.m. (b) 10:00 a.m.
9:00 p.m. cts fxjÝrkj djuk pkgrh gS] rks iqfyl thi
an by
dh U;wure pky fdruh gksuh pkfg,\
SSC CGL 08/12/2022 (Shift- 04) 62.
(c) 11:00 a.m. (d) 11:30 a.m.
Two trains leave Agra for Calcutta at 9:00 a.m.

n
(a) 60 km/h (b) 75 km/h and 9:30 a.m., respectively, and travel at 240
(c) 80 km/h (d) 90 km/h km/h and 300 km/h, respectively. How many
59. ja
A thief running at speed of ‘x’ km/h is chased kilometres from Agra will the two trains meet?
R s
by a policeman running at a speed of 10 km/
nks Vsªusa vkxjk ls dksydkrk ds fy, Øe'k%
9:00 a.m.
a th

h. If the thief is ahead by 100 metres, the

policeman catches the thief after 3 minutes. ij jokuk gksrh gSa vkSj Øe'k%
240 km/h vkSj300
At what speed is the thief running (‘x’ being km/h dh pky ls pyrh gSaA nksuksa Vsªusa vkxjk ls fd
the unknown speed)?
fdyksehVj dh nwjh ij feysaxh\
ty a

'x' km/h dh pky ls nkSM+ jgs ,d pksj dk ihNk]

10
km/h dh pky ls nkSM+ jgs ,d iqfyldehZ }kjk fd;k SSC CHSL 30/05/2022 (Shift- 02)
di M

tkrk gSA ;fn pksj 100 ehVj vkxs gS] rks iqfyldehZ 3 (a) 270 km (b) 300 km
feuV ds ckn pksj dks idM+ ysrk gSA rks crkb, fd (c) 600 km (d) 240 km
pksj fdl pky ls Hkkx jgk gS
('x' vKkr pky gSA
)\
63. From point H, at 6 : 30 pm, a train starts
SSC CGL 09/12/2022 (Shift- 03) moving towards point K at the speed of 90
(a) 4 km/h (b) 8 km/h km/hr. Another train starts moving from point
(c) 10 km/h (d) 6 km/h K at 7:30 p.m. towards point H at the speed
60. Two cities A and B are 135 km apart on a of 72 km/hr. Both the train meet at 11:30
straight track. One car starts from A at 8 a.m. p.m. at point J. What is the ratio of the
and travels towards B at 25 km/h. Another distance HJ and KJ?
car starts from B at 9 a.m. and travels
fcUnqH ls ,d jsyxkM+h 6:30 vijkgu ij K dh vksj
A

towards A at a speed of 30 km/h. At what

time will they meet? 90 fd-eh-@?kaVk dh pky ls pyuk vkjaHk djrh gSA ,d
nks 'kgjA vkSj B ls lh/s jkLrs ij 135 km dh nwjh vU; jsyxkM+h 7:30 vijkgu ij fcUnq K ls fcUnqH

ij gSaA ,d dkj A ls 8 a.m. ij pyuk 'kq: djrh gS dh vksj 72 fd-eh-?kaVk dh pky ls pyuk vkjaHk djrh
vkSjB dh vksj 25 km/h dh pky ls pyrh gSA ,d gSA nksuksa jsyxkfM+;k¡ J ij fcUnq
11:30 vijkgu ij
feyrh gSAHJ rFkkKJ nwjh dk vuqikr D;k gS\
vU; dkj 9 a.m. ij B ls pyuk 'kq: djrh gS vkSj
A dh vksj 30 km/h dh pky ls pyrh gS os fdl SSC CGL 06/12/2022 (Shift- 04)

le; feysaxh\ (a) 25 : 16 (b) 5 : 16

SSC CGL 09/12/2022 (Shift- 01) (c) 36 : 25 (d) 31 : 19

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64. Ajit Singh left from place P at 9.30 a.m. for 67. A and B leave from point M at the same time
place Q, and David Raj left place Q at 1.30 towards point N. B reaches N and starts
p.m. for place P. The distance between them towards M instantly. He meets A at point O
is 416 km. If Ajit Singh’s speed is 44 km/h (between M and N). The distance between M
and David Raj’s speed is 52 km/h, then at and N is 245 km. If the speeds of A and B
are 26 km/h and 65 km/h, respectively, then
what time will they meet each other? what is the distance between O and N?
vftr flag lqcg 9.30 cts LFkkuP ls LFkkuQ ds A vkSjB ,d gh le; ij fcanq M ls fcanqN dh vksj
fy, pyuk 'kq: djrk gS vkSj MsfoM jkt nksigj1.30 pyuk 'kq: djrs gSaA
B, N ij igq¡prk gS vkSj rqjar okil
cts LFkkuQ ls LFkkuP ds fy, pyuk 'kq: djrk gSA M dh vksj pyuk 'kq: djrk gSA og fcanqO (M vkSjN
muds chp dh nwjh 416km gSA ;fn vftr flag dh ds chp) ij A ls feyrk gSAM vkSjN dss chp dh nwjh
pky 44km/h gS vkSj MsfoM jkt dh pky 52km/h 245 fdeh gSA ;fnA vkSjB dh pky Øe'k% 26 fdeh@?kaVk
gS] rks os ,d nwljs ls fdrus cts feysaxs\ vkSj 65 fdeh@?kaVk gS] O vkSj
rks N ds chp dh nwjh
fdruh gS\
SSC CHSL 11/08/2021 (Shift- 2)
SSC MTS 05/07/2022 (Shift- 03)

r
(a) 4.30 p.m. (b) 6 p.m. (a) 115 km (b) 105 km

si
(c) 4 p.m. (d) 5 p.m. (c) 95 km (d) 140 km
65. A train starts running at a uniform speed of 68. X and Y start at the same time to ride from
an by
60 km/h from station P towards station Q. At
the same time another train starts running from
place A to place B, which is 80 km away from
A. X travels 4 km per hour slower than Y. Y

n
station Q towards station P. If the distance reaches place B and at once turns back
between the stations P and Q is 275 km and
meeting X, 16 km from place B. Y's speed (in
ja
the trains meet in two and a half hours, then
R s
what is the speed of the train running towards km/h) is:
station P in km/h? LFkkuA ls LFkku
B rd tks fd LFkkuA ls 80 fdeh nwj
a th

,d jsyxkM+h LVs'kuP ls LVs'kuQ dh vksj 60 fdeh@?kaVk gS] tkus ds fy,X vksj Y ,d gh le; ij ;k=kk 'kq:
dh ,dleku xfr ls nkSM+uk 'kq: djrh gSA mlh le; ,d djrs gSaA
Y dh vis[kk X 4 lseh izfr ?kaVs /heh ;k=kk
vU; jsyxkM+h LVs'kuQ ls LVs'kuP dh vksj pyuk 'kq: djrk gSAY, LFkkuB ij igqapdj okil vkrs gq,] LFkku
ty a

djrh gSA ;fn LVs'kuksaP vkSj Q ds chp dh nwjh 275 B ls 16 lseh nwjh ijX ls feyrk gSA Y dh pky
fdeh gS vkSj jsyxkfM+;k <kbZ ?kaVs esa feyrh P gSa LVs'ku
di M

(fdeh@?kaVk esa) Kkr djsaA

dh vksj pyus okyh Vªsu dh xfr fdeh@?kaVk esa D;k gS\
SSC CHSL 04/08/2021 (Shift- 03)
SSC CHSL 04/08/2021 (Shift- 2)
(a) 8 (b) 12
(a) 50 (b) 40 (c) 19 (d) 9
(c) 44 (d) 48 69. The distance between two stations A and B
66. Menu and Daya travel from point A to B, a is 200 km. A train runs from A to B at a speed
distance of 105 km, at speeds of 10 km/h and of 75 km/h, while another train runs from B
25 km/h, respectively. Daya reaches point B to A at a speed of 85 km/h. What will be the
first and returns immediately and meets Menu
distance between the two trains (in km) 3
at point C. Find the distance from point A
minutes before they meet?
to point C.
A

ehuw vkSj n;k Øe'k%10 km/h vkSj 25 km/h dh

nks LVs'kuksa
A vkSj B ds chp dh nwjh200km gSA ,d

pky ls fcUnq105 km dh nwjh r; djrs gSaA n;k igys Vªsu

A ls B rd 75km/h dh pky ls pyrh gS] tcfd

fcUnqB ij igq¡prh gS vkSj rqjar ykSVrh gS vkSj ehuw nwljh

ls VªsuB ls A rd 85km/h dh pky ls pyrh gSA
fcUnqC ij feyrh gSA fcUnq
A ls fcUnqC rd dh nwjh feyus ls 3 feuV igys nksuksa Vsªuksa ds chp dh nwjh (fd
Kkr dhft,A esa) D;k gksxh\
SSC CGL 09/12/2022 (Shift- 02) SSC CGL 21/04/2022 (Shift- 01)
(a) 35 km (b) 60 km (a) 5 (b) 8
(c) 45 km (d) 62 km (c) 10 (d) 6

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70. A car and a bus were travelling in the same LFkkuA vkSj B ,d nwljs ls 45 fdeh dh nwjh ij
direction. At 7:30 am. the car travelling at a
fLFkr gSA LFkku
A ls ,d dkj pyuk 'kq: djrh gSA
speed of 72 km/h was 4.2 km behind the bus.
At 8:15 a.m. the car was 15.8 km ahead of vkSj mlh le; LFkkuB ls nwljh dk pyuk 'kq: djrh
the bus. What is the ratio of the speed of the gSaA ;fn os leku fn'kk esa pyrh gSa] rks os lk<+s p
car to the speed of the bus? ?kaVs esa feyrh gSa vkSj ;fn os ,d nwljs dh vksj pyrh
,d dkj vkSj ,d cl ,d gh fn'kk eas py jgh FkhA gSa] rks os 27 feuV esa feyrh gSaA rst pyus okyh d
lqcg 7 % 30 am. ij 72 fdeh@?kaVk dh pky ls py dh pky (fdeh@?kaVsa esa) Kkr djsaA
jgh dkj cl ls 4-2 fdeh vkxs FkhA dkj dh pky vkSj SSC CGL 24/08/2021(Shift- 02)
cl dh pky dk vuqikr D;k gS\ (a) 50 (b) 45
SSC Phase IX 2022 (c) 55 (d) 56
(a) 27 : 17 (b) 9 : 5 74. A train leaves a station A at 7 am and reaches
(c) 9 : 4 (d) 36 : 17 another station B at 11 : 00 am. Another train
leaves B at 8 am and reaches A at 11 : 30 am.
71. The driver of a car, which is travelling at a
speed of 75 km/h, locates a bus 80 m ahead The two trains cross one another at
,d Vªsu lqcg 7 cts LVs'ku
A ls fudyrh gS vkSj 11%00

r
of him, travelling in the same direction. After
15 seconds, he finds that the bus is 40 m cts nwljs LVs'ku
B ij igqaprh gSA ,d vU; Vªsu lqcg 8 cts

si
behind the car. What is the speed of the bus B ls fudyrh gS vkSj 11%30 cts A ij igqaprh gSA nks Vªsusa
(in km/h)?
an by
75 fdeh@?kaVk dh pky ls py jgh dkj dk pkyd] 80
ehVj vkxs leku fn'kk esa py jgh ,d cl dks ns[krk gSA
,d nwljs dks fdl le; ikj djrh gSa\
(a) 8 : 36 a.m. (b) 8 : 56 a.m.

n
(c) 9 : 00 a.m. (d) 9 : 24 a.m.
15 lsdaM ckn og ns[krk gS fd cl vc dkj ls 40 75. A train leaves station A at 8 am and reaches
ehVj ihNs gSA cl dh pky (fdeh@?akVk esa) fdruh gS\
ja station B at 12 noon. A car leaves station B
R s
SSC CGL MAINS 03/02/2022 at 8:30 am and reaches station A at the same
time when the train reaches station B. At what
a th

(a) 44.2 (b) 42.5

(c) 47.5 (d) 46.2 time do they meet?
72. The distance between two places A and B is 140 ,d jsyxkM+h] lqcg 8 cts LVs'ku
A ls fudyrh gS vkSj
km. Two cars x and y start simultaneously from nksigj 12 cts LVs'ku
B ij igqaprh gSA ,d dke lqcg
ty a

A and B, respectively. If they move in the same 8 % 30 cts LVs'ku

B ls fudyrh gS vkSj LVs'ku A ij
direction, they meet after 7 hours. If they move
mlh le; igqaprh gS tc jsyxkM+h LVs'kuB ij igqaprh
di M

towards each other, they meet after one hour.

What is the speed (in km/h) of car y if its speed gSA os ,d&nwljs ls fdl le; feyrh gS\
is more than that of car x? SSC CGL 16/08/2021(Shift- 02)
A vkSjB uked nks LFkkuksa ds chp dh140 nwjh
km (a) 9 : 38 am (b) 10 : 22 am
gSA x vkSjy uked nks dkjsa Øe'k% A vkSjB ls ,d (c) 10 : 08 am (d) 9 : 52 am
lkFk pyuk 'kq: djrh gSaA ;fn os ,d gh fn'kk esa pyrh
76. Ram starts from point A at 8 a.m. and reaches
point B at 2 p.m. on the same day. On the same
gSa rks 7os?kaVs ckn ,d&nwljs ls feyrh gSaA ;fn os
day, Raju starts from point B at 8 a.m. and
,d&nwljs dh vksj pyrh gSa rks1 os?kaVs ckn ,d&nwljs reaches point A at 6 p.m. on the same day. Both
ls feyrh gSaA ;fn dkjy dh pky dkj x ls vf/d gS points A and B are separated by only a straight
rks dkj y dh pky (km/h esa ) fdruh gS\ line track. At what time they both meet?
A

SSC CGL MAINS 03/02/2022 jke fcUnqA ls 8 a.m. ij pyuk 'kq: djrk gS vkSj
(a) 60 (b) 100 mlh fnu fcUnq B ij 2 p.m. ij igq¡prk gSA mlh fnu]
(c) 80 (d) 90 jktw fcUnqB ls 8 a.m. ij pyuk 'kq: djrk gS vkSj
73. Places A and B are 45 km apart from each other. mlh fnu fcUnqA ij 6 p.m. ij igq¡prk gSA nksuksa
A car starts from place A and another car starts
from place B at the same time. If they move in fcUnqA vkSj B dsoy ,d lh/h js[kk okys VªSd }kjk
the same direction, they meet in 4 and a half i`Fkd fd, x, gSaA os nksuksa fdrus cts feyrs gSa\
hour and if they move towards each other, they SSC CGL 12/12/2022 (Shift- 03)
meet in 27 minutes. What is the speed (in km/ (a) 11:45 a.m. (b) 9:42 a.m.
h) of the car which moves faster? (c) 10:42 a.m. (d) 12:42 p.a.

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77. A car starts from point A towards point B, (a) 32 : 24 (b) 30 : 56

(c) 20 : 21 (d) 28 : 36
1
travelling at the speed of 20 km/h 1 hours 80. A dog chases rabbit. The rabbit is 125 leaps
2 ahead of itself jumps from dog. The rabbit can
later, another car starts from point A and jump 4 times in a time in which the dog can
travelling at the speed of 30 km/h and reaches jump 3 times. The distances covered by the
rabbit and the dog in one jump are 1.75 and
1 2.75 m respectively. In how many jumps the
2 hours before the first car. Find the
2 dog will catch the rabbit ?
distance between A and B. ,d dqÙkk •jxks'k dk ihNk djrk gSA •jxks'k dqÙks ls 125
,d dkj fcUnq A ls fcUnqB dh vksj 20 km/h dh Nykaxs yxkdj vkxs fudy tkrk gSA •jxks'k ,d ckj esa 4
1 ckj dwn ldrk gS ftls dqÙkk 3 ckj esa dwn ldrk gSA
pky ls pyuk 'kq: djrh gSA1 ?kaVs ckn] nwljh dkj
2 •j x ks 'k vkS j dq Ùkk ,d N yka x es a Øe'k%
fcUnqA ls 'kq: gksrh gS vkSj
30 km/h dh pky ls 1-75 vkSj 2-75 ehVj dh nwjh r; djrs gSaA dqÙkk fdru
1 Nykaxksa esa •jxks'k dks idM+ ysxk\
pyrs gq, igyh dkj ls 2 ?kaVs igys igqaprhAgSA

r
2 (a) 175 (b) 350
vkSjB ds chp dh nwjh Kkr dhft,A (c) 525 (d) 700

si
SSC CGL 03/12/2022 (Shift- 01) 81. Two boys begin together to write out a booklet
(a) 300 km
(c) 260 km
an by (b) 240 km
(d) 280 km
containing 819 lines. The 1st boy starts with
the first line writing at the rate of 200 lines
an hour and the 2nd boy starts with the last

n
78. Two trains, running between Bangalore and
line then writes line 818 and so on. Backward
Chennai, start at the same time from proceeding at the rate of 150 lines an hour.
ja
theirrespective locations and proceed towards
R s
At the end of which line they meet.
each other at the speed of 80km/h and 95km/ 819 ykbuksa okyh ,d cqdysV fy•us ds fy, nks yM+ds
a th

h. When they meet, it is found that one train

,d lkFk 'kq: gksrs gSaA igyk yM+dk ,d ?kaVs esa 200 yk
has travelled 180km more than theother.The
distance between Bangalore and Chennai is
dh pky ls igyh ykbu fy•uk 'kq: djrk gS vkSj nwljk
_______. yM+dk vafre iafÙkQ ds lkFk 'kq: djrk gS vkSj fiQj ykb
ty a

818 fy•rk gS vkSj ,sls gh vkxs HkhA çfr ?kaVs 150 ykbu
csaxyq: vkSj psUubZ ds chp pyus okyh nks Vªsusa vius&vius
LFkkuksa ls ,d gh le; ij pyuk 'kq: djrh gSa vkSj Øe'k% dh pky ls ihNs ls fy•k tkrk gS| os var esa fdl ykbu
di M

80 fdeh@?kaVk vkSj 95 fdeh@?kaVk dh pky ls ,d&nwljs ij feyrs gSa\

(a) 467th (b) 468th
dh vksj c<+rh gSaA muds feyus ds le; rd ,d Vªsu (c) 470th (d) 475th
nwljh Vªsu ls 180 fdeh vf/d nwjh r; dj pqdh gksrh TYPE-10
gSA csaxyq: vkSj psUubZ ds chp dh nwjh Kkr dhft,A
82. Dipak goes to his office covering half of the
SSC CPO 10/11/2022 (Shift-01) distance by auto and rest by metro. Total time
(a) 1200 km (b) 2100 km taken by him to cover complete distance is 50
min. If he covers complete distance by metro,
(c) 345 km (d) 400 km
it would take 35 minutes to reach the office.
79. A is chasing B in the same interval of time.
On a particular day he goes to his office and
A jumps 8 times, while B jumps 6 times. But
returns by auto, find total time taken in
A

the distance covered by A in 7 jumps is the

complete journey.
same as that of B in 5 jumps. The ratio
nhid vius vkWfiQl tkus esa vk/h nwjh vkWVks ls vkSj
between the speeds of A and B is ________.
nwjh esVªks ls r; djrk gSA mUgsa dqy nwjh r; djus es
A leku le; varjky ij B dk ihNk dj jgk gSAA8
feuV yxrk gSA ;fn og laiw.kZ nwjh esVªks ls r; djs rks o
ckj dwnrk gS] tcfdB 6 ckj dwnrk gSA ysfdu
A }kjk
vkWfiQl 35 feuV esa igq¡p tk,xkA fdlh fo'ks"k fnu og
7 dwnksa eas r; dh xbZ nwjh Bhd oghB gS}kjk
tks5
vkWfiQl vkWVks ls tkrk gS vkSj okil vkrk gSA laiw.k
dwnksa esa r; dh tkrh AgSA
vkSj B dh pkyksa ds chp
esa mlds }kjk fy;k x;k le; Kkr dhft,A
vuqikr Kkr djsaA (a) 110 min (b) 120 min
SSC CGL 08/12/2022 (Shift- 01) (c) 130 min (d) 140 min

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83. Ravi travels 300 km partly by train and partly TYPE-11

by car. He takes 4 hours to reach. If he travels
Buses are leaving bus terminal after every 10 minutes
60 km by train and rest by car. He will take 10 (T1) But, a person who is moving towards the terminal
minute more if he were to travel 100 km by train meets the bus after every 8 minutes (T2).
and rest by car. The speed of the train is çR;sd 10 feuV(T1) ckn clsa cl VfeZuy ls fudyrh gSa ysfdu]
jfo vkaf'kd :i ls Vªsu }kjk vkSj vkaf'kd :i ls dkj ,d O;fÙkQ tks VfeZuy dh vksj c<+ jgk gS og gj 8(T
feuV
2
) ds
}kjk 300 fdeh dh ;k=kk djrk gSA mls ;k=kk iwjh djuscknesa
cl 4ls feyrk gSA
?kaVs dk le; yxrk gSA ;fn og Vªsu ls 60 fdeh dh ;k=kk
Speed of man T1 – T2
djrk gS vkSj 'ks"k ;k=kk dkj ls djrk gSA ;fn og VªsuSpeed
ls of bus = T
2
100 fdeh dh ;k=kk djrk gS vkSj 'ks"k ;k=kk dkj }kjk
djrk gS rks mls 10 feuV vf/d le; yxsxkA Vªsu dh Speed of Train T1 – T2
=
pky Kkr djsaA Speed of Sound T2

(a) 50 km/h (b) 60 km/h Here,/;gka]

r
(c) 100 km/h (d) 120 km/h T1 = Time after which buses leaves the terminal.
T1 = le; ftlds ckn clsa VfeZuy ls fudyrh gSaA

si
84. A distance of 600 Km is to be covered in 2
parts. In 1st phase 120 Km is travelled by T2 = Time after which it meets with the person.
an by
train and rest by car and it took total of 8
hours, but if 200 km is covered by train and
T2 = le; ftlds ckn clsa O;fDr ls feyrh gSaA
86. Buses start from a bus terminal with a speed

n
rest by car it takes 20 min more. find the avg of 20 km/hr at intervals of 10 minutes. What
speed of car and train ? is the speed of a man coming from the
ja opposite direction towards the bus terminal if
R s
600 fdyksehVj dh nwjh dks 2 Hkkxksa esa doj fd;k tkukhe meets the buses at intervals of 8 minutes?
gSA çFke pj.k esa 120 fdyksehVj dh ;k=kk Vªsu }kjk vkSj clsa cl VfeZuy ls 10 feuV ds varjky ij 20 fdeh@?kaVk
a th

'ks"k ;k=kk dkjk }kjk dh tkrh gS vkSj blesa dqy 8 ?kaVsdhdkxfr ls fudyrh gSaA cl VfeZuy dh vksj foijhr fn'kk
le; yxrk gS] ysfdu ;fn 200 fdyksehVj dh nwjh Vªsu ls vkus okys O;fÙkQ dh xfr D;k gS ;fn og 8 feuV ds
varjky ij clksa ls feyrk gS\
}kjk r; dh tkrh gS vkSj 'ks"k nwjh dkj }kjk r; dh tkrh (a) 3 km/hr
ty a

(b) 4 km/hr
gS rks blesa 20 feuV vfèkd le; yxrk gSA dkj vkSj Vªsu (c) 5 km/hr (d) 7 km/hr
di M

dh vkSlr xfr Kkr djsa\ 87. Two buses start from a bus terminal with a
speed of 30 km/h at interval of 15 minutes.
(a) 80 & 60 km/h (b) 90 & 60 km/h What is the speed of man coming from the
(c) 120 & 90 km/h (d) 120 & 100 km/h opposite direction towards the bus terminal if
he meets the buses at interval of 10 minutes?
85. A man travels 400 kms in 4 hours partly by air
,d cl VfeZuy ls nks clsa 15 feuV ds varjky ij 30
and partly by train if he had travelled all the
4
fdeh@?kaVk dh xfr ls pyrh gSaA foijhr fn'kk ls cl VfeZuy
way by air he would have saved
5
of the time dh vksj vkus okys O;fÙkQ dh xfr D;k gS ;fn og 10
he was in the train and would have arrived his feuV ds varjky ij clksa ls feyrk gS\
destination 2 hrs early. Find the distance he (a) 15 km/h (b) 12 km/h
travelled by train. (c) 20 km/h (d) 10 km/h
88. The buses are departed after every 20 min, but
A

,d vkneh 400 fdyksehVj dh ;k=kk 4 ?kaVs esa vkaf'kdman going away from the bus depot after every
:i ls gokbZ tgkt }kjk vkSj vkaf'kd :i ls Vªsu }kjk r; 24 min get the buses. Find the speed of buses
if the speed of man is 30 Km/Hr.
djrk gS ;fn og gokbZ ekxZ ls iwjh ;k=kk djrk gS rks og
çR;sd 20 feuV ds ckn clksa dks jokuk fd;k tkrk gS]
4
Vªsu esa yxs le; dk cpkrk vkSj og vius xarO; 2 ysfdu çR;sd 24 feuV ds ckn cl fMiks ls nwj tkus okyh
5
cl vkneh dks ikj dj ysrh gSA ;fn vknehdh xfr 30
?kaVs tYnh igqap tkrkA Vªsu }kjk r; dh xbZ nwjh Kkr djsaA
fdeh@?kaVk gS rks clksa dh xfr Kkr djsaA
(a) 95 km (b) 85 km (a) 120 km/hr (b) 150 km/hr
(c) 90 km (d) 100 km (c) 180 km/hr (d) 210 km/hr

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89. Two guns are fired at 13 minutes interval. But 90.

Two guns are fired from the same place at an
the passenger in the train hears the sound of interval of 6 minutes. A person approaching the
second gun after 12 minute 30 seconds of the place observes that 5 minutes 52 seconds have
first. If the speed of sound is 330 m/s then elapsed between the hearings of the sound of the
the speed of train was two guns. If the velocity of the sound is 330 m/
13 feuV ds varjky ij nks canwdsa nkxh tkrh gSaA ysfdu
sec, then at what speed the person was
Vªsu esa ;k=kh igyh canwd ds nkxs tkus ds 12 feuV 30
approaching that place?
lsdaM ds ckn nwljh canwd dh vkokt lqurk gSA èofu;fn nks rksiksa dks ,d gh LFkku ls 6 feuV ds varjky ij nkxk
dh xfr 330 ehVj@lsdaM gS rks Vªsu dh xfr Kkr djsaA tkrk gSA ml LFkku dh vksj py jgk ,d O;fÙkQ ns•rk gS
13 13
fd nks canwdksa dh vkokt lquus ds chp 5 feuV 52 lsdaM
(a) 47
25
km/hr (b) 45
25
km/hr dk varjky gSA ;fn èofu dh pky 330 eh@ls gS] rks og
13 25 O;fÙkQ fdl xfr ls ml LFkku dh vksj vk jgk Fkk\
(c) 42 km/hr (d) 44 km/hr (a) 25 km/hr (b) 27 km/hr
25 13 (c) 36 km/hr (d) 30 km/hr

Answer Key

r
si
1.(a) 2.(a) 3.(a) 4.(c) 5.(a) 6.(d) 7.(a) 8.(d) 9.(b) 10.(d)

11.(a) 12.(c)
an by
13.(a) 14.(c) 15.(a) 16.(a) 17.(b) 18.(b) 19.(a) 20.(a)

n
21.(a) 22.(b) 23.(b) 24.(a) 25.(a) 26.(b) 27.(b) 28.(b) 29.(d) 30.(b)
ja
R s
31.(a) 32.(b) 33.(a) 34.(b) 35.(b) 36.(b) 37.(d) 38(c) 39.(d) 40.(a)
a th

41.(a) 42.(a) 43.(b) 44.(c) 45.(b) 46.(a) 47.(a) 48.(b) 49.(b) 50.(d)
ty a

51.(c) 52.(c) 53.(b) 54.(d) 55.(d) 56.(d) 57.(c) 58.(d) 59.(b) 60.(a)
di M

61.(c) 62.(c) 63.(a) 64.(c) 65.(a) 66.(b) 67.(b) 68.(b) 69.(b) 70.(a)

71.(d) 72.(c) 73.(c) 74.(d) 75.(c) 76.(a) 77.(b) 78.(b) 79.(c) 80.(d)

81.(b) 82.(c) 83.(b) 84.(a) 85.(d) 86.(c) 87.(a) 88.(c) 89.(a) 90.(b)
A

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Time, Speed

Time, Speed & Distance/le;] pky vkSj nwjh

( Practice Sheet With Solution)
1. A person crosses a 600 m long street in 5 6. An employee may claim Rs 7.00 for each km
minutes, What is his speed in km per hour? when he travels by taxi and Rs 6.00 for each
,d O;fÙkQ 600 ehVj yach lM+d dks 5 feuV esa ikj djrk km if he drives his own car. If in one week he
claimed Rs 595 for traveling 90 km. How many
gS] fdeh çfr ?kaVs esa mldh xfr D;k gS\ km did he travel by taxi ?
(a) 3.6 (b) 7.2
dksbZ deZpkjh tc VSDlh ls ;k=kk djrk gS rks çR;sd fdeh d
(c) 8.4 (d) 10
2. The speed of a car increases by 2 kms after
fy, 7-00 #i;s vkSj ;fn og viuh dkj pykrk gS rks çR;sd
every one hour. If the distance travelling in fdeh ds fy, 6-00 #i;s dk nkok dj ldrk gSA ;fn ,d
lIrkg esa mlus 90 fdeh dh ;k=kk ds fy, 595 #i;s dkkok
n

r
the first one hour was 35 kms. what was the
total distance travelled in 12 hours? fd;kA mlus VSDlh ls fdrus fdyksehVj dh ;k=kk dh\

si
,d dkj dh xfr çR;sd ,d ?kaVs ds ckn 2 fdeh c<+ (a) 55 km (b) 35 km
tkrh gSA ;fn igys ,d ?kaVs esa r; dh xbZ nwjh 35 fdeh-
an by (c) 25 km (d) 65 km
7. With an average speed of 40 km/hr, a train
12 ?kaVs esa r; dh xbZ dqy nwjh fdruh Fkh\ reaches its destination in time. If it goes with

n
(a) 456 kms (b) 482 kms an average speed of 35 km/hr, it is late by 15
(c) 552 kms (d) 556 kms minutes. Find the length of the total journey?
3. A man reaches his office 20 min late, if he
ja 40 fdeh@?kaVk dh vkSlr xfr ls ,d jsyxkM+h vius xarO;
R s
walks from his home at 3 km per hour and
reaches 30 min early if he walks 4 km per
LFkku ij le; ls igq¡prh gSA ;fn ;g 35 fdeh@?kaVk dh
vkSlr xfr ls tkrh gS] rks ;g 15 feuV nsjh ls igq¡prh gSA
a th

hour. How far is his office from his house ?

,d vkneh vius ?kj ls 3 fdeh çfr ?kaVs dh xfr ls pyus dqy ;k=kk dh yackbZ Kkr dhft;s\
ij 20 feuV nsj ls dk;kZy; igqaprk gS vkSj ;fn og 4 (a) 70 km (b) 60 km
(c) 45 km (d) 30 km
ty a

fdeh çfr ?kaVs dh xfr ls pyrk gS rks 30 feuV igys

8. A train overtakes two girls who are walking in
igqaprk gSA mldk dk;kZy; mlds ?kj ls fdruh nwj gS\ the opposite direction in which the train is
di M

(a) 20 km (b) 16 km going at the rate of 3 km/h and 6km/h and

(c) 14 km (d) 10 km passes them completely in 36 seconds and 30
4. A man walking at the rate of 5 km/hr crosses seconds respectively. The length of the train is:
a bridge in 15 minutes. The length of the ,d Vªsu 3 fdeh@?kaVk vkSj 6 fdeh@?kaVk dh xfr ls foijh
bridge (in metres) is
fn'kk esa py jgh nks yM+fd;ksa dks vksojVsd djrh gS vk
,d O;fÙkQ 5 fdeh@?kaVk dh xfr ls pyrs gq, ,d iqy dks
mUgsa Øe'k% 36 lsdaM vkSj 30 lsdaM esa iwjh rjg ls
15 feuV esa ikj djrk gSA iqy dh yackbZ (ehVj esa) gS dj ysrh gSA Vªsu dh yackbZ gS%
(a) 600 (b) 750
(a) 120 m (b) 150 m
(c) 1000 (d) 1250
(c) 125 m (d) None of these
5. A man traveled from the village to the post-
office at the rate of 25 kmph and walked back 9. A person goes to his office at 1/3rd of the
speed at which he returns from his office. If
A

at the rate of 4 kmph. If the whole journey

the average speed during the whole trip is 12
took 5 hours 48 minutes, find the distance of
km/h . what is the speed of the person while
the post-office from the village ?
he was going to his office?
,d vkneh xk¡o ls Mkd?kj rd 25 fdeh çfr ?kaVs dh xfr
,d O;fÙkQ ftl xfr ls vius dk;kZy; ls ykSVrk gS] mldh
ls ;k=kk djrk gS vkSj 4 fdeh çfr ?kaVs dh xfr ls okil
1@3 xfr ls vius dk;kZy; tkrk gSA ;fn iwjh ;k=kk ds
vkrk gSA ;fn iwjh ;k=kk esa 5 ?kaVs 48 feuV yxrs gSa] rks
nkSjku vkSlr xfr 12 fdeh@?kaVk gSA tc og vius dk;kZy;
xk¡o ls Mkd?kj dh nwjh Kkr dhft;s\
tk jgk Fkk rc ml O;fÙkQ dh xfr fdruh Fkh\
(a) 40 km (b) 30 km
(a) 10 (b) 6
(c) 20 km (d) 10 km
(c) 8 (d) Can't be determined

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10. A thief goes away with a maruti car at a speed 14. If Mohit covers three equal distances at the
of 40 kmph. The theft has been discovered speed of 30 km/h, 25 km/h and 20 km/h,
after half an hour and the owner sets off in a respectively, then find his average speed
bike at 50 kmph when will the owner overtake during the whole journey.
the thief from the start ?
;fn eksfgr rhu leku nwfj;ka Øe'k% 30 fdeh@?kaVk] 25
,d pksj 40 fdeh çfr ?kaVs dh xfr ls ,d ek#fr dkj
fdeh@?kaVk vkSj 20 fdeh@?kaVk dh pky ls r; djrk gS
ysdj pyk tkrk gSA vk/s ?kaVs ds ckn pksjh dk irk pyrk
rks iwjh ;k=kk ds nkSjku mldh vkSlr pky Kkr djsaA
gS vkSj ekfyd 50 fdeh çfr ?kaVs dh jÝrkj ls ckbd ls
(a) 34.50 km/h (b) 24.32 km/h
fiNk djrk gS] ekfyd 'kq: ls gh pksj dks dc idM+sxk\
(a) 2 hrs 10 min (b) 2 hrs (c) 25.30 km/h (d) 43.32 km/h
(c) 2 hrs 5 min (d) 2 hrs 30 min 15. Shyam drives his car 30 km at a speed of 45
11. A policeman starts chasing a theif when he was km/h and, for the next 1h 20m, he drives it
800 m ahead. The policeman and the thief run at a speed of 51 km/h. Find his average speed
at rate of 12 km/h and 9 km/h, respectively. (in km/h) for the entire journey.
What will be the distance between them after ';ke viuh dkj dks 30 fdeh] 45 fdeh@?kaVk dh pky ls

r
10 minutes? pykrk gS vxys 1 ?kaVs 20 feuV ds fy, og bls 51
,d iqfyldehZ pksj dk ihNk djuk 'kq: djrk gS tc og fdeh@?kaVk dh pky ls pykrk gSA iwjh ;k=kk ds fy, mld

si
800 ehVj vkxs FkkA iqfyldehZ vkSj pksj Øe'k% 12vkSlr pky (fdeh@?kaVk esa) Kkr dhft,A
fdeh@?kaVk vksj 9 fdeh@?kaVk dh xfr ls nkSM+rs gSaA 10
an by (a) 49 (b) 48
feuV ckn muds chp dh nwjh D;k gksxh\

n
(c) 48.5 (d) 47
(a) 200 m (b) 400 m
(c) 100 m (d) 300 m 16. A car travels at 58 kmph for 5 hours. At what
12. ja
A policeman follows a thief 1800 metres who
speed it should travel for the next 2 hours so
R s
that average speed becomes 50 kmph?
is ahead of him. If the policeman and the thief
,d dkj 5 ?kaVs ds fy, 58 fdeh izfr ?kaVs dh ;k=kk djrh
a th

run at a speed of 12 km/h and 9 km/h,

respectively, how much distance thief will gSA vxys 2 ?kaVs esa mls fdl xfr ls pyuk pkfg, fd
cover from spotting point (1800 meters ahead vkSlr xfr 50 fdeh izfr ?kaVk gks tk,\
to policeman) before catch by policeman?
ty a

(a) 25 kmph (b) 29 kmph

,d iqfyldehZ ,d pksj dk tks mlls 1800 ehVj vkxs gS]
(c) 35 kmph
ihNk djrk gSA ;fn iqfyldehZ vkSj pksj Øe'k% 12 fdeh@?kaVk (d) 30 kmph
di M

vkSj 9 fdeh@?kaVk dh xfr ls nkSM+rs gSa] rks iqfyldehZ }kjkruns at 32.6 kmph for 6 hours and at
17. Nidhi
11.6 kmph for 8 hours. Find out her average
idM+s tkus ls igys pksj LikWfVax@ikWbaV (iqfyldehZ lsspeed.
1800
ehVj vkxs) ls vkxs fdruh nwjh r; djsxk\
(a) 5600 m (b) 6000 m
fuf/ 32-6 fdeh izfr ?kaVs dh jÝrkj ls 6 ?kaVs vkSj 11-6
(c) 4200 m (d) 5400 m fdeh izfr ?kaVs dh jÝrkj ls 8 ?kaVs pyrh gS mldh vkSlr
13. A thief is noticed by a policeman from a xfr Kkr dhft,A
distance of 97 m. The thief starts running and (a) 22.1 kmph (b) 20.6 kmph
the policeman chases him. The thief and the
(c) 18.3 kmph (d) 16.6 kmph
policeman run at a speed of 21 m/sec and
23 m/sec respectively. What is the time taken 18. While travelling from Nashik to Daman, Harsh
drove for 1 hour at a speed of 50 km/h and
A

by the policeman to catch the thief?

for the next three hours at 60 km/h. What was
,d iqfyldehZ dks 97 m dh nwjh ls ,d pksj fn[kkbZ his average speed for the whole trip?
nsrk gSA pksj Hkkxus yxrk gS vkSj iqfyldehZ mldk ihNk
ukfld ls neu dh ;k=kk djrs le;] g"kZ us 1 ?kaVs ds fy,
djrk gSA pksj vkSj iqfyldehZ Øe'k%
21 m/sec vkSj
50 fdeh@?kaVk dh pky ls vkSj vxys rhu ?kaVksa ds f
23 m/sec dh pky ls nkSM+rs gSaA pksj idM+us eas iqfyldehZ
60 fdeh@?kaVk dh pky ls xkM+h pykbZA iwjh ;k=kk es
dks fdruk le; yxrk gS\
vkSlr pky D;k jgh\
SSC CGL 02/12/2022 (Shift- 01)
(a) 40 sec (b) 45 sec (a) 56 km/h (b) 57.5 km/h
(c) 62.5 sec (d) 48.5 sec (c) 55 km/h (d) 58.5 km/h

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19. A car travels for 40 minutes at a speed of 40 22. A train goes from P to Q with a speed µ km/
km/h, for another 50 minutes at a speed of h, then from Q to R (QR = 2PQ) with a speed
45 km/h and for next 90 minutes at a speed 3µ km/h, and returns from R to P with a speed
of 60 km/h. what is the average speed (in km/ µ/2 km/h. What is the average speed (in km/
h) of the car for the entire journey? h) of the train for the entire journey starting
,d dkj 40 fdeh@?kaVk dh xfr ls 40 feuV rd pyrh gS] from P and back to P?
vU; 50 feuV ds fy, 45 fdeh@?kaVk dh xfr ls vkSj vxys ,d VªsuP ls Q rd µ fdeh@?kaVk dh pky ls tkrh gS fiQj
90 feuV ds fy, 60 fdeh@?kaVk dh xfr ls ;k=kk djrh gSA ls R rd (QR = 2PQ) 3µ fdeh@?kaVk dh pky ls tkrh
Q
iwjh ;k=kk esa dkj dh vkSlr xfr (fdeh@?kaVk esa) D;k gS\gS vkSjR ls P rd µ/2 fdeh@?kaVk dh pky ls okil
vkrh gSAP ls 'kq: gksdj P rd okil vkus ds nkSjku bl
1 5
(a) 49 (b) 50 iwjh ;k=kk esa Vªsu dh vkSlr pky (fdeh@?kaVk esa) Kkr
4 9
SSC CHSL 11 July 2019 (Afternoon)
7 5
(c) 51 (d) 50 18 4
18 18 (a) (b)
20. A man travels from point A to B at 40 km/h, 23 3

r
further from B to C at 50 km/h, and then
further from C to D at 60 km/h. the ratio 16 3
(c) (d)

si
between the distance AB, BC and CD is 1:2:3. 23 2
He returns from D to A at x km/h. if his 23. A person travels at a speed of 40 km/hr for

480
an by
average speed for the entire journey is 1
2
of the distance, at a speed of 30 km/hr for

n
km/h, then what is the value of x? 1 rd
13 of the distance and at a speed of 60 km/
3
,d O;fDr fcanqA ls B rd 40 fdeh@?kaVk dh xfr ls]
ja hr for the remaining distance. Find his average
R s
vkxsB ls C rd 50 fdeh@?kaVk dh xfr ls vkSj fiQj vkxs speed.
C ls D rd 60 fdeh@?kaVk dh xfr ls ;k=kk djrk gSA nwjh
a th

1
,d O;fÙkQ viuh nwjh ds fy, 40 fdeh@?kaVk dh xfr
AB, BC vkSjCD ds chp dk vuqikr 1 : 2 : 3 gSA og 2
1
x fdeh@?kaVk dh xfrDlsls A dh vkSj ykSVrk gSA ;fn ls] nwjh ds fy, 30 fdeh@?kaVk dh xfr ls vkSj 'ks"k
3
nwjh ds fy, 60 fdeh@?kaVk dh xfr ls ;k=kk djrk gSA
ty a

480
iwjh ;k=kk esa mldh vkSlr xfr fdeh@?kaVk gS] x rks mldh vkSlr xfr Kkr dhft,A
13
di M

dk eku D;k gS\ 17 17

(a) 35 km/hr (b) 37 km/hr
5 2 19 19
(a) 25 (b) 34
7 7 (c) 27 km/hr (d) 39 km/hr
6 4
(c) 32 (d) 28 24. Pranav went to the bank at the speed of 60
7 7 km/h while returning for his home he covered
21. Pranav walked at 5 km/h for certain part of the half of the distance at the speed of 10 km/
the journey and then he took an auto for the
h. but suddenly he realized that he was getting
remaining part of the journey travelling at 25
late so he increased the speed and reached the
km/h. If he took 10 hours for the entire
home by covering rest half of the distance at
journey, what part of journey did he travelled
the speed of 30 km/h. The average speed of
by auto if the average speed of the entire
the Pranav in the whole length of journey is:
A

journey be 17 km/h?
ç.ko ;k=kk ds ,d fuf'pr Hkkx rd 5 fdeh- çfr ?kaVk ç.ko cSad 60 fdeh@?kaVk dh LihM ij x;k Fkk fdUrq ?
dh xfr ls iSny pyrk gS vksj fiQj og 'ks"k ;k=kk ds fy, okilh ds le; mlus vk/h nwjh 10 fdeh@?kaVk dh xfr ij
25 fdeh- çfr ?kaVk dh xfr ls ,d vkWVks fjD'kk ysrk gSA r; dhA vpkud mls yxk fd og ysV gks jgk Fkk rks mlus
;fn og iwjh ;k=kk ds fy, 10 ?kaVs ysrk gS] rks ;k=kk dkviuh LihM c<+kbZ vkSj ckdh cph gqbZ nwjh og 30 fdeh@
dh xfr ls r; djrs gq, ?kj igqap x;kA iwjh ;k=kk esa ç.ko
fdruk Hkkx mlus vkWVks fjD'kk esa r; fd;k] ;fn iw.kZ ;k=kk
dk vkSlr xfr 17 fdeh@?kaVk gS\ dh vkSlr xfr D;k Fkh\
(a) 750 km (b) 100 km (a) 24 km/hr (b) 16 km/hr
(c) 150 km (d) 200 km (c) 14 km/hr (d) 10 km/hr

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25. A person travels a distance of 300km and then 7500 7500

returns to the starting point. The time taken (a) (b)
100 + x 100 – x
by him for the outward journey is 5 hours more
than the time taken for the return journey. If 7500 7500
he returns at a speed of 10km/h more than the (c) (d)
300 – x 200 – x
speed of going, what is the average speed (in
29. Excluding stoppages, the average speed of a bus
km/h) for the entire journey ?
is 60 km/hr and including stoppages, the
,d O;fDr 300 fdeh dh nwjh r; djrk gS vkSj fiQj average speed of the bus is 40 km/hr. For how
'kq:vkrh fcanq ij ykSVrk gSA tkus dh ;k=kk ds fy, mldsmany minutes does the bus stop per hour ?
}kjk fy;k x;k le; okilh dh ;k=kk ds fy,] fy, x,
Bgjko dks NksM+dj] cl dh vkSlr xfr 60 fdeh@?kaVk g
le; ls 5 ?kaVs vf/d gSA vxj og tkus dh pky ls 10
vkSj Bgjko lfgr] cl dh vkSlr xfr 40 fdeh@?kaVk gSA
fdeh@?kaVk vf/d dh pky ls ykSVrk gS] rks iwjh ;k=kk esa
çfr ?kaVs cl fdrus feuV #drh gS\
vkSlr pky (fdeh@?kaVk esa) D;k gS\
CPO 23/11/2020 (Evening) (a) 2 hrs (b) 20 min
(a) 24 (b) 15 (c) 40 min (d) 30 min
(c) 20 (d) 30

r
30. A train without stoppage travels with an
26. A cyclist travels through the sides of an average speed of 50 km/hr, and with stoppage,

si
equilateral triangle at a speed of 14 km/h, 28 it travels with an average speed of 40 km/hr.
km/h and 12 km/h. What is the average speed For how many minutes does the train stop on
an by
(in km/h) of the cyclist?
,d lkbfdy lokj ,d leckgq f=kHkqt dh Hkqtkvksa ls 14
an average per hour?
,d jsyxkM+h fcuk #ds (LVkWist) 50 fdeh@?kaVk dh vk

n
fdeh@?kaVk] 28 fdeh@?kaVk vkSj 12 fdeh@?kaVk dh xfr ls
xfr ls vkSj :dus ds lkFk 40 fdeh@?kaVk dh vkSlr xfr ls
;k=kk djrk gSA lkbfdy lokj dh vkSlr xfr (fdeh@?kaVk
ja pyrh gSA jsyxkM+h] vkSlru izfr ?kaVk fdrus feuV :drh gS
esa) D;k gS\
R s
(a) 13.50 (b) 16.25 (a) 12 (b) 13
a th

(c) 14.25 (d) 15.75 (c) 14 (d) 15

27. The distance between the two towns is 250
31. A train covers a certain distance at an average
km. Two motorists travel towards each other
speed of 120 km/h without any stoppages.
simultaneously. The speed of one of them is
While returning the same journey the train
ty a

5 km/h faster than the other, and the distance

between them after 1.5 hours of start is 31 covers the distance at an average speed of 80
km. Find the average of their speeds. km/h with stoppages. What is the average
di M

stoppage time per hour taken by the train?

nksuksa dLcksa ds chp dh nwjh 250 fdeh gSA nks eksVj pkyd
,d lkFk ,d nwljs dh vksj ;k=kk djrs gSaA muesa ls ,d dh ,d Vªsu fcuk #ds 120 fdeh@?kaVk dh vkSlr xfr ls ,d
fuf'pr nwjh r; djrh gSA mlh ;k=kk ls ykSVrs le; Vªsu
xfr nwljs dh rqyuk esa 5 fdeh@?kaVk rst gS] vkSj 'kq: gksus
ds 1-5 ?kaVs ds ckn muds chp dh nwjh 31 fdeh gSA mudh Bgjko ds lkFk 80 fdeh@?kaVk dh vkSlr xfr ls nwjh r;
xfr dk vkSlr Kkr dhft,A djrh gSA Vªsu }kjk fy;k x;k çfr ?kaVk vkSlr LVkWist le
(a) 75 (b) 71 D;k gS\
(c) 70 (d) 73 (a) 30 minutes (b) 32 minutes
28. Kamal started his road trip in his car and
moved at a constant speed of 75 kmph. After (c) 20 minutes (d) 24 minutes
completing x% of his total journey, his car 32. A bus covers a distance without stoppages at
started malfunctioning, and therefore, he had 90 km/h, and while returning covers the same
A

to complete his journey at half of his normal distance with stoppages at 75 km/h. Find the
speed. What is the average speed (in kmph) of average stoppage time per hour.
Kamal's whole journey, in terms of x?
,d cl fcuk #ds 90 fdeh@?kaVk dh xfr ls ,d nwjh r;
dey us viuh dkj esa viuh lM+d ;k=kk 'kq: dh vkSj 75
djrh gS] vkSj okil ykSVrs le; leku nwjh dks 75 fdeh@?kaVk
fdeh çfr ?kaVs dh fLFkj xfr ls pykA viuh dqy ;k=kk dk
dh xfr ls :drs gq, ikj djrh gSA çfr ?kaVk vkSlr Bgjko
x» iwjk djus ds ckn] mldh dkj •jkc gksus yxh] vkSj
le; Kkr dhft,A
blfy,] mls viuh ;k=kk dks viuh lkekU; xfr ds vk/h
xfr ls iwjk djuk iM+kA
x ds lanHkZ esa dey dh iwjh ;k=kk (a) 15 min (b) 8 min
dh vkSlr xfr (fdeh çfr ?kaVs esa) D;k gS\ (c) 10 min (d) 12 min

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33. A Person X started at 3 hours earlier at vkfnR; jatu 60 fdeh çfr ?kaVs dh jÝrkj ls pyrh dkj
40km/h from a place P, then another person ls 240 fdeh dh nwjh r; djds nwljs 'kgj x,A fiQj og
Y followed him at 60km/h. Started his journey 100 fdeh çfr ?kaVs dh xfr ls pyus okyh Vªsu ls 400
at 3 O'clock, afternoon. What is the difference fdeh dh nwjh r; djrs gS vkSj fiQj 200 fdeh dh nwjh
in time when X was 30 km ahead of Y and
dks og 50 fdeh çfr ?kaVs dh xfr ls pyus okyh cl ls
when Y was 30 km ahead of X?
r; djrk gSA iwjh ;k=kk ds nkSjku vkSlr xfr Fkh\
,d O;fÙkQX] 3 ?kaVs igys ,d LFkku
P ls 40 fdeh@?kaVk dh
(a) 36 kmph (b) 35 kmph
xfr ls pyuk 'kq: djrk gS] fiQj ,d vU; O;fÙkQY 60 (c) 72 kmph (d) 70 kmph
fdeh@?kaVk dh xfr ls mldk ihNk djrk gSA nksigj 337. cts Mr. Karthik drives to work at an average speed
viuh ;k=kk 'kq: dhA le; esa fdruk varj gS tcX] Y ls of 48 km/hr. Time taken to cover the first
60% of the distance is 20 minutes more than
30 fdeh vkxs Fkk vkSj tc
Y] X ls 30 fdeh vkxs Fkk\
the time taken to cover the remaining
(a) 2 h (b) 3 h distance. Then how far is his office ?
(c) 3.5 h (d) 4.25 h Jh dkfrZd 48 fdeh@?kaVk dh vkSlr xfr ls dke ij tkrs
34. Two men A and B start from place X walking gSaA igyh 60» nwjh dks r; djus esa yxk le; 'ks"k nwjh dk

r
1 3 r; djus esa yxus okys le; ls 20 feuV vf/d gSA rks
at 4 kmph and 5 kmph respectively. How
mldk dk;kZy; fdruh nwj gS \

si
2 4

1 (a) 40 km (b) 50 km
an by
many km apart they are at the after 3

if they are walking in the same direction?

2
hours
38.
(c) 70 km (d) 80 km
Buses start from a bus terminal with a speed

n
of 20 kmph at intervals of 10 minutes. What
1 is the speed of a man coming from the
nks iq#"k
A vkSj B LFkku
ja X ls Øe'k%4 fdeh çfr ?kaVs
2 opposite direction towards the bus terminal if
R s
he meets the buses at intervals of 8 minutes?
3
vkSj5 fdeh çfr ?kaVs dh xfr ls pyuk 'kq: djrs gSaA cl VfeZuy ls clsa 10 feuV ds varjky ij 20 fdeh@?kaVk
a th

4
dh xfr ls pyrh gSaA foijhr fn'kk ls cl VfeZuy dh vksj
1
;fn os ,d gh fn'kk esa py jgs gksa rks
3 ?kaVs ckn os vkus okys ,d O;fÙkQ dh xfr D;k gS ;fn og 8 feuV ds
2
varjky ij clksa ls feyrk gS\
ty a

fdrus fdeh nwj gksaxs\ (a) 5 kmph (b) 6 kmph

di M

9 7 (c) 7.5 kmph (d) 8 kmph

(a) 2 km (b) 3 km
7 5 39. Robert is traveling on his cycle and has
calculated to reach point A at 2 p.m. if he
3 3 travels at 10 km/hr; he will reach there at 12
(c) 1 km (d) 4 km
4 8 noon if he travels at 15 km/hr. At what speed
35. A man in a train notices that he can count 41 must he travel to reach A at 1 p.m. ?
telephone posts in one minute. If they are jkWcVZ viuh lkbfdy ij ;k=kk dj jgk gS vkSj og nksigj 2
known to be 50 metres apart, then at what cts fcanqA ij igq¡psxk ;fn og 10 fdeh@?kaVk dh xfr ls
speed is the train travelling ;k=kk djrk gS ;fn og 15 fdeh@?kaVk dh xfr ls ;k=kk djrk
Vªsu esa ,d vkneh uksfVl djrk gS fd og ,d feuV esa gS rks og ogka nksigj 12 cts igqapsxkA nksigj A rd
1 cts
41 VsyhiQksu iksLV fxu ldrk gSA ;fn og 50 ehVj dh igq¡pus ds fy, mls fdl xfr ls ;k=kk djuh pkfg,\ \
A

nwjh ij gS] rks Vªsu fdl xfr ls py jgh gS (a) 20 kmph

(b) 18 kmph
(a) 60 km/hr (b) 100 km/hr
(c) 12 kmph
(c) 110 km/hr (d) 120 km/hr
(d) 16 kmph
36. Aditya Ranjan went to another town covering
240 km by car moving at 60 kmph. Then he 9
40. A bus is running at of its own speed
covered 400 km by train moving at 100 kmph 10
and then rest 200 km he covered by a bus reached a place in 22 hours. How much time
moving at 50 kmph. The average speed during could be saved if the bus would run at its own
the whole journey was ? speed ?

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9 45. Amit travelled a distance of 50 km in 9 hours.

,d cl viuh xfr dh xfr ls py jgh gS vkSj 22 He travelled partly on foot at 5 km/h and
10
?kaVs esa ,d LFkku ij igq¡p tkrh gSA ;fn cl viuh xfr ls partly by bicycle at 10 km/h. The distance
pyrh rks fdruk le; cpk ysrh gS\ travelled on the bicycle is:
(a) 1.5 hrs (b) 1.7 hrs vfer us 9 ?kaVs esa 50 fdeh dh nwjh r; dhA mlus vkaf'kd
(c) 2.2 hrs (d) 3.5 hrs :i ls 5 fdeh@?kaVk dh iSny ;k=kk dh vkSj vkaf'kd :i
41. The respective ratio between the speed of a ls lkbfdy ls 10 fdeh@?kaVk dh xfr ls ;k=kk dhA lkbfdy
bike, a van and lorry is 3 : 5 : 2. The speed of ij r; dh xbZ nwjh gS%
the van is 250 percent of the speed of the lorry
which covers 360 km in 12 hours. What is the (a) 11 km (b) 10 km
average speed of the bike and the van (c) 13 km (d) 12 km
together? 46. A man travelled at 40 kmph. Had he increased
,d ckbd] ,d oSu vkSj ykWjh dh xfr ds chp lacaf/r his speed by 16 kmph, he would have covered
vuqikr 3 % 5 % 2 gSA oSu dh xfr ykWjh dh xfr dk 250 870 km more in the same time. Find the
çfr'kr gS tks 12 ?kaVs esa 360 fdeh dh nwjh r; djrh gSAactual distance travelled?

r
ckbd vkSj oSu dh feykdj vkSlr xfr fdruh gS\ ,d vkneh 40 fdeh çfr ?kaVs dh xfr ls ;k=kk djrk gSA
(a) 60 kmph (b) 62 kmph ;fn og viuh xfr 16 fdeh çfr ?kaVs c<+k nsrk] rks og

si
(c) 64 kmph (d) 63 kmph mrus gh le; esa 870 fdeh vf/d r; dj ysrkA r; dh
an by
42. A boy walking at the speed of 3 km/hr covers
a certain distance in 3 hours 40 minutes. If
xbZ okLrfod nwjh Kkr dhft;s\
(a) 3045 km (b) 3040 km

n
he covers the same distance by cycle in 11
hours, then what is the speed (in km/hr) of (c) 2000 km (d) 2040 km
cycle?
ja 47. P and Q are at a distance of 240 km from each
R s
,d yM+dk 3 fdeh@?kaVk dh xfr ls pyrs gq, ,d fuf'pr other at 9:00 a.m. After 1 hour, P starts
nwjh dks 3 ?kaVs 40 feuV esa r; djrk gSA ;fn og leku moving towards Q at a speed of 25 km/hr. At
a th

nwjh lkbfdy ls 11 ?kaVs esa r; djrk gS] rks lkbfdy dh 11 a.m. Q starts moving towards P at the speed
xfr (fdeh@?kaVk esa) D;k gS\ of 18 km/hr. At what time (in p.m.) will they
meet?
(a) 1 (b) 2
ty a

(c) 4 (d) 3 P vkSjQ çkr% 9%00 cts ,d nwljs ls 240 fdeh dh nwjh
43. A boy is driving car at the speed of 42 km/hr. ij gSaA 1 ?kaVs dsPckn]
25 fdeh@?kaVk dh xfrQlsdh
di M

He stops for 8 minutes at end of every 11 km. vksj c<+uk 'kq: djrk gSA iwokZÉ Q 1118
ctsfdeh@?kaVk
What will be the time (in minutes) taken by
dh xfr ls P dh vksj c<+uk 'kq: djrk gSA os fdl le;
him to cover a distance of 84 km?
(nksigj esa) feysaxs\
,d yM+dk 42 fdeh@?kaVk dh xfr ls dkj pyk jgk gSA
(a) 6 (b) 5
og çR;sd 11 fdeh ds var esa 8 feuV #drk gSA 84 fdeh
dh nwjh r; djus esa mls fdruk le; (feuVksa esa) yxsxk\ (c) 3 (d) 4
(a) 138 (b) 142 48. A train travels at a speed of 66 km/h and halts
(c) 156 (d) 176 at five junctions for a certain time. If covers
a distance of 1485 km in one day. For how
44. Abhishek had to travel 420 km in 8 hours. If
he travelled at an average speed of 60 km/h long (in minutes) does the train stop at each
and took two breaks in between, the shorter junction, if it halts for the same period of time
A

break being one-third the duration of the at all the junctions?

longer, how many minutes was the longer ,d Vªsu 66 fdeh@?kaVk dh pky ls ;k=kk djrh gS vkSj ,d
break for?
fuf'pr le; ds fy, ik¡p taD'kuksa ij :drh gSA ;g ,d
vfHk"ksd dks 8 ?kaVs esa 420 fdeh dk liQj r; djuk FkkAfnu esa 1485 fdeh dh nwjh r; djrh gSA vxj Vªsu lHkh
;fn og 60 fdeh@?kaVk dh vkSlr xfr ls ;k=kk djrk gS
taD'kuksa ij leku vof/ rd :drh gS rks ;g izR;sd taD'ku
vkSj chp esa nks czsd ysrk gS] rks NksVk czsd yacs le; dh
ij fdrus le; rd (feuVksa esa) :drh gS\
vof/ dk ,d&frgkbZ gS] rks yack czsd fdrus feuV dk Fkk\
(a) 15 (b) 18
(a) 45 (b) 30
(c) 40 (d) 35 (c) 12 (d) 20

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49. X and Y start their journey at the same time nks Vªsusa ftudh yackbZ 450 ehVj vkSj 300 ehVj gS]
from place A to B, respectively.After meeting
each other on the way, X and Y complete their
nwljs dh vksj Øe'k% 162 fdeh@?kaVk vkSj 108 fdeh@?
dh xfr ls vkxs c<+ jgh gSaA ;fn Vªsuksa ds chp dh nw
4
journey in 5 hours and p hours respectively. 300 ehVj gS] rks ;s Vªsu fdrus le; esa ,d nwljs dks ikj
9
djsxh\
4
If the speed of X is 28 % is more than that (a) 28 seconds (b) 35 seconds
7
(c) 14 seconds (d) 21 seconds
of Y, then what is the value of p?
53. Two trains are running on a parallel track with
X vkSjY Øe'k% LFkkuA ls B rd ,d gh le; ij viuh a speed of 63 km/h and 72 km/h, when both
;k=kk 'kq: djrs gSaA jkLrs esa ,d nwljs ls feyusXds ckn] the trains run in opposite directions of each
4 other then crosses in 12 seconds, but when a
vkSjY viuh ;k=kk Øe'k%
5 ?kaVs vkSj
p ?kaVs esa iwjh person is in a fast moving train he saw that
9
the slow-moving train crosses that person in
4 48 seconds when they move in the same
djrs gSaA ;fn
X dh xfr] Y dh xfr ls 28 % vf/d
7 direction, then find out the difference between

r
gS] rks
p dk eku D;k gS\ the length of the train?

si
nks jsyxkM+h 63 fdeh@?kaVk vkSj 72 fdeh@?kaVk dh
1
(a) 4 an by (b) 9 lkekukUrj iVjh ij py jgh gS tc nksuks jsyxkM+h ,d
2
nwljs ds foijhr fn'kk esa pyrh gS rks 12 lsdaM esa ikj dj
(c) 8 (d) 6

n
tkrh gS ysfdu tc ,d O;fÙkQ rst xfr ls py jgh jsyxkM+h
50. A person reaches his destination 32 minutes
late if his speed is 6 km/h, and reaches 18 ij cSBk gS mlus ns[kk dh /heh xfr ls pyus okyh jsyxkM+
ja ml O;fÙkQ dks 48 lsdaM esa ikj dj tkrh gS tc os leku
R s
minutes before time if his speed is 7 km/h.
Find twice the distance (in km) of his fn'kk esa pyrh gS rks nksuksa jsyxkM+h dh yEckbZ d
a th

destination from his starting point.

Kkr djsa\
;fn ,d O;fDr dh pky 6 fdeh@?kaVk gS rks og vius
(a) 210 m (b) 180 m
xarO; ij 32 feuV nsjh ls igaqprk gS vkSj ;fn mldh (c) 240 m (d) 250 m
pky 7 fdeh@?kaVk gS rks og le; ls 18 feuV igys igqap
ty a

54. A takes 2 hours more than B to cover a

tkrk gSA mlds vkjafHkd fcanw ls mlds xarO; dh nksxquhdistance of 40 km. If A doubles his speed, he
di M

nwjh (fdeh esa) Kkr dhft,A

1
(a) 55 (b) 70 takes 1 hours more than B to cover 80 km.
2
(c) 60 (d) 65 To cover a distance of 90 km, how much time
51. A man travels from a city X to city Y. If he will B take travelling at his same speed?
travels 25% faster than his speed, he would
reach Y 15 minutes early. By how many
40 fdeh dh nwjh r; djus esa]
A dksB ls 2 ?kaVs vf/d
minutes would he be late if he travels 40% yxrs gSaA ;fn
A viuh pky dks nksxquk djrk gS] rks mls
slower than his usual speed?
1
,d vkneh 'kgj X ls 'kgj Y dh ;k=kk djrk gSA ;fn og 80 fdeh dh nwjh r; djus esaB ls 1 ?kaVs vf/d yxrsa
2
viuh xfr ls 25» rst ;k=kk djrk gS] rks ogY ls 15 feuV gSaA 90 fdeh dh nwjh r; djus ds fy,]
B dks viuh mlh
igys igqap tkrk gSA ;fn og viuh lkekU; xfr ls 40» /heh
A

pky ls fdruk le; yxsxk\

xfr ls ;k=kk djrk gS rks mls fdrus feuV dh nsjh gksxh\
(a) 36 (b) 50 1 3
(a) 1 hours (b) 1 hours
8 8
(c) 40 (d) 45
52. Two trains whose lengths are 450 meters and 1 1
300 meters are moving towards each other at (c) 1 hours (d) 1 hours
6 3
the speed of 162 km/h and 108 km/h
respectively. If distance between trains is 300 55. A man walking at a speed of 3 km/h crosses a
meters, in how much time, these trains will square field diagonally in 5 minutes. What is
cross each other? the area of the field (in m2)?

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3 fdeh@?kaVs dh pky ls pyus okyk ,d O;fDr] fdlh B dh xfr C ls mruh gh vf/d gS ftruh mldh A ls
oxkZdkj eSnku dks fod.kZr% 5 feuV esa ikj djrk gSA eSnku
de gSAA vkSj C }kjk ,d fuf'pr nwjh r; djus esa
dk {ks=kiQy (eh2 esa) Kkr djsaA Øe'k% 20 feuV vkSj 30 feuV dk le; yxrk gSA ml
(a) 3125 (b) 31250 nwjh dks r; djus esa
B dks fdruk le; yxrk gS\
(c) 3.125 (d) 312.5 (a) 24 min (b) 25 min
56. A and B are travelling towards each other form
(c) 28 min (d) 26 min
the points P and Q respectively. After crossing
60. A man's car failed after he had covered 40%
1
each other. A and B take 6 hours and 8 of the distance from his home to his office.
8 He then boards a bus, which takes him to his
hours respectively, to reach their destinations office. The time he spent traveling by bus is
Q and P respectively. If the speed of B is 16.8
twice the time he spent traveling by car. What
km/hr, then the speed (in km/hr) of A is:
is the ratio of speeds of bus and car?
A vkSjB Øe'k%P vkSjQ fcnaqvksa ls ,d nwljs dh vksj
,d O;fDr dh dkj vius ?kj ls vius dk;kZy; dh 40»
;k=kk dj jgs gSaA ,d nwljs dks ikj djus ds Ackn]
vkSj
nwjh r; djus ds ckn foiQy gks xbZA blds ckn og ,d
B Øe'k% vius xarO;
Q vkSjP rd igqapus ds fy, Øe'k%

r
cl esa p<+rk gS] tkss mls vius dk;kZy; ys tkrh gSA ftruk
1
le; mlus cl ls ;k=kk djus esa fcrk;k] og dkj ls ;k=kk

si
6 ?kaVs] 8 ?kaVs dk le; ysrs gSaA
B dh;fn
xfr 16-8
8
djus esa [kpZ fd, x, le; esa nksxquk gSA cl vkSj dkj dh
fdeh@?kaVk gS] A dh
rksxfr (fdeh@?kaVk) gS%
an by xfr;ksa dk vuqikr fdruk gS\
(a) 20.8 (b) 19.8
(a) 4 : 3 (b) 3 : 2

n
(c) 19.2 (d) 20.4
57. A man travels a certain distance by scooter. (c) 1 : 2 (d) 3 : 4
ja
If he increases his speed by 3 km/hr, he takes 61. Buses start from a terminal every 30 minutes.
R s
40 min less, but if he decreases his speed by A man walking in the same direction, away
2 km/hr, he takes 40 min more. Find the from the terminal, observes that a bus crosses
a th

distance. him every 36 minutes. If he is walking at 9

,d vkneh dksbZ fuf'pr nwjh LdwVj ls tkrk gSA vxj og kmph, then what is the speed of the each bus?
viuh pky 3 fdeh@?kaVk c<+k ns rks 40 feuV de le; VfeZuy ls gj 30 feuV esa cls pyrh gSA VfeZuy ls nwj
ty a

ysrk gS] ijUrq vxj og viuh xfr 2 fdeh@?kaVk ?kVk ns rks,d gh fn'kk esa pyus okyk ,d O;fDr ns[krk gS fd gj
40 feuV T;knk le; yxrk gSA nwjh Kkr djksaa 36 feuV esa ,d cl mls ikj djrh gSA ;fn og 9 fdeh
di M

(a) 20 (b) 30 izfr ?kaVs dh xfr ls py jgk gS] rks izR;sd cl dh xfr
(c) 40 (d) 50 D;k gS\
58. Usually, A takes 3 hours more than B to cover
a certain distance. One day, A increases his (a) 54 km/hr (b) 36 km/hr
speed by 66.66% and takes 5 hours less than (c) 45 km/hr (d) 30 km/hr
B to cover the same distance. What is the time 62. Ram travelled from a place Z to P at an average
taken by B to cover twice the original speed of 130 km/h. He travelled the first 75%
distance?
of the distance in two-third of the time and
vkerkSj ij A ,d fuf'pr nwjh r; djus esa B ls 3 ?kaVs the rest at an average speed of x km/h. The
vf/d ysrk gSA ,d fnu A viuh xfr 66-66» c<+k nsrk x
gS vkSj leku nwjh r; djus esa
B ls 5 ?kaVs de ysrk gSA value of is
A

2
ewy nwjh dh nksxquh nwjh r; djus B dks
esa fdruk le;
yxsxk\ jke us ,d LFkkuZ ls P rd 130 fdeh@?kaVk dh vkSlr
(a) 24 (b) 17 pky ls ;k=kk dhA mlus igyh 75» nwjh nks&frgkbZ le; es
(c) 40 (d) 34 r; dh vkSj 'ks"k nwjh
x fdeh@?kaVk dh vkSlr pky ls r;
59. The speed of B is as much more than C as its x
is less than A. The time taken by A and C to dhA dk eku crkb,A
2
cover a certain distance are 20 minutes and
30 minutes respectively. What is the time (a) 51 (b) 48.75
taken by B to cover that distance? (c) 97.5 (d) 19.25

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63. Shyam went from Delhi to Shimla via 66. Vinay fires two bullets from the same place at
Chandigarh by car. The distance from Delhi to an interval of 12 minutes Raju sitting in a train
3 approaching the place hears the second report
Chandigarh is times the distance from
4 11 minutes 30 seconds after the fires. What is
Chandigarh to Shimla. The average speed from the approximate speed of train (if sound trav-
1 els at the speed of 330 metre per second)?
Delhi to Chandigarh is 1 times of the
2
average speed from Chandigarh to Shimla. If fou; 12 feuV ds varjky ij ,d gh LFkku ls nks xksfy;ka
the average speed for the entire journey was pykrk gSA vkx yxus ds 11 feuV 30 lsdaM ckn Vªsu esa cS
49 kmph. What was the average speed from
Chandigarh to Shimla?
jktw nwljh fjiksVZ lqurk gSA Vªsu dh vuqekfur xfr D;
(;fn èofu 330 ehVj çfr lsdaM dh xfr ls pyrh gS)\
';ke dkj }kjk fnYyh ls f'keyk] p.Mhx<+ gksdj x;kA
fnYyh ls p.Mhx<+ dh nwjh] p.Mhx<+ vkSj f'keyk dh nwjh
(a) 660/23 m/s (b) 220/7 m/s
3 (c) 330/23 m/s (d) 110/23 m/s
dk xq.kk gSA fnYyh ls p.Mhx<+ dh vkSlr pky] p.Mhx<+
67. A car driver, driving in a fog, passes a pedes-
4
1 trian who was walking at the rate of 2 km/h in
ls f'keyk dh vkSlr pky dh 1 xq.kk gSA ;fn laiw.kZ

r
2 the same direction. The pedestrian could see
;k=kk dh vkSlr pky 49 fdeh@?kaVk gS rks p.Mhx<+ ls car for 6 minutes and it was visible to him
the

si
f'keyk dh vkSlr pky D;k gS\ up to a distance of 0.6 km. What was the speed
(a) 39.2 km/h (b) 63 km/h of the car?

64.
(c) 42 km/h
an by (d) None of these
45 pillars are standing in a line such that
,d dkj pkyd] dksgjs esa xkM+h pykrs gq,] ,d iSny ;k=kh
dks ikj djrk gS tks mlh fn'kk esa 2 fdeh@?kaVk dh xfr ls

n
distance between any two consecutive pillars
is same. A car travelling with uniform speed py jgk FkkA iSny ;k=kh dks dkj 6 feuV rd fn•kbZ nh vkSj
ja
of 72 km/h takes 18 seconds to reach from ;g mls 0-6 fdeh dh nwjh rd fn•kbZ nhA dkj dh LihM D;k
R s
1st pole to 10th pole. What is the distance
Fkh\
between 10th and 31st pole (in metres)?
a th

45 •EHks ,d lh/h iafÙkQ esa bl çdkj •M+s gS fd dksbZ Hkh(a) 30 km/h (b) 15 km/h
nks Øekxr •EHkksa ds chp dh nwjh ,d leku gSA ,d dkj (c) 20 km/h (d) 8 km/h
72 fd-eh- çfr ?kaVk dh xfr ls pyus ij igys ls 10 osa68. On a straight road, a bus is 30 km ahead of
ty a

•EHks rd igq¡pus esa 18 lsdaM ysrh gSA 10 osa •EHksa rFkk car travelling in the same direction. After
3 hours, the car is 60 km ahead of the bus.
31 osa •EHks ds chp dh nwjh (ehVj esa) D;k gksxh\
di M

If the speed of the bus is 42 km/h, then find

(a) 800 (b) 820
the speed of the car.
(c) 840 (d) 910
65. A boy starts from his home at a certain time ,d lh/h lM+d ij] dksbZ cl mlh fn'kk esa py jgh
with a certain speed to pick up his girlfriend fdlh dkj ls 30 fdeh vkxs gSA 3 ?kaVs ckn] dkj cl
from office at 5:00 pm. One day his girlfriend ls 60 fdeh vkxs fudy tkrh gSA ;fn cl dh pky 42
left the office at 3:00 pm and start walking to
home with a speed of 40 km/hr and meet the fdeh@?kaVk gS] rks dkj dh pky Kkr djsaA
boy in the way who left his home at his usual SSC CPO 09/11/2022 (Shift-01)
time. They reached home 40 min earlier than (a) 67 km/h (b) 72 km/h
their usual time. find the speed of boy.
(c) 65 km/h (d) 59 km/h
,d yM+dk vius ?kj ls fdlh fuf'pr le; ls viuh çsfedk
dks 'kke 5%00 cts dk;kZy; ls ysus ds fy, fdlh fuf'pr 69. A car cover the first 100 km at a speed of
A

50 km/h. It covered next 140 km at a speed

xfr ls pyuk 'kq: djrk gSA ,d fnu mldh çsfedk nksigj of 70 km/h. What is its average speed?
3%00 cts dk;kZy; ls ckgj fudyh vkSj 40 fdeh@?kaVk
dh xfr ls ?kj dh vksj pyuk 'kq: fd;k vkSj yM+ds ls ,d dkj us igys 100 km dh nwjh50 km/h dh xfr
jkLrs esa feyh] tks vius lkekU; le; ij ?kj ls fudyk ls r; dhA blus vxys 140 km dh nwjh70 km/h
FkkA os vius lkekU; le; ls 40 feuV igys ?kj igqap x,A dh xfr ls r; dhA bldh vkSlr xfr D;k gS\
yM+ds dh xfr dk irk yxk,aA SSC CPO 10/11/2022 (Shift-01)
(a) 80 km/hr (b) 120 km/hr (a) 60 km/h (b) 62 km/h
(c) 160 km/hr (d) 200 km/hr (c) 58 km/h (d) 64 km/h

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70. A truck goes from Haryana to Banglore with 74. Kamal started his road trip in his car and
an average speed of 60 km/h. The journey moved at a constant speed of 75 kmph. After
takes 30 hours. It returns from Banglore to completing x% of his total journey, his car
Haryana on the same road with an average started malfunctioning, and therefore, he had
speed of 40 km/h. What was the average speed to complete his journey at half of his normal
of the truck during the whole journey? speed. What is the average speed (in kmph) of
,d Vªd gfj;k.kk ls cSaxyksj rd 60 fdeh@?kaVs dh vkSlr Kamal's whole journey, in terms of x?
dey us viuh dkj esa viuh lM+d ;k=kk 'kq: dh vkSj 75
pky ls tkrk gSA ;k=kk esa 30 ?kaVs yxrs gSaA ;g cSaxyksj
ls gfj;k.kk ds fy, mlh lM+d ij 40 fdeh@?kaVk dh fdeh çfr ?kaVs dh fLFkj xfr ls pykA viuh dqy ;k=kk dk
vkSlr pky ls ykSVrk gSA iwjs ;k=kk ds nkSjku Vªd xdh » iwjk djus ds ckn] mldh dkj •jkc gksus yxh] vkSj
vkSlr pky D;k Fkh\ blfy,] mls viuh ;k=kk dks viuh lkekU; xfr ds vk/h
SSC CPO 10/11/2022 (Shift-02) xfr ls iwjk djuk iM+kA
x ds lanHkZ esa dey dh iwjh ;k=kk
(a) 60 km/h (b) 40 km/h dh vkSlr xfr (fdeh çfr ?kaVs esa) D;k gS\
(c) 50 km/h (d) 48 km/h
CRPF HCM 27/02/2023 (Shift - 03)
71. A bus travels at 100 km/h for the first 1/2
hour. Later it travels at 80 km/h. Find the 7500 7500
(a) (b)

r
time taken by the bus to travel 290 km. 100 + x 100 – x
,d cl igys 1@2 ?kaVsa ds fy, 100 fdeh@?kaVk dh 7500 7500

si
(c) (d)
pky ls pyrh gSA ckn esa ;g cl 80 fdeh@?kaVk dh 300 – x 200 – x
pky ls pyrh gSA 290 fdeh dh nwjh r; djus ds fy, 75.
an by A man covers a certain distance at a certain
speed. Had he moved 8 km/h faster, he would
cl }kjk fy;k x;k le; Kkr dhft,A have taken 4 hours less. If he had moved 7 km/

n
SSC CPO 10/11/2022 (Shift-03) h slower, he would have taken 7 hours more.
(a) 4 hours (b) 3.5 hours What is the usual speed (in km/h) of the man?
(c) 3 hours ja (d) 2.5 hours ,d vkneh ,d fuf'pr nwjh dks ,d fuf'pr xfr ls r;
R s
72. The ratio of the lengths of trains A and B is
2:3 and their speeds are 60 km/h and 72 km/
djrk gSA ;fn og 8 fdeh@?kaVk rsth ls pyrk] rks mls 4
a th

h, respectively. Trains A and B cross each ?kaVs de yxrsA ;fn og 7 fdeh@?kaVk /heh xfr ls pyrk]
other completely in 15 seconds, when rks mls 7 ?kaVs vf/d yxrsA vkneh dh lkekU; xfr
travelling in opposite directions. How much (fdeh@?kaVk esa) D;k gS\
ty a

time (in seconds) will train B take to cross a

CRPF HCM 28/02/2023 (Shift - 03)
370 m long bridge completely? (a) 20 (b) 24
Vªsuksa
A vkSj B dh yackbZ dk vuqikr 2%3 gS vkSj mudh (c) 22
di M

(d) 28
xfr Øe'k% 60 fdeh@?kaVk vkSj 72 fdeh@?kaVk gSA 76. foijhr
A man travels from a place A to place B at x
fn'kkvksa esa ;k=kk djrs le; AVªsu
vkSj B ,d nwljs dks km/h and returns to A by increasing his speed
iwjh rjg ls 15 lsdaM esa ikj djrh gSaAB Vªsu
dks 370 by 20%. His average speed for the whole
ehVj yacs iqy dks iwjh rjg ls ikj djus esa fdruk le; 7
journey is 163 km/h. How much time (in
(lsdaM esa) yxsxk\ 11
CRPF HCM 22/02/2023 (Shift - 02) hours) will he take to travel 294 km at a speed
(a) 27 (b) 35 of 1.4 x km/h?
(c) 30 (d) 32 ,d O;fÙkQ ,d LFkku A ls LFkkuB rd x fdeh@?kaVk dh
73. A person travelled one-fourth of his journey at xfr ls ;k=kk djrk gS vkSj viuh xfr dks 20» c<+kdj
A
30 km/h, another one-fourth of his journey at
36 km/h and the rest at y km/h. If his average 7
ij okil vkrk gSA iwjh ;k=kk esa mldh vkSlr163
xfr
A

7
speed for the whole journey is 37 , then the 11
29
value of y is: fdeh@?kaVk gSA og x fdeh@?kaVk
1-4 dh xfr ls 294 fdeh
,d O;fÙkQ us viuh ;k=kk dk ,d&pkSFkkbZ Hkkx 30 fdeh@?kaVk
dh ;k=kk djus esa fdruk le; (?kaVksa esa) ysxk\
dh xfr ls r; fd;k] vU; ,d&pkSFkkbZ ;k=kk 36 fdeh@?kaVk dh CRPF HCM 11/03/2023 (Shift - 02)
xfr ls vkSj 'ks"k ;k=kk
y fdeh@?kaVk dh xfr ls r; dhA ;fn
7 1 3
iwjh ;k=kk esa mldh vkSlr37xfr29 gS] rks
y dk eku gS% (a) 1
3
(b) 1
4
CRPF HCM 23/02/2023 (Shift - 02) 2 2
(a) 38 (b) 40 (c) 1 (d) 1
5 9
(c) 45 (d) 43.2

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77. A car left 60 minutes early than the scheduled nks LFkkuB1 vkSjB2 ,d&nwljs ls 500 fd-eh- nwj gSA lksfur
time but in order to reach its destination 280 vkSj jkWfu ,d gh le; ij B1 ls B2 dh vksj xfr djuk
km away in time, it has to slow its usual speed
by 14 km/hr. What is the usual speed of the
'kq: djrs gSaA
B2 ij igq¡pus ds ckn os okil B1 ij ykSV
car? vkrs gSaA lksfur dh pky jkWfcu ls 80 fd-eh-@?kaVk vf/d
,d dkj fu/kZfjr le; ls 60 feuV igys fudy tkrh gS ;fn os 6 ?kaVs ds ckn feyrs gSa] rks fuEuyf[kr esa ls dkSu&l
ysfdu 280 fd-eh- nwj vius xarO; rd le; ij igq¡pus ds dFku lgh gS@gSa\
fy, mls viuh lkekU; pky 14 fd-eh-@?kaVk /heh djuh I. Distance covered by Sonit is 600 km.
iM+rh gSA dkj dh lkekU; pky D;k gS\ lksfur }kjk r; dh xbZ nwjh 600 fd-eh- gSA
SSC CHSL 09/03/2023 (Shift-03) II. Speed of Robin is 120/3 km/hr.
(a) 77 km/hr (b) 70 km/hr jkWfcu dh pky
120/3 fd-eh-@?kaVk gSA
(c) 66 km/hr (d) 63 km/hr
SSC CHSL 10/03/2023 (Shift-04)
78. Ram needs to reach the examination center in 6 (a) Only I
hours, the journey itseif is 250 km. If Ram has
(b) Only II
covered (3/5 )th of the distance in 3.5 hours then
(c) Neither I nor II

r
what is the speed required to reach the destination
30 minutes early than the required time? (d) Both I and II

si
jke dks ijh{kk dsUnz rd 6 ?kaVs esa igq¡prk gS] ijh{kk dsUnz
80. 250 makes four trips of equal distances. His
A man
fd-eh- dh nwjh ij gSA ;fn jke us bl nwjh dk (3@5) Hkkx speed on first trip was 720 km/hr and in each
an by
3-5 ?kaVs esa r; fd;k] rks fu;r le; ls 30 feuV igys ijh{kk
dsUnz igq¡pus ds fy, vko';d pky fdruh gksuh pkfg,\
subsequent trip his speed was half of the
previous trip. What is the average speed of the

n
man in these four trips ?
SSC CHSL 10/03/2023 (Shift-02) ,d vkneh leku nwjh dh pkj ;k=kk,¡ djrk gSA igyh ;k=kk esa
(a) 50 km/hr ja (b) 90 km/hr mldh pky 720 fdeh-@?kaVk Fkh vkSj ckn dh izR;sd ;k=kk
R s
(c) 40 km/hr (d) 60 km/hr mldh pky fiNyh ;k=kk ls vk/h FkhA bu pkjksa ;k=kkvks
a th

79. Two places B1 and B2 are 500 km apart from vkneh dh vkSlr pky D;k gS\
each other. Sonit and Robin start moving B1
SSC CHSL 14/03/2023 (Shift-04)
towards B2 at the same time. After reaching
B2, they return back to B1. Speed of Sonit is (a) 104 km/hr (b) 156 km/hr
ty a

80 km/hr more than the Robin. If they meet (c) 192 km/hr (d) 288 km/hr
after 6 hours, then which of the following
di M

statements is /are correct?

ANSWER KEY
1.(b) 2.(c) 3.(d) 4.(d) 5.(c) 6.(a) 7.(a) 8.(b) 9.(c) 10.(b)

11.(d) 12.(d) 13.(d) 14.(b) 15.(a) 16.(d) 17.(b) 18.(b) 19.(c) 20.(d)

21.(c) 22.(a) 23.(b) 24.(a) 25.(a) 26.(d) 27.(d) 28.(d) 29.(b) 30.(a)
A

31.(c) 32.(c) 33.(b) 34.(d) 35.(d) 36.(d) 37.(d) 38.(a) 39.(c) 40.(c)

41.(a) 42.(a) 43.(d) 44.(a) 45.(b) 46.(a) 47.(b) 48.(b) 49.(b) 50.(b)

51.(b) 52.(c) 53.(a) 54.(a) 55.(b) 56.(c) 57.(c) 58.(d) 59.(b) 60.(d)

61.(a) 62.(b) 63.(c) 64.(c) 65.(d) 66.(c) 67.(d) 68.(b) 69.(a) 70.(d)

71.(b) 72.(b) 73.(d) 74.(d) 75.(c) 76.(c) 77.(b) 78.(a) 79.(c) 80.(b)

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Train/ jsyxkM+h
( Practice Sheet With Solution)
1. A train running at the speed of 56 km/hr ,d leku pky ls pyrs gq,] fdlh jsyxkM+h dks 370
crosses a pole in 18 seconds. What is the fdeh- dh nwjh r; djuh FkhA 100 fdeh- pyus ds ckn
length of the train?
dqN rduhdh [kjkch ds dkj.k jsyxkM+h viuh lkekU; pky
56 fdeh@?kaVk dh xfr ls py jgh ,d Vªsu ,d •aHks dks ls 5 fdeh-@?kaVk dh de pky ls pyrh gSA jsyxkM+h
18 lsdaM esa ikj djrh gSA Vªsu dh yackbZ fdruh gS\ feuV nsjh ls igq¡phA jsyxkM+h dh lkekU; pky (fdeh@?
(a) 280 m (b) 250 m fdruh Fkh\
(c) 325 m (d) 140 m (a) 48 (b) 45

r
2. The speed of a train is 78 km/h. It crosses a (c) 40 (d) 50
tunnel in 45 s and overtakes a person walking

si
at a speed of 6 km/h, in the samed direction, 5. A train's journey is disrupted due to an
in 15 s. The length (in m) of the tunnel is : accident on its track after it has travelled 30
an by
km Its speed then come down to fourth- fifth
fdlh jsyxkM+h dh pky 78 km/h gSA ;g fdlh lqjax dh of its original and consequently, If runs 45 min

n
45 s esa ikj djrh gS vkSj mlh fn'kk es 6 dh pky
km/h late Had the accident taken place 18 km
ls pyus okys O;fDr dks 15 s es vksojVsd djrh gSA lqjax farther away, it would have been 36 min late.
ja
dh yackbZ (ehVj esa) Kkr djsaA Find the original speed of the train.
R s

(a) 675 (b) 650 30 fdeh pyus ds ckn VªSd ij fdlh nq?kZVuk ds dkj.k
a th

(c) 975 (d) 780 ,d Vªsu dh ;k=kk ckf/r gks tkrh gS] fiQj mldh xfr viuh
3. The speed of a car is 40% more than that of a 4
ewy xfr ls rd de gks tkrh gS vkSj ifj.kkeLo:i] ;fn
5
ty a

1
bus. A train covers 1020 km in 8
2
hours. How 45 feuV nsjh ls pyrh gS] ;fn nq?kZVuk 18 fdeh nwj gks
rks ;g gksrh 36 feuV nsj gks xbZ gS- Vªsu dh ewy xfr
di M

3
much distance will the the car cover in 1 dhft,A
4
hours if the speed of the bus is half the speed (a) 25 (b) 36
of the train? (c) 30 (d) 20
,d dkj dh pky] ,d cl dh rqyuk esa 40» vf/d gSA 6. A train after travelling a distance of 110 km
1 develops a problem in the engine and proceeds
,d Vªsu 1020 km dh nwjh ls8 ?kaVs esa r; djrh at 3/4th of its former speed and arrives at the
2
destination 60 min late. Had the problem
3 developed 30 km further on, the train would
gSA
1 ?kaVs esa dkj fdruh nwjh r; djsaxh ;fn cl dh pky have arrrived a12 min sooner from last one.
4
Find the original speed of train.
A

Vªsu dh pky dh vis{kk vk/h gSA

(a) 164 km (b) 145 km ,d Vªsu esa 110 fdeh dh ;k=kk djus ds ckn batu esa [kjkc
(c) 147 km (d) 174 km
gksrh gS vkSj ;g viuh okLrfod pky dh3/4th pky ls
vkxs c<+rh gS vkSj xarO; ij 60 feuV ysV igqaprh gSA
4. A train is to cover 370 km at a uniform speed.
After running 100 km, the train could run at [kjkch 30 fdeh vkxs gqbZ gksrh rks Vªasu igys ls 12 f
a speed 5 km/h less than its normal speed due tYnh igq¡ap tkrhA Vªsu dh okLrfod pky crkvksaA
to some techical fault. The train got delayed (a) 45 (b) 60
by 36 minutes. What is the normal speed of the
train, in km/h? (c) 50 (d) 55

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7. Two guns were fired from the same placed at 48 fdeh@?kaVk dh xfr ls ;k=kk djus okyh ,d Vªsu foijh
an interval of 10 minutes and 30 seconds but
a person in the train approaching the place
fn'kk esa 42 fdeh@?kaVk dh xfr ls vk/h yackbZ okyh n
hears the second shot 10 minutes after the Vªsu dks 12 lsdaM esa ikj djrh gSA ;g ,d jsyos IysViQkW
first. The speed of the train ( in km/hr) Hkh 45 lsdaM esa ikj djrh gSA jsyos IysViQkeZ dh yackb
supposing that sound speed travels at 330 (a) 455 m (b) 400 m
metres per second. (c) 420 m (d) 450m
11.
10 feuV vkSj 30 lsdaM ds varjky ij ,d gh LFkku ls nks A passengered sitting in a train of length L m,
which is running with the speed of 60 km/h
canwdsa pykbZ xbZa ysfdu ml LFkku ij vk jgh Vªsu esa ,d
passing through two bridges, notice that he
O;fÙkQ igyh xksyh ds 10 feuV ckn nwljh xksyh lqurk gSA crosses the first bridge and the second bridge
Vªsu dh xfr (fdeh@?kaVk esa) eku yhft, fd èofu dh xfr in time intervals which are in the ratio of 7 :
330 ehVj çfr lsdaM dh xfr ls ;k=kk djrh gSA 4 respectively If the length of first bridge is
280 m, then the length of second bridges is :
(a) 56 (b) 59.4
L ehVj yackbZ dh ,d Vªsu] tks nks iqyksa ls gksdj
(c) 52.8 (d) 55.5 fdeh@?kaVk dh xfr ls py jgh gS] esa cSBk ,d ;k=kh ns•

r
8. A 320 metre long train moving with an average gS fd og igys iqy vkSj nwljs iqy dks le; Øe'k% 7 % 4

si
speed of 120 km/hr crosses a platform in 24 ds vuqikr varjky esa ikj djrk gS ;fn igys iqy dh yackbZ
seconds. A man crosses the same platform in
280 ehVj gS] rks nwljs iqy dh yackbZ gS%
an by
4 minutes. What is the speed of the man in
metre/second? (a) 155 m (b) 160 m
(c) 120 m (d) 140 m

n
,d 320 ehVj yach Vªsu 120 fdeh@?kaVk dh vkSlr xfr ls A cave whose length is 2 km. A train enters
12.
pyrs gq, ,d IysViQkWeZ dks 24 lsdaM esa ikj djrh gSA ,dthe cave from one end and another train from
ja
vkneh mlh IysViQkeZ dks 4 feuV esa ikj djrk gSA ehVj@lsdaM
R s

the other end and they both meet after 1.5

esa vkneh dh xfr D;k gS\ minutes. At the time of meeting, the first train
a th

had covered a distance of 400 m more than the

(a) 2.4 (b) 105 second train. And they cross each other in 4.5
(c) 1.3 (d) 2.0 seconds. After 57 seconds, the first train
completely exits the cave. Then what is the
ty a

9. Two trains run on parallel tracks at 90 km/hr

length of both the trains?
and 72 km/hr respectively. When they are
,d xqiQk ftldh yEckbZ 2 fdeh gSA ,d Vªsu ,d fljs ls rFkk
di M

running in the opposite direction they cross

each other in 5 seconds. When they are nwljh Vªsu nwljs fljs ls xqiQk esa izos'k djrh gS vkSj 1-5
running in the same direction at same speeds ckn os nksuksa feyrh gSaA feyrs oDr igyh Vªsu] nwljh
as before a passenger sitting in the faster train 400 eh nwjh T;knk r; dj pqdh FkhA vkSj os ,d nwljs dks 4-
sees the other passing him in 25 seconds. Find lsdaM esa ikj dj ysrh gSaA blds 57 lsdaM ckn igyh Vªsu x
the length of each train:
ls iwjh ckgj gks tkrh gSA rks nksuksa Vªsuksa dh yEckbZ
nks Vªsusa lekukarj iVfj;ksa ij Øe'k% 90 fdeh@?kaVk vkSj
(a) 72
78m, 16m. (b) 68m, 15m
fdeh@?kaVk dh xfr ls pyrh gSaA tc os foijhr fn'kk esa(c) 85, 20m. (d) 80m, 20.
nkSM+rh gSa rks os ,d nwljs dks 5 lsdaM esa ikj djrh gSaA tc
13. An express train travelling at 80 km/hr
os leku xfr ls mlh fn'kk esa nkSM+ jgs gksrs gSa rst xfr
overtakes a goods train, twice as long and
going at 40 km/hr on a parallel track, in 54 s.
okyh Vªsu esa cSBk ;k=kh 25 lsdaM esa nwljs dks vius ikl ls
A

How long will the express train take to cross a

xqtjrs gq, ns•rk gSA çR;sd Vªsu dh yackbZ Kkr dhft,% platform of 400 m long?
(a) 125m, 90m (b) 125 m 100m 80 fdeh@?kaVk dh xfr ls ;k=kk djus okyh ,d ,Dlçsl
(c) 120 m, 100m (d) 125m,120m Vªsu 54 lsdaM esa lekukarj VªSd ij 40 fdeh@?kaVk dh
10. A train travelling at 48 km/h crosses another ls pyus okyh ,d ekyxkM+h ls nksxquh yach ekyxkM+
train, having half its length and travelling in vkxs fudy tkrh gSA ,Dlçsl Vªsu 400 ehVj yacs IysViQ
opposite direction at 42 km/hr, in 12 seconds dks ikj djus esa fdruk le; ysxh\
It also passes a railway platform in 45 seconds. (a) 36 (b) 45
The length of the railway platform is : (c) 27 (d) none of these

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14. The ratio of the speeds of the train and the 18. Two trains of the same length are running on
man is 6 : 1. The length of the train is 650m parallel tracks in the same direction at 54 km/
and crosses a pole in 1 minute 5 seconds. In h and 42 km/h respectively. The faster train
how much time will the man cross the 240m passes the other train in 63 seconds. What is
long platform? the length (in metres) of each train?
leku yackbZ dh nks Vªsusa lekukarj iVfj;ksa ij ,d gh fn
Vªsu vkSj vkneh dh xfr dk vuqikr 6%1 gSA Vªsu dh yackbZ
650 ehVj gS vkSj ,d iksy dks 1 feuV 5 lsdaM esa ikj esa Øe'k% 54 fdeh@?kaVk vkSj 42 fdeh@?kaVk dh
djrh gSA vkneh 240 ehVj yacs IysViQkeZ dks fdrus le; py jgh gSA rst Vªsu nwljh Vªsu dks 63 lsdaM esa ihN
esa ikj djsxk\ nsrh gSA çR;sd Vªsu dh yackbZ (ehVj esa) Kkr djsaA
(a) 1 minute 24 sec (b) 2 minutes 30 sec SSC CHSL 2 July 2019 (Morning)
(c) 2 minutes (d) 2 minutes 24 sec (a) 90 (b) 81
15. Two trains, A and B start from stations X and (c) 105 (d) 210
Y towards Y and X respectively. After passing 19. The platform of a station 400 m long starts
exactly where the last span of a bridge 1.2 km
each other, They take 4 hours 48 minutes and
long ends. How long will a train 200 m long
3 hours 20 minutes to reach Y and X
and travelling at the speed of 72 km/h take

r
respectively. If train A is moving at 45 km/hr.,
to cover the distance between the starting
then the speed of the train B is
point of the span of the bridge and the far end

si
nks Vªsusa]
A vkSj B Øe'k%X vkSj Y LVs'kuksa Y ls
vkSjX of the platform?
dh vksj pyrh gSaA ,d nwljs dks ikj djus ds ckn] os fdlh LVs'ku dk 400 ehVj yack IysViQkWeZ Bhd ogha l
an by
Øe'k%Y vkSj X rd igq¡pus esa 4 ?kaVs 48 feuV vkSj 3 gksrk gS tgk¡ 1-2 fdeh yacs iqy dk vafre ikV lekIr gksrk
?kaVs 20 feuV dk le; ysrh gSaA ;fnA Vªsu
45 fdeh@?kaVk gSA 72 fdeh@?kaVk dh pky ls py jgh 200 ehVj yach ,d

n
dh xfr ls py jgh gS] rks Vªsu
B dh xfr gS Vªsu dks iqy ds ikV ds vkjafHkd fcanq rFkk IysViQ
vafre fcanq rd tkus esa fdruk le; yxsxk \
ja
(a) 60 km/hr (b) 64.8 km/hr
R s

(c) 54 km/hr (d) 37.5 km/hr SSC CHSL 11 July 2019 (Morning)
a th

16. The time taken for the tail end of a train to (a) 1.6 min (b) 1.5 min
cross a pole is 53 seconds. If the length of the (c) 1.8 min (d) 1.2 min
trains is 110 m and speed of the train is 36 20. Renu was sitting inside train A, which was
km/hr, find the initial distance of the pole travelling at 50 km/h. Another train, B whose
ty a

from the front end of the train. length was three times the length of A crossed
,d jsyxkM+h ds fiNys fljs dks ,d •aHks dks ikj djus esa her in the opposite direction in 15 seconds. If
di M

the speed of train B was 58 km/h, then the

yxus okyk le; 53 lsdaM gSA ;fn Vªsuksa dh yackbZ 110 length of train A (in m) is :
ehVj gS vkSj Vªsu dh xfr 36 fdeh@?kaVk gS] rks Vªsu ds ,d Vªsu ds Hkhrj cSBh gqbZ Fkh] tks 50 fdeh@?
js.kq
lkeus ds Nksj ls •aHks dh çkjafHkd nwjh Kkr dhft,A pky ls py jgh FkhAA dh yackbZ ls frxquh yackbZ dh ,d
(a) 420 m (b) 530 m vU; VªsuB us mls foijhr fn'kk ls 15 lsdaM esa ikj
(c) 640 m (d) 1798 m fd;kA ;fn VªsuB dh pky 58 fdeh@?kaVk Fkh] rks A Vªsu
17. A train, 500 m long, passes a railway platform dh yackbZ (ehVj esa) Kkr djsaA
400 m long, in one minute with uniform speed. SSC CGL TIER II (12 September 2019)
What is the time (in seconds) taken by the (a) 210 (b) 180
train to pass a man riding a motorbike, (c) 160 (d) 150
travelling opposite to the direction of the train,
21. A train x running at 84 km/h crosses another
at a speed of 18 km/h ?
A

train y running at 52 km/h in opposite direction

500 ehVj yach Vªsu ,d 400 ehVj jsyos IysViQkWeZ dks in ,d 12 seconds. If the length of y is two-third that
leku pky ls 1 feuV esa ikj djrh gSA 18 fdeh@?kaVk dh of x, then what is the length of x ?
pky ls Vªsu ds foijhr ;k=kk djrs gq, ,d eksVjlkbfdy 84 fdeh@?kaVk dh pky ls py jgh ,d Vªsu x lkeus ls
lokj O;fDr dks ikj djus esa Vªsu }kjk fy;k x;k le; 52 fdeh@?kaVk dh pky ls vk jgh nwljhyVªsu dks 12
(lsdaM esa) fdruk gksxk\ lsdaM esa ikj djrh gSA y;fndh yackbZ x dh yackbZ ls nks
SSC CHSL 2020 Tier-I frgkbZ gS] rks
x dh yackbZ fdruh gS\
SSC CHSL 2 July 2019 (Evening)
(a) 30 (b) 48 (a) 250 m (b) 242 m
(c) 54 (d) 25 (c) 272 m (d) 408 m

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22. Two trains are moving in the same direction 26. Train A takes 2 hours more than train B to
at 1.5 km/minute and 60 km/hour cover a distance of 40 km. If train A doubles
respectively. A man in the faster train observes
that it takes 27 seconds to cross the slower 1
his speed, he takes 1 hour more than train
train. The length of the slower train is 2
nks jsyxkfM+;k¡ Øe'k% 1-5 fdeh@feuV vkSj 60 fdeh@?kaVk
B to cover 80 km. To cover a distance of 120
dh pky ls lkeku fn'kk esa py jgh gSaA rst jsyxkM+h esa
km, how much time (in hours) will train B take
lokj dksbZ O;fÙkQ ns•rk gS fd /heh jsyxkM+h dks ikj djus
travelling at his same speed?
40 fdeh dh nwjh r; djus esa] Vsªu
esa mls 27 lsdaM yxrs gSaA /heh jsyxkM+h dh yackbZ gS% A, VsªuB ls 2 ?kaVs

(a) 225 m (b) 230 m

vf/d ysrh gSA vxj VsªuA viuh pky dks nksxquh djrk

(c) 240 m (d) 250 m 1

gS] rks
80 fdeh nwjh r; djus esa og Vsªu
B ls 1 ?kaVk
23. Two trains are moving in the same direction 2
at the speed of 36 km/hr and 48 km/hr. The vfèkd ysrk gSA VsªuB dks viuh pky ls 120 fdeh dh
time taken by faster train to cross a man nwjh r; djus esa fdruk le; (?kaVksa esa) yxsxk\
sitting in the slower train is 33 seconds. What

r
will be the length of the faster train? 1 2
(a) 1 (b) 1
nks jsyxkfM+;k¡ 36 fd-eh@?kaVk rFkk 48 fd-eh-@?kaVk 3dh 3

si
pky ls leku fn'kk esa py jgh gSA rhoz pky okyh
jsyxkM+h }kjk /heh pky okyh jsyxkM+h esa cSBs ,d iq#"k 1 1
an by
(c) 1 (d) 1
dks ikj djus esa fy;k x;k le; 33 lsd.M gSA rhoz 4 2
pky okyh jsyxkM+h dh yEckbZ D;k gksxh\

n
27. Two trains started simultaneously at 9 A.M.
SSC CGL 07/12/2022 (Shift- 04) from A and B towards B and A respectively.
Both of them take 12 hr to reach their
ja
(a) 770 metres (b) 90 metres
R s

respective destinations. If the first train met

(c) 110 metres (d) 180 metres with an accident at 1 pm and thereafter travels
a th

24. A 240 m long train overtakes a man walking at half its original speed, when will the two
at 6 km/h, in the same direction, in 9 seconds. trains meet?
How much time (in seconds) will it take to pass
a 372 m long tunnel with the same speed?
lqcg 9 cts nks Vªsusa ,d lkFk pyhaA
A vkSjB ls Øe'k%B
ty a

vkSjA dh vksjA nksuksa dks vius&vius xarO; rd igqapu

240 eh- yEch jsyxkM+h] leku fn'kk 6 fdeh@?kaVk
es dh
12 ?kaVs yxrs gSaA ;fn igyh Vªsu nksigj 1 cts nq?kZV
pky ls pyus okys O;fDr dks 9 lsdaM esa ikj dj tkrh gSA
di M

gks tkrh gS vkSj mlds ckn viuh ewy xfr ls vk/h xfr ls
mlh pky ls ;g jsyxkM+h] 372 eh- yEch lqjax dks fdrus
pyrh gS] rks nksuksa Vªsusa dc feysaxh\
le; esa (lsdaM esa) ikj djsxk\
(a) 2 : 40 (b) 3 : 40
(a) 21.6 (b) 20
(c) 18 (d) 20.4 (c) 4 : 50 (d) 4 : 10
25. A train runs first 75 km at a certain uniform 28. One train is 140 m longer than the other train
speed and next 90 km at an average speed of when they move in opposite direction they
10 km/h more than the normal speed. If it cross each other in 35 seconds and when they
takes 3 hours to complete the journey, then move in same direction they take 4 times time.
how time will the train take to cover 300 km If speed of slower train is 27 km/h find the
with normal speed? speed of faster train.
A

,d jsyxkM+h] igys 75 fdehdh nwjh ,d fuf'pr ,dleku ,d Vªsu nwljh Vªsu ls 140 ehVj yach gS tc os foijhr
pky ls r; djrh gS vkSj vxys 90 fdeh dh nwjh lkekU; fn'kk esa pyrh gSa rks os ,d nwljs dks 35 lsdaM esa
pky ls 10 fdeh@?kaVkvf/d dh vkSlr pky ls r; djrh djrh gSa vkSj tc os leku fn'kk esa pyrh gSa rks mUg
gSA ;fn ;k=kk dks iwjk djus es 3 ?kaVs dk le; yxrk gS] rks
xquk le; yxrk gSA ;fn /heh Vªsu dh xfr 27 fdeh@?kaV
lkekU; pky ls jsyxkM+h dks 300 fdeh dh nwjh r; djus gS rks rst Vªsu dh xfr Kkr dhft,A
esa fdruk le; yxsxk\ (a) 45km/h (b) 40km/h
(a) 5 hours 15 minutes (b) 5 hours
(c) 33km/h (d) 54km/h
(c) 6 hours (d) 5 hours 25 minutes

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29. Train A travelling at 63 kmph takes 27 sec to 33. Two trains whose length difference is 170 m,
cross Train B when travelling in opposite crosses each other in 16 sec when move in
direction whereas it takes 162 seconds to opposite direction but crosses each other in 36
overtake it when travelling in the same sec when move in the same direction. Find the
direction. If the length of train B is 500 meters, speed of faster train if speed of slower train is
find the length of Train A. 35 km/hr.
VªsuA 63 fdeh çfr ?kaVs dh xfr ls ;k=kk djrs gq, foijhr
nks jsyxkfM+;ksa dh yEckbZ;ksa dk varj 170 ehVj gSA
fn'kk esa ;k=kk djrs le; Vªsu
B dks ikj djus esa 27 lsdaM
fn'kkvksa esa pyrh gqbZ ;s ,d nwljh dks 16 lsdaM esa
dk le; ysrh gS tcfd leku fn'kk esa ;k=kk djrs le; bls
leku fn'kk esa pyrh gqbZ 36 lsdaM esa ikj dj tkrh gS
vksojVsd djus esa 162 lsdaM dk le; ysrh gSA ;fnB Vªsu
;fn /heh xfr okyh jsyxkM+h dh pky 35 fdeh@?kaVk g
dh yackbZ 500 ehVj gS] rks A Vªsu
dh yackbZ Kkr dhft,A
rks rst xfr okyh jsyxkM+h dh pky D;k gksxh\
(a) 400 m (b) 810 m
(c) 500 m (d) 310 m (a) 65 km/hr (b) 70 km/hr
30. A starts from X at 9:00 am and reaches Y at (c) 78 km/hr (d) 91 km/hr
1:00 pm. B starts from Y at 9:00 am and 34. Train A running at 81 km/h takes 72 sec to

r
reaches X at 3 pm. At what time do the two overtake train B, when both the trains are
meet? running in the same direction, but it takes 36

si
A lqcg 9%00 ctsX ls pyuk 'kq: djrk gS vkSj nksigj sec to cross each other if the trains are running
1%00 ctsY ij igq¡prk gSA
B] Y ls lqcg 9%00 cts pyuk in the opposite direction. If the length of train
an by
'kq: djrk gS vkSj nksigj 3 ctsX ij igq¡prk gSA nksuksa B is 600 metres, then find the length of train
A. (in metres)

n
fdl le; feyrs gSa\
(a) 11 : 00am (b) 11 : 24am 81 km/h dh pky ls pyus okyh VªsuA, Vsu B ls
vkxs fudyus esa 72 sec dk le; rc ysrh gS] tc
ja
(c) 11 : 30am (d) 11 : 50am
R s

31. A train of length 500 m crosses a platform of nksuksa Vªsusa ,d gh fn'kk esa py jgh gksrh gSa] ysf
Vªsusa
foijhr fn'kk esa py jgh gS] rks ,d&nwljs dks ikj
a th

length 50% more than the length of the train

in 50 seconds. Find the time taken by this djus esa36 sec dk le; ysrh gSaA ;fn Vsªu
B dh yackbZ
train to cross another train of same length 600 ehVj gS] rks Vªsu
A dh yackbZ Kkr djsaA (ehVj esa)
running with double the speed of first train in
ty a

the opposite direction. SSC CGL 13/12/2022 (Shift- 03)

500 ehVj yach Vªsu] Vªsu dh yackbZ ls 50» vf/d yackbZ(a) 600 (b) 480
di M

okys IysViQkWeZ dks 50 lsdaM esa ikj djrh gSA foijhr (c)
fn'kk590 (d) 900
esa igyh Vªsu dh xfr ls nksxquh xfr ls py jgh leku
35. Two trains are moving in the opposite direction
yackbZ dh nwljh Vªsu dks ikj djus esa bl Vªsu }kjk fy;k
at the speed of 48 km/hr and 60 km/hr
x;k le; Kkr dhft,A respectively. The time taken by the slower
train to cross a man sitting in the faster train
1 is 12 seconds. What is the length of the slower
(a) 13sec (b) 15 sec train?
2

1 1
nks jsyxkfM+;k¡ Øe'k% 48 fd-eh-@?kaVk rFkk 60
(c) 13 sec
2
(d) 13 sec
3 @?kaVk dh pky ls foijhr fn'kk eas py jgh gSA /he
32. On a station, a train is stopped for 6 minutes, pky okyh jsyxkM+h }kjk rst pky okyh jsyxkM+h esa
A

but after this its speed is increased by 4 km/ ,d O;fDr dks ikj djus esa fy;k x;k le; 12 lsd.M
hr. When the train covers 36 km it manages gSA /heh pky okyh jsyxkM+h dh yEckbZ D;k gS\
its delay. What is the initial speed of the train?
SSC CGL 08/12/2022 (Shift- 02)
,d LVs'ku ij ,d Vªsu dks 6 feuV ds fy, jksdk tkrk gS]
ysfdu blds ckn bldh xfr 4 fdeh@?kaVk c<+k nh tkrh gSA(a) 480 metres
tc Vªsu 36 fdeh dh nwjh r; djrh gS rks ;g viuh nsjh (b) 720 metres
dk çca/u djrh gSA Vªsu dh çkjafHkd xfr D;k gS\
(c) 180 metres
(a) 32 km/h (b) 36 km/h
(c) 40 km/h (d) 42 km/h (d) 360 metres

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36. A train travels at a speed of 18 m/s in the first nks jsyxkfM+;k¡ 44 fdeh@?kaVk vkSj 70 fdeh@?kaVk
5 minutes, covers 7.5 km in the next 10 ,d gh fn'kk esa py jgh gSaA rst Vªsu }kjk /heh Vªsu esa cS
minutes and covers 12 km in another 10
minutes. What is its average speed (in km/h,
O;fÙkQ dks ikj djus esa 72 lsdaM dk le; yxrk gSA rst Vª
rounded off to 1 decimal place) for the entire dh yackbZ D;k gksxh\
journey? SSC MTS 15/06/2023 (SHIFT-02)
(a) 520 metres (b) 620 metres
,d Vsªu igys 5 feuV esa18 m/s dh xfr ls ;k=kk
(c) 450 metres (d) 500 metres
djrh gS] vxys 10 feuV esa 7.5 km dh nwjh r; djrh
gS vkSj nwljs 10 feuV12 esakm dh nwjh r; djrh gSA 40. A goods train, travelling at constant speed, crossed
two persons walking in the same direction (as that
iwjh ;k=kk ds fy, bldh vkSlr xfr(km/h esa 1 n'keyo
of the train) in 11.6 seconds and 11.8 seconds,
ds LFkku rd iw.kkZafdr
) D;k gS\
respectively. The first person was walking at 5.85
SSC CGL 13/12/2022 (Shift- 03) km/h, while the second was walking at 6.3 km/h.
What was the speed of the train (in km/h)?
(a) 59.8 (b) 71.2
,d ekyxkM+h fLFkj pky ls ;k=kk djrs gq,] ,d gh fn'kk esa (Vs
(c) 45.7 (d) 64.6 dh fn'kk esa) py jgs nks O;fDr;ksa dks
%11-6
Øe'klsdaM
vkSj 11-

r
37. The distance covered by a train in (5y – 1) 8 lsdaMesa ikj djrh gSA igyk O;fDr 5-85 fdeh@?kaVkpky dh
hours is (125y³ – 1) km. The speed of the train ls py jgk Fkk] tcfd nwljk 6-3 fdeh@?kaVk dh pky ls py jgk

si
is:
FkkA Vªsu dh pky (fdeh@?kaVk esa) D;k Fkh\
,d jsyxkM+h }kjk
(5y – 1) ?kaVks esa r; dh xbZ nwjh
an by
SSC PHASE XI 27/06/2023 (Shift-03)
gSA jsyxkM+h dh pky Kkr dhft,A
(125y³ – 1) km
(a) 32.5 (b) 32.6

n
SSC CGL 02/12/2022 (Shift- 02) (c) 32.4 (d) 32.2
41. A train takes 7 seconds to pass man standing
(a) (5y³ – 1) km/h
ja
on a platform and another train whose length is
R s

(b) (25y² – 5y + 1) km/h double that of the first train, and moving in the
a th

(c) (5y + 1) km/h opposite direction, takes 10 seconds to pass him.

The time taken (in seconds, to the nearest
(d) (25y² + 5y + 1) km/h integer) by the trains to pass each other will be:
38. A train starts at 3:00 pm from Mumbai and ,d Vªsu dks IysViQkeZ ij •M+s vkneh dks ikj djus esa 7 ls
ty a

moves towards Ahmedabad at the speed of 20 yxrs gSa vkSj nwljh Vªsu] ftldh yackbZ igyh Vªsu dh yac
km/hr. Another train starts from Ahmedabad nksxquh gS] vkSj foijhr fn'kk esa pyrh gS] mls ikj djus es
di M

at 8 pm and moves towards Mumbai at the lsdaM ysrh gSA Vªsuksa }kjk ,d nwljs dks ikj djus esa fy
speed of 60 km/hr. If the distance between
le; (lsdsaM esa] fudVre iw.kkZad rd) gksxk%
Mumbai and Ahmedabad is 600 km. then at
what time both the trains will meet? SSC PHASE XI 27/06/2023 (Shift-01)
(a) 8 (b) 9
,d Vªsu nksigj 3%00 cts eqacbZ ls pyrh gS vkSj 20 (c) 10 (d) 12
fdeh@?kaVk dh xfr ls vgenkckn dh vksj pyrh gSA nwljh 42. The ratio of the lengths of trains A and B is 2:3 and
Vªsu jkr 8 cts vgenkckn ls 'kq: gksrh gS vkSj 60 fdeh@?kaVk
their speeds are 60 km/h and 72 km/h, respectively.
Trains A and B cross each other completely in 15
dh xfr ls eqacbZ dh vksj pyrh gSA ;fn eqacbZ vkSj vgenkckn
seconds, when travelling in opposite directions. How
ds chp dh nwjh 600 fdeh gSA rks nksuksa jsyxkfM+;k¡ fdl time (in seconds) will train B take to cross a
much
le; feysaxh\ 370 m long bridge completely?
A

Vªsuksa
A vkSj B dh yackbZ dk vuqikr 2%3 gS vkSj mud
SSC MTS 13/06/2023 (SHIFT-02)
xfr Øe'k% 60 fdeh@?kaVk vkSj 72 fdeh@?kaVk gSA
(a) 1:30 am (b) 12:30 am fn'kkvksa esa ;k=kk djrs le; AVªsu
vkSj B ,d nwljs dks
(c) 2:00 am (d) 2:15 am iwjh rjg ls 15 lsdaM esa ikj djrh gSaA
B dks
Vªsu370 ehVj
yacs iqy dks iwjh rjg ls ikj djus esa fdruk le; (lsdaM
39. Two trains are moving in the same direction at
the speed of 44 km/hr and 70 km/hr. The time esa) yxsxk\
taken by faster train to cross a man sitting in CRPF HCM 22/02/2023 (Shift - 02)
the slower train is 72 seconds. What will be the (a) 27 (b) 35
length of the faster train? (c) 30 (d) 32

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43. The length of train A is 100 m more than the 46. A train travelling at the speed of x km/h crossed
length of a platform. What is the time taken a 300 m long platform in 30 seconds, and
by train A to cross train B travelling in the overtack a man walking in the same direction at
opposite direction if the speed of train B is 70 6 km/h in 20 seconds. What is the value of x?
km/h and the speed of train A is 90 km/h and
the time taken by train A and B to cross the
x km/h dh pky ls pyus okyh jsyxkM+h 300 m yacs
same platform is 24 seconds and 36 seconds, IysViQkWeZ30 dks
lsd.M esa ikj djrh gS vkSj mlh fn'kk esa
respectively? 6 km/h dh pky ls py jgs O;fDr dks 20 lsd.M esa
VªsuA dh yackbZ ,d IysViQkeZ dh yackbZ ls 100 ehVj vf/ ikj djrh gSAx dk eku Kkr djsaA
d gSA VªsuA }kjk foijhr fn'kk esa ;k=kk dj jgh Vªsu
B dks SSC CPO 24/11/2020 (Shift-2)
ikj djus esa fdruk le; yxrk gS] ;fn VªsuB dh xfr 70 (a) 60 (b) 96
fdeh@?kaVk gS vkSj A dhVªsu
xfr 90 fdeh@?kaVk gS vkSj Vªsu(c) 48 (d) 102
A vkSjB leku IysViQkeZ dks ikj djus esa Øe'k% 24 lsdaM
47. Two trains A and B having the lengths 195 m
vkSj 36 lsdaM dk le; yxrk gS\ and 165 m respectively, are running in the
same direction on parallel lines. If the speed
CRPF HCM 23/02/2023 (Shift - 02)

r
of A and B be 77 km/h and 85 km/h
(a) 15 seconds (b) 18 seconds respectively, then what will be the time (in

si
(c) 14 seconds (d) 16 seconds seconds) taken by them to cross each other?
nks Vªsusa
A vkSj B ftudh yackbZ Øe'k% 195 eh vkSj 165
an by
44. The distance between two stations P and Q is
400 km. A and B start from stations P and Q eh gS] lekukarj iVfj;ksa ij ,d gh fn'kk esa py jgh gSaA

n
respectively at the same time towards each
other, and the speed of B is 10 km/h more than
;fn A vkSj B dh pky Øe'k% 77 fdeh@?kaVk vkSj 85
the speed of A If the difference between the fdeh@?kaVk gS] rks muds }kjk ,d nwljs dk ikj djus
ja
R s

distance of A and B after 3 hours since starting fdruk le; (lsadM esa) fy;k tk,xkA
is 70 km, find the speed of B (in km/h).
(a) 162 (b) 164
a th

nks LVs'kuksa
P vkSjQ ds chp dh nwjh 400 fdeh gSAA vkSj (c) 160 (d) 166
B ,d gh le; esa Øe'k% LVs'kuP vkSj Q ls ,d&nwljs 48. Two trains start from Delhi and Puna towards
dh vksj pyuk 'kq: djrs gSa] vkSj
B dh xfr A dh xfr ls each other at 7 am with speeds of 85 km/h
ty a

10 fdeh@?kaVk vf/d gSA ;fn 'kq: djus ds 3 ?kaVs A ckn and 67 km/h, respectively. If they cross each
other at 3.30 p.m., the distance between the
vkSjB ds chp dh nwjh dk varj 70 fdeh gS] (fdeh@?kaVk
di M

stations is:
esa)B dh xfr Kkr dhft,A nks Vªsusa
7 am ij fnYyh vkSj iwuk ls Øe'k% 85 fdeh@?kaV
CRPF HCM 28/02/2023 (Shift - 02) vkSj 67 fdeh@?kaVk dh pky ls ,d nwljs dh vksj pyuk
(a) 60 (b) 45
izkjaHk djrh gSaA ;fn os nksuksa ,d nwljs dks
3.30 pm
ØkWl djrh gSa] rks nksuksa LVs'kuksa ds chp dh nwj
(c) 55 (d) 50
45. A train x running at 74 km/h crosses another (a) 1245 km (b) 1292 km
train y running at 52 km/h in the opposite (c) 1283 km (d) 1227 km
direction in 12 seconds. If the length of y is
49. Two trains A and B start running at 80 km/h
two-thirds that of x, then what is the length of
and 82 km/h towards each other from two
y (in m)?
different stations. They meet after 1 hour 30
A

74 km/h dh pky ls py jgh ,d jsyxkM+hx, 52 km/ minutes. How far were they from each other
h dh pky ls foijhr fn'kk esa vk jgh gS rFkk nwljh when they started?
jsyxkM+h
y dks 12 lsd.M esa ikj djrh gSA ;fn jsyxkM+h
y nks jsyxkfM+;ka
A vkSjB nks vyx&vyx LVs'kuksa ls ,d
x dh yackbZ ls nks&frgkbZ vf/d gS rksnwljs dh vksj 80 fdeh@?kaVk vkSj 82 fdeh@?kaVk d
dh yackbZ jsyxkM+h
jsyxkM+h
y dh yackbZm ( esa) fdruh gksxh\ ls pyuk 'kq: djrh gSaA os 1 ?kaVsa 30 feuV ds ck
feyrh gSaA tc jsyxkfM+;ksa us pyuk 'kq: fd;k rks os ,d&n
SSC CPO 25/11/2020 (Shift-1)
ls fdruh nwjh ij Fkha\
(a) 252 (b) 200 (a) 19 km (b) 262 km
(c) 168 (d) 210 (c) 243 km (d) 224 km

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50. Two stations are 120 km apart on a straight nks LVs'ku ,d lh/h js[kk esa 120 fdeh dh nwjh ij gS
line. A train starts from station A at 8 a.m. ,d Vªsu LVs'kuA ls lqcg 8 am ij pyuk 'kq: djrh
and moves towards station B at 20 km/h and gS vkSj LVs'ku
B dh vksj 20 fdeh@?kaVk dh pky ls
another train starts from station B at 9 a.m. pyrh gS vkSj nwljh Vªsu LVs'ku
B ls lqcg 9 am ij
and travels towards station A at a speed of 30
pyuk 'kq: djrh gS vkSj LVs'kuA dh vksj 30 km/h
km/h. At what time will they meet?
dh pky ls pyrh gSA os fdl le; feysaxh\
(a) 10:30 am (b) 10:00 am
(c) 11:00 am (d) 11:30 am

......-------......

r
si
an by
n
ja
Answer Key
R s
a th

1.(a) 2.(a) 3.(c) 4.(d) 5.(c) 6.(c) 7.(b) 8.(d) 9.(b) 10.(b)

11.(b) 12.(d) 13.(c) 14.(d) 15.(c) 16.(a) 17.(d) 18.(c) 19.(b) 20.(d)
ty a

21.(c) 22.(a) 23.(c) 24.(a) 25.(c) 26.(d) 27.(a) 28.(a) 29.(d) 30.(b)
di M

31.(d) 32.(b) 33.(d) 34.(b) 35.(b) 36.(a) 37.(d) 38.(d) 39.(a) 40.(c)

41.(b) 42.(b) 43. (b) 44. (a) 45.(c) 46.(b) 47.(a) 48.(b) 49.(c) 50.(c)
A

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QUESTIONS BASED ON TRAIN

+h ij vk/kfjr iz'u)
(jsyxkM
(CLASSROOM SHEET)
3.Train 1 crosses Train 2
BASIC CONCEPT OF TRAINS D = L1 + L2
jsyxkM+h laca/h iz'uksa dh ewyHkwr ladYiukS = S1 – S2 (Same Direction)
S1 + S2 ( O p p o s i t e
 Distance = Speed × Time Direction)
nwjh = p ky × l e; 4. Train 1 Train 2
 Difference between Meeting and Crossing L 1
L 2
S1 S2
feyus vkSj ikj djus ds chp varj

r
A person sitting in Train 1 crosses Train 2.
 Speed/pky  Relative Speed/l kis{k pky D = L2

si
S = (SA – SB) [Same Direction] (l eku fn'kk) S = S1 – S 2
S = (SA + SB) [Opposite Direction] ( foijhr fn'kk) Train 1 crosses a person sitting in Train 2.
an by
Time =
Distance
] l e; =
w
nj
p ky
h
D = L1
S = S1 – S 2

n
Speed
Generally, Length of the train is given in m
and Speed is given in km/hr.
ja EXERCISE
R s
So, always focus on the units.
vr% lnSo bdkbZ ij è;ku nsaA TYPE - 01
a th

Basic points which will help in solving 1. The time taken by a 180 m long train running
questions at a speed of 54 km/h to cross a man standing
on the platform is:
ty a

1. When a train crosses a man (stationary),

crosses a man walking @ 2km/hr or crosses a 54 km/h d h xfr ls py jgh 180 m yach jsyxkM+h }kjk IysViQk
ij [kM+s ,d O;fDr dks ikj djus esa fy;k x;k le; fdruk gS\
di M

man walking @ 10 km/hr.

tc ,d jsyxkM+h ,d O;fÙkQ (fLFkj) dks ikj djrh gS] 2 SSC CHSL 25/05/2022 (Shift- 2)
fdeh@ ?kaVk dh pky ls pyus okys ,d O;fÙkQ dks ikj (a) 10 Seconds (b) 12 Seconds
djrh gS ;k 10 fdeh@?kaVk dh pky ls pyus okys ,d (c) 11 Seconds (d) 9 Seconds
O;fÙkQ dks ikj djrh gSA 2. A train running at the speed of 63 km/h crosses
In every case : D = LT (Length of the train) a pole in 24 seconds. What is the length of the
(jsyxkM+h dh yackbZ) train?
Here, D refers to the distance which the train 63 km/h dh xfr ls py jgh ,d jsyxkM+h ,d [kEHks dks
has covers extra with respect to the man. 24 lsd.M esa ikj djrh gSA VSªu dh yECkkbZ D;k gksxh\
;gkaD jsyxkM+h dh nwjh ls lanfHkZr gS tks jsyxkM+h O;fÙkQ SSC CHSL 06/06/2022 (Shift 01)
ds lanHkZ esa vfrfjÙkQ r; djrh gSA (a) 360 m (b) 320 m
A

2. Distance covered by the train when the train (c) 380 m (d) 420 m
crosses an object: 3. A train passes a man standing on a platform
fdlh oLrq dks ikj djus esa jsyxkM+h }kjk r; dh xbZ nwjh in 8 seconds and also crosses the platform
D = LT + LO which is 264 metres long in 20 seconds. The
length of the train (in metres) is:
Where:/tg k¡
, d jsyxkM+h fdlh IysViQkWeZ ij •M+s O;fÙkQ dks 8 ls
LT = Length of Train
ikj djrh gS vkSj 264 ehVj yacs IysViQkeZ dks 20 lsdaM
LT = jsyxkM+h dh yackbZ
ikj djrh gSA jsyxkM+h dh yackbZ (ehVj esa) gS%
LO = Length of Object
(a) 188 (b) 176
LO = oLrqdh yackbZ
(c) 175 (d) 96

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4. Length of a train is 330 metres and it is moving SSC CPO 24/11/2020 (Shift-2)
at the speed of 72 km/hr. In how much time will (a) 60 (b) 96
it takes cross a platform of length 710 metres?
(c) 48 (d) 102
,d jsyxkM+h dh yackbZ 330 ehVj gS rFkk og 72 fdeh@?kaVk
9. A 240 m long train overtakes a man walking
dh pky ls py jgh gSA 710 ehVj yacs fdlh IysViQkWeZ dks
at 6 km/h, in the same direction, in 9 seconds.
ikj djus esa ;g fdruk le; ysxh\
How much time (in seconds) will it take to pass
SSC CGL MAINS (08/08/2022)
a 372 m long tunnel with the same speed?
(a) 52 seconds (b) 72 seconds
(c) 56 seconds (d) 64 seconds 240 ehVj yEch jsyxkM+h] leku fn'kk esa 6 fdeh@?kaVk
5. A 240 m long train crosses a 360 m long pky ls pyus okys O;fDr dks 9 lsdaM esa ikj dj tkrh
tunnel in 30 seconds. What is the speed of the gSA mlh pky ls ;g jsyxkM+h 372 ehVj yEch lqjax dk
train (in km/h)? fdrus le; esa (lsadM esa) ikj djsxk\
240 ehVj yach ,d Vªsu 360 ehVj yach lqjax dks 30 lsdaM eas SSC CGL 13/08/2021(Shift 02)
ikj djrh gSA Vªsu dh pky (fdeh@?ka
Vk esa) D;k\ gS (a) 21.6 (b) 20
SSC CGL 21.04.2022 (3 Shift)
rd (c) 18 (d) 20.4

r
(a) 60 (b) 28.8 10. A train running at 48 km/h crosses a man
(c) 72 (d) 43.2 going with the speed of 12 km/h, in the same

si
direction, in 18 seconds and passes a woman
TYPE - 02 coming from the opposite direction in 12
6.
an by 1
A train running at 40 km\h takes 24 second to
2
seconds. The speed (in km/h) of the woman is:
48 fdeh@?kaVk dh pky ls pyrh jsyxkM+h mlh fn'kk e

n
cross a pole. How much time (in second) will it 12 fdeh@?kaVk dh pky ls pyrs O;fDr dks 18 lsdaM esa
take to pass a 450 m long bridge? ikj djrh gS vkSjh foijhr fn'kk esa pyrh efgyk dks 12
ja lsdaM esa ikj djrh gSA efgyk dh pky (fdeh@?kaVk) e
R s
1
40 km/h dh pky ls pyus dh okyh ,d jsyxkM+h
2 Kkr djsaA
a th

,d [kEHks dks ikj djus esa 24 lsdaM dk le; ysrh gSA

SSC CGL 23/08/2021(Shift 03)
450 ehVj yacs iqy dks ikj djus esa fdruk le; (lsdaM
(a) 8 (b) 9
esa) yxsxk\
(c) 6 (d) 10
ty a

SSC CGL 13/08/2021(Shift 03)

11. A railway engine passes two bridges of length
(a) 56 (b) 52
400 m and 235 m in 100 seconds and 60
di M

(c) 60 (d) 64 seconds, respectively. Twice the length of the

7. A 750 metres long train crosses a stationary railway engine (in m) is:
pole in 15 sec. Travelling at the same speed,
this train crosses a bridge completely in 25
,d jsyos batu 400 m vkSj235 m yacs nks iqyksa dks
sec. What is the length of this bridge? Øe'k% 100 lsdaM vkSj 60 lsdaM esa ikj djrk gSA jsy
750 ehVj yach ,d Vªsu ,d fLFkj [kaHks dks 15 lsdaM esa batu dh yackbZ dk nqxquk
(m esa
) fdruk gS%
ikj djrh gSA blh pky ls ;k=kk djrq gq,] ;g Vsªu ,d iqy SSC CGL 18.04.2022 (2nd Shift)
dks 25 lsdaM esa iwjh rjg ikj dj tkrh gSA iqy dh yackbZ(a) 12.5 (b) 12
fdruh gS\ (c) 24 (d) 25
SSC MTS 25/07/2022 (Shift- 3) 12. A train crosses a 400 m-long platform in 50
(a) 1000 m (b) 750 m seconds. It crosses another 600 m-long
A

(c) 1250 m (d) 500 m platform in 60 seconds. What are the length
8. A train travelling at the speed of x km/h crossed and the speed of the train
a 300 m long platform in 30 seconds, and overtook ,d jsyxkM+h
400 m yacs IysViQkWeZ dks 50 lsds.M esa vkS
a man walking in the same direction at 6 km/h vU; 600 m yacs IysViQkWeZ dks 60 lsds.M esa ikj djrh
in 20 seconds. What is the value of x? jsyxkM+h dh yackbZ vkSj pky fdruh&fdruh gS\
x km/h dh pky ls pyus okyh jsyxkM+h 300 m yacs
SSC CHSL 31/05/2022 (Shift- 1)
IysViQkWeZ 30 dks
lsd.M esa ikj djrh gS vkSj mlh fn'kk
esa6 km/h dh pky ls py jgs O;fDr dks 20 lsd.M (a) 600 m; 72 km/h (b) 550 m; 75 km/h
esa vksojVsad djrhxgSA dk eku Kkr djsaA (c) 500 m; 70 km/h (d) 650 m; 74 km/h

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13. A 250 m-long train passes a man going at a (a) 210 (b) 180
speed of 10 km/h, in the opposite direction, (c) 160 (d) 150
in 9 seconds. How much time (in seconds) will 17. A train corsses a pole in 12 sec and crosses a boy
sitting in another train coming from opposite
the train take to overtake a 200 m-long train
direction in 4 sec. If speed of another train in
completely, running at a speed of 63 km/h 108 km/hr then find the length of first train.
in the same direction? ,d jsyxkM+h fdlh [kaHks dks 12 lsd.M esa vkSj foijh
,d 250 m yach Vsªu 10 km/hr dh pky ls foijhr fn'kk ls vk jgh fdlh nwljh jsyxkM+h esa cSBs ,d yM+ds d
fn'kk esa tk jgs ,d O;fDr dks
9 lsdaM esa ikj djrh 4 lsd.M esa ikj djrh gSA ;fn nwljh jsyxkM+h dh pky
gSA blh Vsªu dks leku fn'kk
63esa
km/hr dh pky ls 108 fdeh@?kaVk gks rks igyh jsyxkM+h dh yackbZ Kkr d
py jgh 200 m yach Vsªu dks iwjh rjg ls ikj djus esa (a) 150 m (b) 180 m
(c) 160 m (d) 200 m
fdruk le; (lsdaM esa) yxsxk\
18. A 150 m long train crosses a man sitting in
ICAR Assistant 29/07/2022 (Shift- 01)
another train coming from opposite direction
(a) 40 (b) 60 in 5 sec. If speed of another train is 60 km/
(c) 45 (d) 50 hr then find time taken by first train to cross

r
250 m long platform.
TYPE - 03

si
150 ehVj yach dksbZ jsyxkM+h foijhr fn'kk esa tk jgs fdl
14. A 50 m long train crosses a man sitting in nwljh jsyxkM+h esa cSBs fdlh O;fDr dks 5 lsd.M esa
an by
another train going in same direction in 10
sec. If speed of first train is 40 km/hr then djrh gSA ;fn nwljh jsyxkM+h dh pky 60 fdeh@?kaVk
rks igyh jsyxkM+h }kjk 250 ehVj yEcs IysViQkWeZ d

n
find speed of second train.
djus esa fy;k x;k le; Kkr dhft,A
50 ehVj yach dksbZ jsyxkM+h mlh fn'kk esa tk jgs fdlh
nwljh jsyxkM+h esa cSBs fdlh O;fDr dks 10 lsd.M esa ikj 20 sec
ja (a) (b) 25 sec
R s
djrh gSA ;fn igyh jsyxkM+h dh pky 40 fdeh@?kaVk gks (c) 30 sec (d) 35 sec
rks nwljh jsyxkM+h dh pky Kkr dhft,A 19. Two trains are moving on two parallel tracks
a th

(a) 18 km/hr (b) 20 km/hr but in opposite directions. A person sitting on

(c) 21 km/hr (d) 22 km/hr a train running at 80km/hr passes the second
15. Two trains are moving in the same direction train in 18 sec. If the length of 2nd train is
ty a

at the speed of 36 km/hr and 48 km/hr. The 1000m, its speed is : (in km/hr)
time taken by faster train to cross a man nks jsyxkfM+;k¡ nks lekukarj iVfj;ksa foijhr fn'kkvksa e
jgh gSaA 80 fdeh@?kaVk dh pky ls pyus okyh jsyxkM+
di M

sitting in the slower train is 33 seconds. What

will be the length of the faster train?
cSBk dksbZ O;fÙkQ nwljh jsyxkM+h dks 18 lsdaM esa
nks jsyxkfM+;k¡ 36 fd-eh@?kaVk rFkk 48 fd-eh-@?kaVk dh
gSA ;fn nwljh jsyxkM+h dh yackbZ 1000 eh gS rks m
pky ls leku fn'kk esa py jgh gSA rhoz pky okyh
pky (fdeh@?kaVk esa) gS %
jsyxkM+h }kjk /heh pky okyh jsyxkM+h esa cSBs ,d iq#"k
(a) 100 (b) 120
dks ikj djus esa fy;k x;k le; 33 lsd.M gSA rhoz
(c) 140 (d) 150
pky okyh jsyxkM+h dh yEckbZ D;k gksxh\
SSC CGL 07/12/2022 (Shift- 04) 20. Trains P and Q are running in the same direction
(a) 770 metres (b) 90 metres on parallel tracks with speeds of x km/h and 90 km/
(c) 110 metres (d) 180 metres h (90 > x), respectively. The faster train passes a man
16. Renu was sitting inside train A, which was sitting in the slower train in 30 seconds. If the length
travelling at 50 km/h. Another train, B whose of train Q is 225 m, then what is the value of x ?
A

length was three times the length of A crossed

her in the opposite direction in 15 seconds. VªsuP vkSjQ lekukarj iVfj;ksa ij ,d gh fn'kk esa Øe'k% x
If the speed of train B was 58 km/h, then the fdeh@?kaVk vkSj 90 fdeh@?kaVk dh pky ls py jgh gSa
length of train A (in m) is : (90 > x) gSA rst pky ls pyus okyh Vªsu /heh pky ls ls
js.kq ,d Vªsu ds Hkhrj cSBh gqbZ Fkh] tks 50 fdeh@?kaVk
pyus dh
okyh Vªsu esa cSBs ,d O;fDr dks 30 lsdaM esa ikj djr
pky ls py jgh FkhAA dh yackbZ ls frxquh yackbZ dh ,d gSA ;fn Vsªsu
Q dh yackbZ 225 ehVj gS]
x dk
rkseku D;k gksxk\
vU; VªsuB us mls foijhr fn'kk ls 15 lsdaM esa ikj SSC PHASE IX 2022
fd;kA ;fn VªsuB dh pky 58 fdeh@?kaVk Fkh] rksA Vªsu
(a) 65 (b) 60
dh yackbZ (ehVj esa) Kkr djsaA
SSC CGL TIER II (12/09/2019) (c) 68 (d) 63

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25. Two trains whose lengths are 450 metres and

TYPE - 04
300 metres are moving towards each other at
21. Two trains each 200m long are moving in the speed of 162 km/hr and 108 km/hr
opposite directions. They cross each other in respectively. If distance between trains is 300
10 seconds. If the speed of one train is 90km/ metres, then in how much time, these trains
h, find the speed of the other train. will cross each other?
nks Vsªusa] ftuesa ls izR;sd dh200
yackbZ
m gS] foijhr nks jsyxkfM+;k¡ ftudh yEckbZ 450 ehVj rFkk 300 ehVj
fn'kkvksa esa py jgh gSaA os 10 lsd.M esa ,d&nwljs dks ,d
ikjnwljs dh vksj Øe'k% 162 fdeh@?kaVk dh pky ls py
90 km/h gS] rks nwljh Vsªu jgh gSA ;fn jsyxkfM+;ksa ds chp dh nwjh 300 ehVj gS] r
djrh gSaA ;fn ,d Vsªu dh pky
dh pky Kkr dhft,A jsyxkfM+;k¡ ,d nwljs dks fdrus le; esa ikj dj ysaxh\
SSC CHSL 25/05/2022 (Shift- 3) SSC CGL MAINS (08/08/2022)
(a) 35 seconds (b) 21 seconds
(a) 90 km/h (b) 45 km/h
(c) 14 seconds (d) 28 seconds
(c) 54 km/h (d) 36 km/h
26. Two trains are running on parallel tracks in
22. A train of length 287m, running at 80 km/h,

r
the same direction at the speed of 80 km/h
crosses another train moving in the opposite and 90 km/h, respectively. The trains crossed

si
direction at 37 km/h in 18 seconds. What is
each other in 3 minutes. If the length of one
the length of the other train ?
train is 230 m, then what is the length (in m)
an by
,d jsyxkM+h ftldh yackbZ 287 eh] pky 80 fdeh@?kaVkof the other train?
gS] nwljh jsyxkM+h] ftldh pky 37 fdeh@?kaVk gS dks nks 18 Vªsusa lekukarj iVfj;ksa ij ,d gh fn'kk esa Øe'k% 80 fdeh@

n
lsdaM esa ikj djrh gSA rks nwljh jsyxkM+h dh pky D;k gS\
vkSj 90 fdeh@?kaVk dh pky ls py jgh gSaA Vªsusa 3 feu
CGL 2019 Tier-II (15/11/2020 )
ja ,d nwljs dks ikj djrh gSaA ;fn ,d Vªsu dh yackbZ 230 ehVj
R s
(a) 300 m (b) 298 m
gS] rks nwljh Vªsu dh yackbZ (ehVj esa) D;k gS\
(c) 285 m (d) 289 m
a th

SSC CGL 21.04.2022 (2nd Shift)

23. Two trains of equal length crosses each other
(a) 270 (b) 300
in same direction in 1 min and in opposite
(c) 250 (d) 230
direction in 10 sec. Find the speed (in km/hr)
ty a

of trains. 27. A 640 metre long train travelling at 80 km/h

leku yackbZ dh nks jsyxkM+h ,d gh fn'kk esa pyrs gq, 1overtook a 540 metre long train travelling at 72
di M

km/h in the same direction. How long did it take

feuV esa vkSj foijhr fn'kk esa pyrs gq, 10 lsd.M esa
the faster train to cross the other train completely?
,d&nwljs dks ikj djrh gSA nksuksa jsyxkM+h dh pky (fdeh@?kaVs
esa) Kkr djsaA 80 km/h dh pky ls py jgh 640 ehVj yEcs jsyxkM+h us
mlh fn'kk eas
72 km/h dh pky ls py jgh 540 ehVj
(a) 60, 72
yEch jsyxkM+h dks ikj fd;kA rst pky okyh jsyxkM+h }k
(b) 60, 54
nwljh jsyxkM+h dks iwjh rjg ls ikj djus esa fdruk le; yxk\
(c) 54, 48
(d) Cannot be determined SSC CHSL 06/06/2022 (Shift 03)
24. Two trains having lengths of 230 m and 240 m (a) 1. 8 minutes 41 seconds
are 130 m apart. They start moving towards
(b) 2. 9 minutes 09 seconds
each other on parallel tracks, at speeds of 160
A

km/h and 200 km/h, respectively. In how much (c) 3. 9 minutes 01 seconds
time will the trains cross each other? (d) 4. 8 minutes 51 seconds
230 m vkSj240 m yEckbZ okyh nks130 Vªsusa
m dh nwjh 28. Train A running at 81 km/h takes 72 sec to
ij gSaA os lekukrj iVfj;ksa ij Øe'k%
160 km/h vkSj overtake train B, when both the trains are
200 km/h dh pky ls ,d&nwljs dh vksj pyuk 'kq: running in the same direction, but it takes
djrh gSaA Vsªusa ,d nwljs dks fdrus le; esa ikj djsaxh\ 36 sec to cross each other if the trains are
SSC CHSL 08/06/2022 (Shift- 2) running in the opposite direction. If the length
(a) 5 Sec (b) 6 Sec of train B is 600 metres, then find the length
(c) 8 Sec (d) 7 Sec of train A. (in metres)

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81 km/h dh pky ls pyus okyh VªsuA, VsuB ls VsªuA vkSj Vsªu

B dh yackbZ dk vuqikr 2 : 3 gSA A dh
vkxs fudyus esa 72 sec dk le; rc ysrh gS] tc pky 36 km/h gS vkSj B dh pky 54 km/h gSA foijhr
nksuksa Vªsusa ,d gh fn'kk esa py jgh gksrh gSa] ysfdufn'kkvksa
;fn esa ;k=kk djrs le;]
10;slsdaM esa ,d nwljs dks
Vªsusa
foijhr fn'kk esa py jgh gS] rks ,d&nwljs dks ikj iwjh rjg ls ikj djrh gSaA VsªuB fdrus le; esa (lsdaM
djus esa36 sec dk le; ysrh gSaA ;fn Vsªu
B dh yackbZ
esa)450 m yach lqjax dks iwjh rjg ls ikj djsxh\
600 ehVj gS] rks Vªsu
A dh yackbZ Kkr djsaA (ehVj esa)
ICAR Assistant 29/07/2022 (Shift- 02)
SSC CGL 13/12/2022 (Shift- 03)
(a) 60 (b) 45
(a) 600 (b) 480
(c) 40 (d) 50
(c) 590 (d) 900
4
29. The lengths of two trains are 380 m and 220 m. 32. The length of Train A is of the length of
The faster of these two trains takes 20 seconds to 5
overtake the other, when travelling in same Train B. The speeds of A and B are 63 km/h
direction. The trains take 12 seconds to cross each and 45 km/h, respectively. Trains A and B

r
other, when travelling in opposite directions. What take 15 seconds to cross each other
is the speed (in km/h) of the faster train? completely when running in opposite

si
nks Vªsuksa dh yackbZ 380 ehVj vkSj 220 ehVj gSA ,d gh directions.
fn'kk How much time (in seconds) will
an by
esa ;k=kk djrs le; bu nksuksa Vªsuksa esa ls rst xfr ls pyus okyh
nwljh Vªsuksa dks ikj djus esa 20 lsdaM dk le; yxrk gSA
Train C of length 160 m, running at a speed
of 90 km/h, take to cross Train A when both

n
the trains are running in the same direction?
foijhr fn'kkvksa esa ;k=kk djrs le; Vªsusa ,d nwljs dks ikj
djus esa 12 lsdaM dk le; ysrh gSaA rst Vªsu dh xfr
ja 4
VsªuA dh yackbZ] Vsªu B dh yackbZ dh gSA A vkSj B
R s
(fdeh@?kaVk esa) D;k gS\ 5
dh pky Øe'k% 63 km/h vkSj45 km/h gSA foijhr
a th

SSC PHASE IX 2022

(a) 108 (b) 126 fn'kkvksa esa pyrs le; VsªuA vkSjB ,d nwljs dks iwjh

(c) 144 (d) 90 rjg ls ikj djus esa 15 lsdaM dk le; ysrh gSaA
90 km/
ty a

30. A train x running at 74 km/h crosses another h dh pky ls py jgh 160 m yackbZ okyh Vsªu C, Vsªu
train y running at 52 km/h in the opposite A dks ikj djus esa (tc nksuksa Vsªusa ,d gh fn'kk esa py
di M

direction in 12 seconds. If the length of y is jgh gSa) fdruk le; (lsdaM esa) ysxh\
two-thirds that of x , then what is the length
of x (in m)? ICAR Assistant 29/07/2022 (Shift- 03)

74 km/h dh pky ls cpus okyh jsyxkM+h x, foijhr (a) 42 (b) 50

fn'kk esa
52 km/h dh pky ls pyus okyh jsyxkM+h y (c) 45 (d) 48
dks12 lsd.M eas ikj djrh gSA ;fn jsyxkM+h
y dh yackbZ]33. Two trains whose length difference is 170 m,
jsyxkM+h
x dh yackbZ dh nks&frgkbZ gS] rksxjsyxkM+h
dh crosses each other in 16 sec when move in
yackbZm( eas) Kkr djsaA opposite direction but crosses each other in
36 sec when move in the same direction. Find
SSC CPO 23/11/2020 (Shift-1) the speed of faster train if speed of slower
A

(a) 168 (b) 252 train is 35 km/hr.

(c) 210 (d) 200

nks jsyxkfM+;ksa dh yEckbZ;ksa dk varj 170 ehVj gSA
fn'kkvksa esa pyrh gqbZ ;s ,d nwljh dks 16 lsdaM esa v
31. The ratio of lengths of Train A and Train B is
2 : 3. The speed of A is 36 km/h and that ofB leku fn'kk esa pyrh gqbZ 36 lsdaM esa ikj dj tkrh gSA
is 54 km/h. They cross each other completely ;fn /heh xfr okyh jsyxkM+h dh pky 35 fdeh@?kaVk gk
in 10 seconds when travelling in opposite rks rst xfr okyh jsyxkM+h dh pky D;k gksxh\
directions. In how much time (in seconds) does
(a) 65 km/hr (b) 70 km/hr
Train B cross completely a tunnel of length
450 m? (c) 78 km/hr (d) 91 km/hr

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TYPE - 05 TYPE - 06
34. Two trains having same length cross an
electric pole in 27 sec. and 24 sec. 39. A train crosses two cyclists in same direction
respectively. Then in how much time they will in 12 seconds and 15 seconds respectively.
cross each other if they are moving in opposite Speed of cyclists are 18 km/hr and 21 km/hr
direction. respectively. Length of train is :
leku yEckbZ dh nks jsyxkM+h fctyh ds ,d •EHks dks
,d jsyxkM+h leku fn'kk esa] 18 fdeh@?kaVk vkSj
Øe'k% 27 lsdaM vkSj 24 lsdaM esa ikj djrh gSA rks fdrus
le; esa os ,d nwljs dks ikj djsaxh ;fn os foijhr fn'kk fdeh@?kaVk dh pky ls pyus okys nks lkbZfdy pkydksa d
esa py jgh gSA Øe'k% 12 lsdaM vkSj 15 lsdaM esa ikj djrh gSA jsyxkM
(a) 22.6 sec (b) 25.4 sec dh yackbZ gS %
(c) 28.2 sec (d) 30.8 sec
(a) 40 m (b) 45 m
35. Two trains of equal length cross a pole in 5
sec and 7 sec respectively. In what time they (c) 50 m (d) 55 m
will cross each other going in same direction
40. A train passes two persons walking with speed
nks leku yackbZ dh jsyxkM+h ,d [kaHks dks Øe'k% 5 lsd.M

r
of 5 m/s and 10 m/s in 6 seconds and 5
vkSj 7 lsd.M esa ikj djrh gSA leku fn'kk esa pyrs gq, os seconds respectively. Both persons are walking

si
,d&nwljs dks fdrus le; esa ikj djsxh\ in opposite direction train. Find the length of
(a) 35 sec
(c) 20 sec
an by (b) 30 sec
(d) 32 sec
train?
,d jsyxkM+h 5 eh@ls ,oa 10 eh@ls dh pky ls py jgs

n
36. Two trains of length 160 m and 180 m
respectively cross a pole in 5 sec and 6 sec nks O;fÙkQ;ksa dks Øe'k% 6 lsds.M ,oa 5 lsds.M esa ikj
respectively. In what time they will cross each
ja ysrh gSA ;s nksuksa O;fÙkQ jsyxkM+h ds foijhr fn'kk
R s
other going in same direction?
jgs gSaA xkM+h dh yEckbZ crk,¡\
nks jsyxkM+h ftldh yackbZ Øe'k% 160 ehVj vkSj 180 ehVj
a th

gS fdlh [kaHks dks Øe'k% 5 lsd.M vkSj 6 lsd.M esa ikj (a) 125 m (b) 150 m
djrh gSA leku fn'kk esa pyrs gq, os ,d&nwljs dks fdrus (c) 160 m (d) 170 m
le; esa ikj djsxh\
ty a

41. A train passes two persons walking in the same

(a) 150 sec (b) 160 sec directions as of train at a speed of 3 km/hr and
(c) 170 sec (d) 180 sec
di M

5 km/hr respectively in 10 seconds and 11

37. Two trains cross a man standing on a platform seconds respectively. The speed of the train is
in 27 sec and 17 sec respectively while in op-
posite direction crosses each other in 23 sec. ,d jsyxkM+h leku fn'kk esa] 3 fdeh@?kaVk vkSj 5 fdeh@
Find ratio of speed of the trains? dh pky ls pyus okys nks O;fÙkQ;ks dks Øe'k% 10 lsdaM
nks jsyxkM+h fdlh IysViQkWeZ ij [kM+s ,d O;fDr dks Øe'k%
vkSj 11 lsdaM esa ikj djrh gSA jsyxkM+h dh pky gS%
27 lsd.M vkSj 17 lsd.M esa ikj djrh gS tcfd foijhr
(a) 28 km/hr (b) 27 km/hr
fn'kk esa pyrs gq, ,d&nwljs dks 23 lsd.M esa ikj djrh
(c) 25 km/hr (d) 24 km/hr
gSA jsyxkM+h ds pky dk vuqikr Kkr dhft,A
(a) 2 : 1 (b) 1 : 3 42. A train crosses two persons travelling at 4 km/
(c) 3 : 5 (d) 3 : 2 h and 6 km/h in the same direction in 12sec
and 14 sec, respectively. The speed of the
A

38. Two trains cross a man standing in a platform

in 18 sec and 24 sec. While crosses each other train is ________.
coming from opposite direction in 20 sec. Find
,d Vªsu mlh fn'kk eas 4 km/h vkSj 6 km/h dh
ratio of speed of the trains.
pky ls py jgs nks O;fDr;ksa dks Øe'k%
nks jsyxkM+h fdlh IysViQkWeZ ij [kM+s ,d O;fDr dks Øe'k% 12 sec vkSj
18 lsd.M vkSj 24 lsd.M esa ikj djrh gS tcfd foijhr 14 sec esa ikj dj tkrh gSA Vªsu dh pky Kkr dhft,A
fn'kk esa pyrs gq, ,d&nwljs dks 20 lsd.M esa ikj djrh SSC CPO 11/09/2022 (Shift - 02)
gSA jsyxkM+h ds pky dk vuqikr Kkr dhft,A (a) 18 km/h (b) 26 km/h
(a) 3 : 2 (b) 4 : 3
(c) 2 : 1 (d) 3 : 1 (c) 20 km/h (d) 24 km/h

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TYPE - 07 ,d Vªsu 6 ?kaVs esa vius xarO; LFkku rd igq¡pus ds fy, 54

fdeh çfr ?kaVs dh xfr ls ;k=kk dj jgh gS] ysfdu 20» nwjh
43. A carriage driving in fog passed a man who was r; djus ds ckn] batu foiQy gks tkrk gS ftlds dkj.k Vªsu
walking at the rate of 6km/hr, in the same
33 feuV dh nsjh ls pyrh gSA le; ij xarO; LFkku rd
direction. He could see the carriage for 4
igq¡pus ds fy, Mªkboj dks Vªsu dh xfr esa fdrus çfr'kr dh
minutes and if visibility was 200m, the speed
o`f¼ djus dh vko';drk gS (nks n'keyo LFkkuksa rd lgh)\
of the carriage was:
CRPF HCM 28/02/2023 (Shift - 01)
dksgjs esa pyus okyh ,d xkM+h] leku fn'kk esa
(a) 11.54%
6 fdeh@?kaVk dh pky ls pyus okys ,d O;fDr dks ikj
(b) 12.94%
djrh gSA og xkM+h dks 4 feuV rd ns• ldrk gS vkSj
(c) 10.96%
;fn n`';rk 200 ehVj Fkh] rks xkM+h dh pky Fkh%
(d) 10.24%
(a) 8.75 km/h (b) 8.5 km/h
47. A train met with an accident 120 km from
(c) 8 km/h (d) 9 km/h
station A. It completed the remaining journey
44. A man could see 400 m during fog when he

r
was moving with 4 Km/hr, he saw a train 5
at of its previous speed and reached 2 hours
coming from behind & disappeared in 3 6

si
minute if the length of train is 200 m, find the late at station B. Had the accident taken place
an by
speed of the train? 300 km further, it would have been only 1
hour late. What is the speed of the train?
,d O;fÙkQ dksgjs ds nkSjku 400 ehVj ns• ldrk gS tc og
LVs'kuA ls 120 fdeh nwj ,d Vªsu nq?kZVukxzLr gks xbZA

n
4 fdeh@?kaVk ls pyrk gS rks mlus ns•k fd ,d jsyxkM+h
ihNs ls vkrh gS vkSj 3 feuV esa xk;c gks tkrh gS ;fn jsyxkM+h 5
ja viuh fiNyh xfr ds ij 'ks"k ;k=kk iwjh dh vkSj LVs'ku
R s
6
dh yackbZ 200 ehVj gS] rks jsyxkM+h dh pky Kkr djsa\
B ij 2 ?kaVs nsjh ls igqaphA vxj nq?kZVuk 300 fdeh vk
a th

(a) 20 km/hr (b) 24 km/hr

(c) 30 km/hr (d) 40 km/hr
gksrh] rks ;g dsoy 1 ?kaVk
nsj gks
rh Vªsu dh xfr D;k gS\
45. A train crosses a man going along the railway (a) 100 km/h
track at 6 Km/hr. The man could see the train (b) 120 km/h
ty a

upto 2 minute and find the speed of the train (c) 60 km/h
if at the time of disappearance the distance
di M

(d) 50 km/h
between train to man was 1200 metre & length
48.
A train meets with an accident after travelling
of train is 300 metre ? 4
6 fdeh@?kaVk dh pky ls tk jgs fdlh O;fÙkQ dks leku 30 kms, after which it moves with 5 of its
original speed and arrives at the destination
fn'kk esa gh pyrh gqbZ ,d jsyxkM+h ikj djrh gSA O;fÙkQ
45 minute late. Had the accident occurred 18
jsyxkM+h dks 2 feuV rd ns• ldrk gS vkSj ;g mldks kms farther, it would have reached 9 minute
1200 eh rd fn•kbZ nsrh gSA ;fn jsyxkM+h dh yEckbZ 300
earlier. Find the distance of the journey and
original speed of the train.
eh gks] rks jsyxkM+h dh pky crk,a\
(a) 39 km/hr (b) 45 km/hr ,d jsyxkM+h dh 30 fdyksehVj dh ;k=kk djus ds ckn
(c) 51 km/hr (d) 57 km/hr nq?kZVukxzLr gks tkrh gS] ftlds ckn og viuh ewy pky
A

4
TYPE - 08 ds ds lkFk pyrh gS vkSj 45 feuV nsjh ls xarO; ij
5
igqaprh gSA ;fn nq?kZVuk 18 fdyksehVj vkSj vkxs gqb
46. A train is travelling with a speed of 54 kmph to rks ;g 9 feuV igys igqap tkrhA ;k=kk dh nwjh vkSj jsyxkM
reach its destination in 6 hours, but after reaching
dh ewy pky Kkr dhft,\
20% of the distance, the engine fails due to which
the train gets delayed by 33 minutes. By how (a) 120 km, 25 km/hr
much percentage does the driver need to increase (b) 125 km, 25 km/hr
the train’s speed to reach the destination on time (c) 130 km, 30 km/hr
(correct to two decimal places)? (d) 120 km, 30 km/hr

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49. A train starts from Delhi at 8:00 am. After 6 50. A man starts from his home to his office with
Hrs. there was a breakdown in the train, due a certain speed but after 1 hr., meets with an
2 accident & resumes his journey after 1 Hr and
to which it travels of its normal speed and becomes 1 hr 36 min late due to reducing his
3
hence becomes 40 mins late. If the breakdown 5
speed to . If the accident had occurred after
occurred 200 km farther then it would have 6
reached its destination 30 min late. Find the 50 Km then he will be late by 1 Hr 20 min.
Find the distance from home to office?
distance covered by the train ?
,d O;fÙkQ ,d fuf'pr pky ls vius ?kj ls vius nÝrj
,d jsyxkM+h fnYyh ls lqcg 8%00 cts pyuk çkjaHk djrh ds fy, fudyrk gS] ysfdu 1 ?kaVs ds ckn] mlds lkFk ,d
gSA 6 ?kaVs ckn] jsyxkM+h esa ,d czsdMkmu gqvk ftlds ckn
nq?kZVuk gksrh gS vkSj og viuh ;k=kk 1 ?kaVs ds ck
2
;g viuh lkekU; pky ds ls ;k=kk djrh gS vkSj blfy, 5
djrk gS vkSj viuh pky dks rd de djus ds dkj.k
3 6
40 feuV nsjh ls igq¡prh gSA ;fn czsdMkmu 200 fdyksehVj 1 ?kaVs 36 feuV nsjh ls igqaprk gSA ;fn nq?kZVuk 50 fdy
vkSj nwj gqvk gksrk rks ;g 30 feuV nsjh ls vius xarO; ds ckn ?kfVr gksrh] rks og 1 ?kaVs 20 feuV nsjh ls igqap
rd igqap tkrhA jsyxkM+h }kjk r; dh xbZ nwjh Kkr dhft,\ ?kj ls nÝrj dh nwjh dk irk yxk,a\

r
(a) 2800 km (b) 3600 km (a) 112.5 km (b) 150 km

si
(c) 4400 km (d) 5200 km (c) 187.5 km (d) 225 km

an by
n
Answer Key
ja
R s
1.(b) 2.(d) 3.(b) 4.(a) 5.(c) 6.(d) 7.(d) 8.(d) 9.(a) 10.(c)
a th

11.(d) 12.(a) 13.(b) 14.(d) 15.(c) 16.(d) 17.(b) 18.(c) 19.(b) 20.(d)
ty a

21.(c) 22.(b) 23.(d) 24.(b) 25.(c) 26.(a) 27.(d) 28.(b) 29.(c) 30.(b)
di M

31.(c) 32.(d) 33.(b) 34.(b) 35.(a) 36.(c) 37.(d) 38.(c) 39.(c) 40.(b)

41.(c) 42.(a) 43.(d) 44.(b) 45.(c) 46.(b) 47.(c) 48.(d) 49.(c) 50.(b)
A

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RACE /nkSM+
(CLASSROOM SHEET)

1000 m 850 m
COMMON STATEMENTS USED IN 
T sec (T + 10) sec
Dead Heat : A dead heat situation is when all
RACE BASED QUESTIONS participants reach the finishing point at the
same instant of time.
nkSM+ vk/kfjr iz'uksa esa iz;qDr lkekU; dFku
MsM ghV ,d ,slh fLFkfr gS ftlesa lHkh izfrHkkxh var
ij ,d gh le; ij igq¡prs gSaA
In a race of 1 km, A beats B by 100 metre.

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

1 fdeh dh nkSM+A,esaB dks 100 ehVj ds varj ls gjkrk EXERCISE

si
gSA 1. In a 100-m race, A beats B by 20 m and B
100 m beats C by 20 m. By how much distance does
an by
A beat C.
B A 100 m dh nkSM+A,esa
B dks 20 m ls gjkrk gS vkSj

n
B, C
A B A:B
1000 m 900 m Speed 10 : 9 dks20 m ls gjkrk gSA
A, C dks fdruh nwjh ls gjkrk gS\
ja
T T SSC CGL 02/12/2022 (Shift- 03)
R s

 In a race of 1 km, A beats B by 10 sec. (a) 64 m (b) 24 m

1 fdeh dh nkSM+A,esa
B dks 10 lsdaM ds varj ls gjkrk gSA
a th

(c) 25 m (d) 36 m
×B A
2. In a 1500 m race, Anil beats Bakul by 150
m and in the same race Bakul beats Charles
A B A:B by 75 m. By what distance does Anil beat
ty a

1000 m 1000 m Charles?

T (T + 10) sec.
1500 m dh nkSM+ eas] vfuy us cdqy150dks m ls
di M

 In a race of 1 km, A can give B a start of 100

metre. gjk;k vkSj mlh nkSM+ esa cdqy us pkYLkZ
75 m lsdks
1 fdeh dh nkSM+A,esa
B dks 100 ehVj dh 'kq:vkr nsrk gSA gjk;kA vfuy us pkYlZ dks fdruh nwjh ls gjk;k gS\
A, B SSC CGL 01/12/2022 (Shift- 01)
100 m
(a) 217.50 m (b) 200.15 m
A B (c) 293.50 m (d) 313.75 m
A B
1000 m 900 m 3. In a1500-m race, if A beats B by 100 m and B
T sec T sec beats C by 150 m, then by what distance (in m)
 A can give B a start of t minutes : This statement does A beat C?
implies that A will start t minutes after B starts
from the starting point. 1500-m dh nkSM+ easA, ;fnB dks100 m ls ijkLr djrk
A, B dks t feuV dh 'kq:vkr nsrk gS % bl dFku dk vFkZ gSA vkSj
B, C dks 150 m ls ijkLr djrk gS] rksA, C dks
A

gS fd 'kq:vkrh fcUnqBlsds t feuV ckn A 'kq: djrk gSA fdruh nwjh(m esa
) ls ijkLr djrk gS\
 In a race of 1 km, A gives B a start of 150 metre SSC CHSL 03/06/2022 (Shift- 2)
and still wins by 10 sec.
(a) 140 (b) 150
1 fdeh dh nkSM+A,esaB dks 150 ehVj dh 'kq:vkr nsrk gS
vkSj fiQj Hkh 10 lsdaM ds varj ls thr tkrk gSA (c) 100 (d) 240
150 m 4. Acan beat B ina 100-metre race by 10 metres.
B can beat C in a 100-metre race by 10 metres.
A B B A What is the ratio (tA : tB : tC), which are the
A B respective times taken by A, B and C to
complete the race?

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A 100 ehVj dh nkSMBesa dks 10 ehVj ls gjk ldrk gSA (a) 15 (b) 20
B 100 ehVj dh nkSM+ C esa
dks 10 ehVj ls gjk ldrk gSA (c) 30 (d) 25
vuqikr (tA : tB : tC) D;k gS] tks nkSM+ dks iwjk djus ds
9. Geeta runs 5/2 times as fast as Babita. In a
race, if Geeta gives a lead of 40 m toBabita,
fy, A, B vkSjC }kjk fy;k x;k lacaf/r le; gS\
find the distance from the starting point where
SSC MTS 07/07/2022 (Shift- 1) both of them will meet (correctup to two
(a) 100 : 90 : 81 (b) 90 : 81 : 100 decimal places).
(c) 100 : 81 : 90 (d) 81 : 90 : 100 xhrk] cchrk ls 5@2 xquk rst nkSM+rh gSA ,d jsl
5. In a linear race of 500 m, A can beat B by
50 m and in a race of 600 m, B can beat C
;fn xhrk] cchrk dks 40 ehVj dh c<+r nsrh gS] rk
by 60 m. By how many metres will A beat C izkjafHkd fcanq ls ml fcanq rd dh nwjh Kkr dhft, tg
in a race of 400 m? os nksuksa feysaxh (n'keyo ds ckn nks LFkkuksa rd iw
500 m dh ,d js[kh; nkSM+ esa] A, B dks 50 m ls SSC CPO 10/11/2022 (Shift-01)
gjk ldrk gS vkSj600 m dh nkSM+ B, esaC dks 60 (a) 66.67 m (b) 65 m
m ls gjk ldrk gSA 400 m dh nkSM+ A, esaC dks (c) 65.33 m (d) 66 m
fdrus ehVj ls gjk,xk\ 10. If the ratio of speeds of A and B is 5 : 6 and

r
SSC CGL 08/12/2022 (Shift- 03) B allows A a start of 70 meters in a 1.2 km
(a) 70 (b) 68 race, who will win the race and by what

si
(c) 76 (d) 72 distance?
6. In a 1200 m race, bike A beats bike B by 100 A vkSjB dh xfr dk vuqikr 5 % 6 gS vkSj B 1.2
an by
m. Bike B beats bike C by 100 m in a 600 m fdeh dh nkSM+Aesa dks 70 ehVj dh 'kq#vkr nsrk gS]
race. If bike A beats bike C by 30 sec in a fdruh nwjh ls vkSj dkSu nkSM+ thrsxkA

n
720 m race, then what is the speed of bike C?
(a) 30m, A
1200 m dh nkSM+ eas ckbd A, ckbd B dks 100 m (b) 200m, B
ja
ls gjkrh gSA 600 m dh nkSM+ esa ckbd B, ckbd C
R s

(c) 130m, B
dks 100 m ls gjkrh gSA ;fn ckbdA 720 m dh (d) The race finishes in a dead heat
a th

nkSM+ eas ckbd C dks 30 lsd.M ls gjk nsrh gS] rks11. In a 1400 m race John reaches the finish point
ckbd C dh crk,aA in 1 min 6 sec, while James reaches the finish
point in 77 sec. By how much distance does
SSC CGL 03/12/2022 (Shift- 01)
ty a

John beat James?

(a)
17
m / sec (b)
26
m / sec 1400 m dh nkSM+ esa tkWu 1 feuV 6 lsd.M esa var f
3
di M

9 rd igqprk gS] tcfd tsEl 77 lsd.M eas var fcUnq rd

17 26 igq¡prk gSA tkWu] tsEl dks fdruh nwjh ls gjkrk gS\
(c) m / sec (d) m / sec
9 3 SSC Phase X 03/08/2022 (Shift- 02)
2 (a) 240 m (b) 220 m
7. A is 1 times faster than B, A gives 60m start (c) 180 m (d) 200 m
3
to B in a race find the length of race if both 12. A can run 1 km in 4 min, and B can cover
finished race at same time. the same distance in 4 min 10 sec. By what
distance can A beat B in a 1 km race?
2
A, B dh rqyuk eas
1 xquk rst gS]
A ,d nkSM+ esa
B A 4 feuV esa 1 fdeh NkSM+ ldrk gSBvkSj
mruh gh
3
nwjh 4 ehVj 10 lsadM esa r; dj ldrk gSA 1 fdeh dh
dks 60 ehVj dh 'kq#vkr nsrk gS] ;fn nksuksa ,d gh
nkSM+A,esa B dks fdruh nwjh ls gjk ldrk gS\
A

le; esa nkSM+ iwjh djrs gSa rks nkSM+ dh yackbZ Kkr(a)djsaA
45 m (b) 40 m
(a) 90 (b) 150 (c) 35 m (d) 30 m
(c) 120 (d) 180 13. Amit and Beenu can cover a 400 m race in
8. In a 500m race, ratio of speed of bobby & Lala 44 seconds and 50 seconds, respectively.
is 3 : 4. If bobby has a start of 140m. Then When Amit finished the race, then Beenu is
bobby wins by? at what distance from the finishing line?
500 ehVj dh ,d nkSM+ esa ckch rFkk ykyk dh pky vfer vkSj chuw 400 ehVj dh nkSM+ Øe'k% 44 ls
dk vuqikr 3 % 4 gS ;fn ckch ds ikl 140 ehVj dh vkSj 50 lsdaM esa iwjh dj ldrs gSaA tc vfer nkSM+
'kq#vkr gS rks ckch fdrus ehVj ls thrsxk\ dj ysrk gS] rks chuw lekiu js[kk ls fdruh nwj gksrh

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(a) 50 m (b) 52 m 19. In a 1500 m race, if vehicle P gives vehicle

(c) 48 m (d) 45 m Q a start of 200 m, then vehicle P wins the
race by 8 sec. Alternatively, if vehicle P gives
14. In a 400-metre race, A runs at a speed of 16
vehicle Q a start of 400 m, the race ends in
m/sec. If A gives B a start of 15 metres and
a dead heat. How long does vehicle P take to
still beats him by 10 sec, then what is the
run 1500 m?
speed of B?
400 ehVj dh nkSM+Aesa]
16 ehVj@lsdaM dh pky ls 1500 m dh jsl eas] ;fn okgu P okgu Q dks 200
nkSM+rk gSA A,;fn
B dks 15 ehVj dh 'kq#vkr nsrk gS m dh c<+r nsrk gS] rks okguP, 8 lsd.M jsl thr
vkSj fiQj Hkh mls 10 lsdaM ls gjk nsrk gS]
B dhrks tkrk gSA blds foijhr] ;fn okguP okgu Q dks 400
pky D;k gS\ m dh c<+r nsrk gS] rks jsl cjkcjh ij lekIr gksrh gSA

SSC CGL 02/12/2022 (Shift- 02)

okgu P dks 1500 m pyus esa fdruk le; yxrk gS\
(a) 11 m/sec (b) 10 m/sec SSC CGL 07/12/2022 (Shift- 01)
(c) 13 m/sec (d) 9 m/sec (a) 44 sec (b) 45 sec
15. In a 100 m race, A runs at 6 km/hr. If A gives (c) 40 sec (d) 60 sec
B a start of 8 m and still beats him by 9 20. In a 200m race, if a gives B a start of 25

r
seconds, what is the speed of B? meters, then A wins the race by 10 seconds.
100 ehVj dh nkSM+A esa6 fdeh@?kaVk dh xfr ls nkSM+rk Alternately, if A gives B a start of 45 meters

si
gSA ;fnA, B dks 8 feuV dh 'kq:vkr nsrk gS vkSj fiQj the race ends in a dead heat. How long does
A take to run 200 m?
an by
Hkh og 9 lsdaM ls gjk nsrk gS]B dh
rksxfr D;k gS\
(a) 4.6 km/hr (b) 4.8 km/hr 200 ehVj dh nkSM+ esa]A,;fnB dks 25 ehVj dh

n
(c) 5.2 km/hr (d) 5.4 km/hr 'kq:vkr nsrk gS] rks
A 10 lsdaM ls nkSM+ thr tkrk gS
16. In a 300 m race A runs at a speed of 9 km/hr. oSdfYid :i ls] ;fn A, B dks 45 ehVj dh 'kq:vkr
ja
He gives a start of 30 m to B and still defeats nsrk gS rks nkSM+ MsM ghV esa lekIr gks A dks
tkrh g
R s

him by 15 sec. What is the speed of B?

200 ehVj nkSM+us esa fdruk le; yxrk gS\
300 ehVj dh nkSM+ A9esa
fdeh@?kaVk dh xfr ls nkSM+rk gSA
a th

og B dks 30 ehVj igys nkSM+us dh nwV nsrk gS vkSj (a) mls77.5 sec (b) 122.5 sec
fiQj Hkh 15 lsdaM ls gjk nsrk
B gSA
dh xfr fdruh gS\ (c) 32.5 sec (d) 22.5 sec
(a) 6.3 km/hr (b) 8.1 km/hr 21. In a 1000 m race, Arjun, Balaji and Charan
ty a

(c) 7.2 km/hr (d) 8 km/hr are running. Arjun beats Balaji by 100 m, and
17. A’s speed is 30% more than that of B. If A Balaji beats Charan by 100 m. In the next
di M

and B run a race on a 117 m length race, what 1000 m race (the speeds are the same as in
part of the length of the race should A give the previous), Balaji gives Charan a head start
B as a head start, so that the race ends in a of 100 m, and Arjun gives Balaji a head start
dead heat? of 100 m. Find the distance by which the
A dh pky B dh pky ls 30» vf/d gSA ;fn A vkSj winner is ahead of the person just behind him.
B, 17 ehVj yach nkSM+ yxkrs gSa] A dksrksnkSM+ dh 1000 m dh nkSM+ esa vtqZu] ckykth vkSj pj.k n
yackbZ dk fdruk Hkkx
B dks 'kq:vkrh c<+r ds :i esa jgs gSaA vtqZu us ckykth
100dks
m ls vkSj ckykth us
nsuk pkfg,] rkfd nkSM+ cjkcjh ij lekIr gks lds\ pj.k dks 100 m ls gjk;kA vxyh 1000 m nkSM+ esa
(a) 90 m (b) 117 m (xfr fiNys dh rjg gh gS) ckykth] pj.k dks 100
(c) 27 m (d) 36 m m dh 'kq#vkr nsrs gSaA vkSj vtqZu] ckykth 100dks
18. In a race of senior citizens, Mr. A can give his m dh 'kq#vkr nsrs gSaA og nwjh Kkr dhft,A ftll
A

friend Mr. B a start of 20 m and Mr. C a start fotsrk Bhd ihNs okys O;fDr ls vkxs gSA
of 39 m in a race of 100 m. How much start SSC CGL 13/12/2022 (Shift- 01)
can Mr. B give Mr. C in a 100 m race?
(a) 100 m (b) 40 m
ofj"B ukxfjdksa dh 100 ehVj dh nkSM+ esa
A vius
Jheku~
(c) 30 m (d) 20 m
nksLrA Jheku B dks 20 ehVj vkSj Jheku~
C dks 39
Jheku~ dks 100 ehVj 22.
ehVj dh c<+r nsrs gSaA Jheku
B, C
A can beat B ina 100-metre race by 10 metres.
B can beat C in a 100-metre race by 10 metres.
dh nkSM+ esa fdrus ehVj dh c<+r nsaxs\ What is the ratio (tA : tB : tC), which are the
(a) 10 m (b) 15 m respective times taken by A, B and C to
(c) 18 m (d) 23.75 m complete the race?

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A 100 ehVj dh nkSMBesa dks 10 ehVj ls gjk ldrk gSA 10

B 100 ehVj dh nkSM+ C esa
dks 10 ehVj ls gjk ldrk gSA (a) 1
19
vuqikr (tA : tB : tC) D;k gS] tks nkSM+ dks iwjk djus ds
fy, A, B vkSjC }kjk fy;k x;k lacaf/r le; gS\ (b)
10
SSC MTS 07/07/2022 (Shift- 1) 19
(a) 100 : 90 : 81 (b) 90 : 81 : 100 9
(c) 100 : 81 : 90 (d) 81 : 90 : 100 (c)
19
23. Priya can run 250 m in 15 seconds and Payal
in 20 seconds. How many meters start can 9
Priya give to Payal in one km race so that the (d)
10
race may end in a dead-heat?
25. A and B run 1 km and A wins by 25 second. A
fç;k 15 lsdaM esa 250 ehVj vkSj ik;y 20 lsdaM esa 250 and C run 1 km and A wins by 275 metre.
ehVj nkSM+ ldrh gSA fç;k ,d fdeh dh nkSM+ esa ik;y dks When B and C run the same distance, B wins
fdrus ehVj rd igys nkSM+us dk volj ns ldrh gS rkfd by 30 sdeconds. The time taken by A to run 1
;g nkSM+ cjkcjh ij lekIr gks\ km is :

r
(a) 100 m (b) 250 m A vkSj B, 1 fdeh nkSM+rs gSaA vkSj25 lsdaM ls thr
tkrk gSA vkSj 1 fdeh nkSM+rs gSaA,vkSj
275 ehVj

si
(c) 150 m (d) 50 m A C
24. In a linear race of 1000 m, A beats B by 50 ls thrrk gSA tc B vkSj C leku nwjh nkSM+rs B, gSa]
30
an by
m or 5 seconds. What is the difference between lsdaM ls thr tkrk gSA
A dks 1 fdeh nkSM+us esa yxus ok
the speeds (in m/s) of A and B? le; gS %

n
1000 m dh jSf[kd nkSM+A,esa B dks 50 m ;k 5 (a) 2 min 25 sec
lsdaM ls gjk nsrk gSA A vkSj B dh pky (m/s eas ) ds (b) 2 min 50 sec
ja
(c) 3 min 20 sec
chp fdruk varj gS\
R s

(d) 3 min 30 sec

SSC CGL 06/12/2022 (Shift- 03)
a th
ty a
di M

Answer Key
1.(d) 2.(a) 3.(d) 4.(d) 5.(c) 6.(a) 7.(b) 8.(b) 9.(a) 10.(c)

11.(d) 12.(b) 13.(c) 14.(a) 15.(b) 16.(c) 17.(c) 18.(d) 19.(a) 20.(a)

21.(d) 22.(d) 23.(b) 24.(b) 25.(a)

A

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Race & Circular Motion/nkSM+ rFkk o`Ùkh;

( Practice Sheet With Solution)
1. In a kilometre race, A beats B by 30 metres 5. A can give 40 metres start to B and 70 metres
or 6 seconds . Find the time taken by A to to C in a race of one kilometre. How many
finish the race. metres start can B give to C in a race of one
kilometre ?
,d fdyksehVj dh nkSM+A,esa
B dks 30 ehVj ;k 6 lsdaM ls
A }kjk nkSM+ iwjh djus esa yxk le; Kkr dhft,A ,d fdyksehVj dh nkSM+A]esa
gjk nsrk gSA B dks 40 ehVj dh LVkVZ
(a) 3 minute ns ldrk gS vkSj
C dks 70 ehVj dh LVkVZ ns ldrk gS]
(b) 3 minute 14 seconds
,d fdyksehVj dh nkSM+Besa] C dks fdrus ehVj dh
(c) 4 minute
LVkVZ ns ldrk gS\

r
(d) 4 minute 14 seconds 1
(a) 31 metre (b) 32 metre
4

si
2. In a 125 m race , A runs at 10 km/hour. A
gives B a start of 5 metres and still beats him 3
an by
by 5 seconds . Find the speed of B. (c) 31 metre (d) 30 metre
4
125 ehVj dh nkSM+Aesa]
10 fdeh@?kaVk dh xfr ls nkSM+rk
6. Ram and Shyam run at 4 km on a course 250

n
gSAA] B dks 5 ehVj dh 'kq#vkr nsrk gS vkSj fiQj Hkh mls m round . If their rates be 5 : 4 , how often
5 lsdaM ls gjk nsrk gSA
B dh xfr Kkr dhft,A does the winner pass the other?
ja
R s

(a) 8 km/h (b) 8.64 km/h jke vkSj ';ke 250 ehVj ds pDdj esa 4 fdeh nkSM+rs gS
(c) 9 km/h (d) 10 km/h ;fn mudh njsa 5 % 4 gSa] rks fotsrk nwljs dks fdruh c
a th

3. In a race of 200 metres, B can give a start of ikl djrk gS\

10 metres to A, and C can give a start of 20 (a) Ram passes Shyam thrice
metres to B. The start that C can give to A,
(b) Ram passes Shyam twice
ty a

in the same race, is

(c) Ram passes Shyam one
200 ehVj dh nkSM+Besa]
] A dks 10 ehVj dh 'kq#vkr ns
di M

(d) Shyam passes Ram twice

ldrk gS] vkSjC, B dks 20 ehVj dh 'kq#vkr ns ldrk
7. In a km race, A beats B by 30 seconds and B
gSA mlh nkSM+C, Aesa]
dks fdruh 'kq#vkr ns ldrk gS\
beats C by 15 seconds. If A beats C by 180
(a) 25 metres (b) 27 metres metres, the time taken by A to run 1 km is.
(c) 29 metres (d) 30 metres ,d fdyksehVj dh nkSM+A, esa]
B dks 30 lsdaM ls gjkrk
4. In a race of one kilometre, A gives B a start gS gS vkSjB, C dks 15 lsdaM ls gjkrk gSA A,
;fnC dks
of 100 metres and still wins by 20 seconds.
180 ehVj ls gjkrk gS] rks
A }kjk 1 fdyksehVj nkSM+us e
But if A gives B a start of 25 seconds, B wins
by 50 metres. The time taken by A to run one fy;k x;k le; gS%
kilometre is (a) 250 sec (b) 205 sec
,d fdyksehVj dh nkSM+A,esa
B dks 100 ehVj dh 'kq#vkr (c) 200 sec (d) 210 sec
nsrk gS vkSj fiQj Hkh 20 lsdaM ls thr tkrk gSA 8. ysfduIn a one-kilometre race A, B and C are the
A

vxj A] B dks 25 lsdaM dh 'kq#vkr nsrk gS]B rks

50 three participants. A can give B a start of 50
m. and C a start of 69 m. The start, which B
ehVj ls thr tkrk gSAA }kjk ,d fdyksehVj pyus esa can allow C is
fy;k x;k le; gS
,d fdyksehVj dh nkSM+ esavkSjC rhu izfrHkkxh gSaA
A,B A,B a
500 700 dks 50 ehVj dh 'kq#vkr ns ldrk gS vkSj
C dks 69 ehVj dh
(a) seconds (b) seconds
29 29 'kq#vkr ns ldrk gSA
B,C dks fdruh 'kq#vkr ns ldrk gS\
(a) 17 m (b) 20 m
1200
(c) seconds (d) 17 seconds (c) 19 m (d) 18 m
29

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9. A takes 4 min 54 sec to run 1 km while B 13. P, Q and R start running around a circular field
takes 5 min in this run. How many meters having circumference 88 metre at the same
ahead of A should B stand at the start so that time from the same point. Speeds of P, Q and
both reach together at the end point of the R are 4 m/minute, 8 m/minute and 11 m/
race, then the distance from the starting point minute. Find after how much time, they will
to the end point is how far is? meet again at the same point for the first time.
P, Q vkSjR ,d gh fcanq ls ,d gh le; esa 88 ehVj
A, 1 fdeh nkSM+ esa 4 feuV 54 lsdaM ysrk gS B tcfd
bl nkSM+ esa 5 feuV ysrk gS- vkjEHk
A ls B esa
fdrus ehVj ifjf/ okys ,d xksykdkj {ks=k ds pkjksa vksj nkSM+uk
djrs gSaA
P, Q vkSjR dh xfr 4 ehVj@feuV] 8 ehVj@feuV
vkxs [kM+k gks fd nkSM+ ds vafre fcanq ij nksuksa lkFk& lkFk
vkSj 11 ehVj@feuV gSA Kkr dhft, fd fdrus le; ckn
igqaps] rks vafre Nksj izkjfEHkd fcanq ls fdruh nwj gS\
os iqu% mlh LFkku ij igyh ckj feysaxsA
(a) 14.5 metre (b) 16 metre (a) 88 min (b) 44 min
(c) 18 metre (d) 20 metre (c) 40 min (d) 60 min
10. In a race P covers a distance of 1 km in 4 14. In 2016 Rio olympic race of 600 m, Bolt beats
minutes and Q in 4 minutes 10 seconds . How Gatlin by 60 m and in race of 500 m, Gatlin
many meters can P give Q a head start in a beats Blake by 25 m. By how many metres will

r
race of 1 km so that both of them reach the Bolt beat Blake in a 400 m race?
target together? 2016 fj;ks vksyafid dh 600 ehVj nkSM+ esa cksYV us x

si
fdlh nkSM+ esaa 1 fdeh dh nwjhP, 4dks
feuV esa rFkk dks 60 ehVj ls gjk;k vkSj 500 ehVj dh nkSM+ esa xSV
an by
Q,4 feUkV 10 lsdaM esa r; djrk gS- 1 fdeh dh nkSM+ esa us Cysd dks 25 ehVj ls gjk;kA 400 ehVj dh nkSM+
P,Q dks fdrusa ehVj dh 'kq#vkr ns ldrk gS fd os nksuksacksYV Cysd dks fdrus ehVj ls gjk,xk\

n
,d lkFk y{; ij igaqPkas\ (a) 170 m (b) 100 m
(c) 58 m (d) 75 m
(a) 40 metre (b) 50 metre
ja
15. A and B run a 7.5 km race on a round course
R s

(c) 30 metre (d) None of these of 270 m. If their speeds are in the ratio 5:3,
the number of times, the winner passes the
a th

11. Two people P and Q start running towards a

circular track of length 400 m in opposite other is:
directions with initial speeds of 10 m/s and A rFkkB, 7-5 fdeh dh ,d nkSM+ 270 ehVj ds ,d o`Ùkkdkj
40 m/s respectively. Whenever they meet, P's eSnku esa nkSM+uk 'kq: djrs gSaA ;fn mudh pky dk vuq
ty a

speed doubles and Q's speed halves. After what % 3 gS rks fotsrk gkjus okys dks fdruh ckj ikj djsxk\
time from the start will they meet for the third
(a) 11 (b) 13
di M

time?
(c) 9 (d) 15
nks O;fÙkQ
P vkSj Q Øe'k% 10 eh@ls vkSj 40 eh@ls 16. dh In a race of 1200 m, Ram can beat Shyam
çkjafHkd xfr ds lkFk foijhr fn'kk esa 400 ehVj yackbZ dsby 200 m or by 20 sec. What must be the
,d xksykdkj VªSd dh vksj nkSM+uk 'kq: djrs gSaA tc Hkhspeed
os of Ram?
feyrs gSa]
P dh xfr nksxquh gks tkrh gSQvkSj
dh xfr vk/h 1200 m dh jsl esa jke] ';ke dks200 m ;k 20
gks tkrh gSA çkjaHk ls fdrus le; ckn os rhljh ckj feysaxs\ lsd.M ls gjk ldrk gSA jke dh pky D;k gksuh pkfg,\
(a) 20 sec (b) 26 sec SSC CPO 11/11/2022 (Shift-01)
(a) 14 m/sec (b) 12 m/sec
(c) 30 sec (d) 15 sec
(c) 10 m/sec (d) 16 m/sec
12. There is a track with a length of 120 meters 17. A gives B a head-start of 10 seconds in a 1500
and 2 people, A & B, are running around it at m race and both fininsh the race at the same
A

12 m/min and 20 m/min respectively in the time. What is the time taken by A (in minutes)
same direction. At how many points will A and to finish the race if speed of B is 6 m/s?
B meet?
A, 1500 ehVj dh nkSMBesa dks 10 lsadM dh 'kq:vkr
120 ehVj dh yackbZ okyk ,d VªSd gS vkSj 2A yksx
vkSj nsrk gS vkSj nksuksa ,d gh le; esa nkSM+ iwjh dj
B blds pkjksa vksj Øe'k% 12 ehVj@feuV vkSj 20 ;fn B dh pky 6 eh@ls- gS] rks A dks nkSM+ iwjh djus
ehVj@feuV dh xfr ls ,d gh fn'kk esa nkSM+ Ajgs gSaAesa fdruk le; (feuV esa) yxk\
vkSjB fdrus fcanqvksa ij feysaxs\ SSC CPO 11/11/2022 (Shift-02)
(a) 1 (b) 2 (a) 3 (b) 4
(c) 3 (d) 4 (c) 8 (d) 5

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18. A can run 250 m in 25 sec and B in 30 sec. 22. In a circular race of 4225 m, X and Y start from
How many metres start can A give to B in a the same point and at the same time at speeds of
km race so that the race may end in a dead- 54 km/h and 63 km/h. When will they meet again
for the first time on the track when they are
heat?
running in the opposite direction?
250 eh dh nwjh r; djus esa
A dks 25 sec dk le; 4225 m dh ,d o`Ùkkdkj nkSM+ X vkSj
esa Y ,d gh fcanq ls vkSj
yxrk gS tcfd mruh gh nwjh r; djus esaB dks 30 ,d gh le; esa 54 km/h vkSj63 km/h dh pky ls nkSM+uk
sec dk le; yxrk gSA ,d fdeh dh nkSM+ esaA, B vkjaHk djrs gSaA ;fn os foijhr fn'kk esa nkSM+ jgsa gksa] rks V
dks fdrus ehVj dh c<+r ns ftlls nkSM+ VkbZ gks tk,A ls dc feysaxs\
SSC CPO 11/11/2022 (Shift-03) SSC CGL (PRE) 24/07/2023 (Shift-2)
(a) 140 seconds (b) 150 seconds
(a) 169.53 m (b) 173.82 m
(c) 130 seconds (d) 120 seconds
(c) 166.67 m (d) 186.34 m
23. In a 200m linear race, if A gives B a start of 25 m,
19. How much percentage should a racer increase then A wins the race by 10 seconds. Alternatively,
speed to reduce the time by 20% to cover a if A gives B a start of 45 m, the race ends in a dead
fixed distance? heat. How long does A take to run 200 m ?
200m dh jSf[kd nkSM esaA,
;fnB dks25 m dk LVkVZ ('kq:vkrh

r
,d fuf'pr nwjh dks r; djus gsrq 20» le; de djus
ykHk) nsrk gS]Arks
nkSM+10dkslsdaM ls thr tkrk gSA oSdfYid
ds fy, /kod dks fdrus izfr'kr pky c<+kuh pkfg,A

si
:i ls ;fn A, B dks45 m dk LVkVZ ('kq:vkrh ykHk) nsrk gS
SSC CPO 10/11/2022 (Shift-03) rks nkSM+ MsM ghV (Ckjkcjh) esa lekIr Agks dks
tkrh
200mgSA
an by
(a) 25% (b) 30% nkSM+us esa fdruk le; yxrk gS \
(c) 40% (d) 35%

n
SSC CGL PRE, 24/07/2023 (Shift-3)
20. In a race of 1200 m on a circular track, A and (a) 78 sec (b) 77 sec
B start from the same place at the same time (c) 78.5 sec (d) 77.5 sec
ja
R s

in the same direction with speeds of 18 km/ 24. Ram and Shyam are racing along a circular track.
h and 27 km/h respectively. How long after The speed of Ram is thrice the speed of Shyam. The
a th

length of the circular track is 1440 m. After the

the start of the race will they meet for the first
start of the race from the same point simult-
time on the track? aneously, Ram meets Shyam for the first time at
o`Ùkkdkj VªSd ij gks1200
jgh m dh ,d nkSM+ A esavkSj the end of the 8th minute. If Ram and Shyam start
ty a

the race again from the same starting point

B ,d gh LFkku ls ,d gh le; ij] ,d gh fn'kk esa
simultaneously, then the time taken by Shyam to
Øe'k%18 km/h vkSj27 km/h dj pky ls nkSM+uk finish the race is: (given that the length of the race
di M

'kq: djrs gSaA nkSaM+ 'kq: gksus ds fdrus le; ckn os VªSd
is same as the length of the track)
ij igyh ckj feysaxsa\ jke vkSj ';ke ,d o`Ùkkdkj iFk ij nkSM+ jgs gSaA jke dh pky ';k
dh pky ls rhu xquh gSA o`Ùkkdkj iFk dh yackbZ m gSA
1440,d
SSC CHSL TIER II 26/06/2023
gh fcanq ls ,d lkFk nkSM+ 'kq: gksus ds ckn] jke 8osa feuV d
(a) 240 sec (b) 520 sec esa igyh ckj ';ke ls feyrk gSA ;fn jke vkSj ';ke ,d gh
(c) 300 sec (d) 480 sec çkjafHkd fcanq ls ,d lkFk fiQj ls nkSM+ 'kq: djrs gSa] rks nkSM
djus esa ';ke }kjk fy;k x;k le; gS (Kkr gS fd nkSM+ dh yackbZ
4 iFk dh yackbZ ds leku gS)
21. A runs times as fast as B. In a race, if A
3
SSC CGL (PRE) 26/07/2023 (Shift-2)
gives a lead of 80 m to B, find the distance (a) 7.5 min (b) 16 min
from the starting point where they both will
(c) 30 min (d) 22.5 min
A

meet.
25. In a kilometre race, Ajay beats Bijay by 100
4 m and Bijay beats Chand by 100 m. By how
A, B dh rqyuk esa xquk rst nkSM+rk gSA ,d nkSM+ esa]many ;fn metre does Ajay beat Chand in the same
3
race?
A, B dks 80 ehVj dh c<+r nsrk gS] rks izkjafHkd fcanq ls og
,d fdyksehVj dh nkSM+ esa] vt; us fct; dks 100 ehVj
nwjh Kkr dhft, tgk¡ os nksuksa feysaxsA
ls gjk;k vkSj fct; us pk¡n dks 100 ehVj ls gjk;kA mlh
SSC PHASE XI 30/06/2023 (Shift-04) nkSM+ esa vt; us pa¡kn dks fdrus ehVj ls gjk;k\
(a) 300 m (b) 360 m (a) 100 m (b) 200 m
(c) 320 m (d) 340 m (c) 190 m (d) 119 m

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26. In a race of 300 m. Abhishek beats Bijay by 400ehVj dh ,d nkSM+ A, esaB dks 5 ehVj ls gjkrk gS-
30 m while Bijay beats Chandan by 50 m. By blh jkLrs ij B, C ls 4 ehVj ls thr tkrk gS] blh jkLrs
what distance should Abhishek beat Chandan
in the same 300 m race?
ij D ,C ls 16 ehVj ls thr tkrk gS] ;fn A rFkkD bl
jkLrs ij nkSM+sa rks dkSu rFkk fdrus ehVj ls thrsxk
300 ehVj dh nkSM+ esa- vfHk"ksd us fct; dks 30 ehVj ls
gjk;k tcfd fct; us panu dks 50 ehVj ls gjk;kA mlh (a) A, 7.2 metre (b) A, 8.4 metre
300 ehVj nkSM+ esa vfHk"ksd dks panu dks fdruh ehVj(c)ls D, 7.3 metre (d) D, 8.4 metre
gjk;k\ 31. In a 1547m race, Arjun reaches in 78 seconds,
while Karan reaches the finish point in 91
(a) 80 m (b) 40 m
second. By how much distance does Arjun beat
(c) 160 m (d) 75 m
Karan?
27. Two friends Manoj and Sagar start running
simultaneously in an opposite direction on a 1547 ehVj dh nkSM+ es vtZqu 78 lsdaM esa vafre f
circular track of the length 2100 m with speed rd ig¡qprk gS] tcfd dj.k 91 lsdaM esa vafre fcUnq rd
of 7m/s and 3 m/s respectively. With every igq¡prk gSA vtZqu] dj.k dks fdruh nwjh ls gjkrk gS\
meeting they exchange their speed and they
(a) 245 m (b) 231 m
meet for a total of ten times. How much

r
distance did sagar cover in total? (c) 220 m (d) 221 m
nks nksLr eukst vkSj lkxj 2100 ehVj yacs ,d xksykdkj
32. The runners are running in a circular track and

si
VªSd ij Øe'k% 7 ehVj@lsdsaM vkSj 3 ehVj@lsdsaM dh they xfr complete one round in 20, 30 and 35
minutes respectively. When will the next meet
an by
ls foijhr fn'kk esa nkSM+uk 'kq: djrs gSaA çR;sd eqykdkratdsthe starting point?
lkFk os viuh xfr dk vknku&çnku djrs gSa vkSj os dqy
/kod ,d xksykdkj VªSd esa nkSM+ jgs gSa vkSj os Øe'k

n
feykdj nl ckj feyrs gSaA lkxj us dqy fdruh nwjh r;
30 vkSj 35 feuV esa ,d pDdj iwjk djrs gSaA 'kq:vkrh
dh\
fcanq ij vxyh ckj dc feysaxs\
ja
R s

(a) 1400 m (b) 700 m

(c) 1050 m (d) None of these (a) After 3 hours 30 min
a th

28. A and B start simultaneously at one end of a (b) After 4 hours 30 min
swimming pool whose length is 50 m. The (c) After 3 hours
swimming race is a race of 1000 m. If A beats (d) After 7 hours
B and meets him 17 times during the course
ty a

and A's speed is 5 m/s, then the speed of B 33. Anil , Sunil, and Ravi run along a circular path
could be. of length 3 km, starting from the same point
at the same time, and going in the clockwise
di M

A vkSj B ,d fLofeax iwy ds ,d Nksj ij ,d lkFk direction. If they run at speeds of 15 km/hr ,
pyuk 'kq: djrs gSa ftldh yackbZ 50 ehVj gSA rSjkdh nkSM+10 km/hr and 8 km/hr respectively, how much
1000 ehVj dh nkSM+ gSA A] ;fn
B dks gjkrk gS vkSj nkSM+ distance in km will Ravi have run when Anil
ds nkSjku mlls 17 ckj feyrk gS vkSj
A dh xfr 5 m/s and Sunil meet again for the first time at the
starting point ?
gS rks
B dh xfr gks ldrh gSA
(a) 1 m/s (b) 3 m/s vfuy] lquhy vkSj jfo ,d gh fcanq ls ,d gh le; ij
(c) 4 m/s (d) 6 m/s nkSM+ 'kq: djrs gS] vkSj nf{k.kkorZ fn'kk esa pyrs g
29. A and B run a 5 km race on a round course of fdeh dh yackbZ ds ,d o`Ùkkdkj iFk ds lkFk nkSM+r
400 m. If their speed are in the ratio 5 : 4, ;fn os Øe'k% gSaA ;fn os Øe'k% 15 fdeh@?kaVk]
the number of times, the winner passes the fdeh@?kaVk vkSj 8 fdeh@?kaVk dh xfr ls nkSM+rs gS
other is
vkSj lquhy ds fiQj ls 'kq:vkrh fcanq ij fiQj ls feyus ij
A

A vkSjB, 400 ehVj ds ,d o`Rrkdkj iFk ij 5 fdeh jfo fdeh esa fdruh nwjh r; djsxk\
nkSM+ yxkrs gSA ;fn mudh xfr 5 % 4 ds vuqikr esa gS] rks
(a) 4.8 (b) 4.5
fdruh ckj] fotsrk nwljs O;fDr dks ikj djrk gS\
(c) 4 (d) 4.2
(a) 1 (b) 2
(c) 3 (d) 5 34. A and B run on a circular path of perimeter
1200 m at different speeds. If they start at the
30. In a race of 400 metres, A beats B by 5 metres.
same time and from the same place, but run
on the same way B beats C by 4 metres, on the
in opposite directions, they meet for the first
same way D beats C by 16 metres, if A and D
time in 3 minutes. If the speed of B is 10.8
run then who will win and by how many meters km/h, then what is the speed (in km/h) of A?

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A vkSjB, 1200 ehVj ifjeki okys ,d o`Ùkkdkj iFk ij A ,d B o`Ùkkdkj iFk ij ,d gh le; vkSj ,d gh LFkku
fHkUu&fHkUu pky ls nkSM+rs gSaA ;fn os ,d gh le; vkSj ,dlsgh nkSM+uk 'kq: djrsAgSA
,d pDdj 40 lasdsUM esa RkFkk
LFkku ls izkjaHk djrs gSa] ysfdu foijhr fn'kkvksa esa nkSM+rs
B ,d gSa]
pDdjrks
50 lasdsUM esa yxkrk gSA rks fdrus le; ckn
os igyh ckj 3 feuV esa feyrs gSaAB;fndh pky 10-8 os nksuksa ,d gh LFkku ij feysxsaA
fdeh@?kaVk gS]A dh
rkspky (fdeh@?kaVk esa) D;k gS\ (a) 200 sec
(a) 12.8 (b) 13.2 (b) 300 sec
(c) 12.5 (d) 13.5 (c) 250 sec
35. In a circular race of 2500 m, a man and a (d) 400 sec
woman start from a point towards opposite 37. A, B and C run on a circular track of length of
directions with speeds of 37 km/h and 35 km/ 1.2 km with speeds of 6 km/hr, 8 km/hr and
h respectively. After how much time from the 9 km/hr respectively. A and B run in the same
start of the race will they meet for the first direction but C runs in the opposite direction.
time? If they all start at the same time and from
2500 ehVj dh ,d o`Ùkkdkj nkSM+ esa] ,d iq#"k vkSj ,dsame place, how many times will A and C meet
efgyk Øe'k% 37 fdeh@?kaVk vkSj 35 fdeh@?kaVk dh pky anywhere on the track by the time A and B

r
meet for the first time anywhere on the track?
ls foijhr fn'kkvksa dh vksj ,d gh fcUnq ls nkSM+uk 'kq:

si
djrs gSaA nkSM+ 'kq: gksus ds fdrus le; ckn os igyh ckjA, B, C ,d 1-2 fdeh yEcs o`Ùkkdkj iFk ij Øe'k% 6
feysaxs\ fdeh@?kaVs] 8 fdeh@?kaVs vkSj 9 fdeh@?kaVAls nkS
an by
(a) 2 min 40 sec (b) 2 min 30 sec o B ,d gh fn'kk esa tcfd C foijhr fn'kk esa nkSM+rk gS
lHkh ,d gh le; ,d gh fcanw ls nkSM+uk 'kq: djrs gS] rk

n
(c) 2 min 5 sec (d) 2 min 20 sec
A vkSjB ds igyh ckj feyus ls igys A o C fdruh ckj
36. A and B start running at the same time and
feysssssaxs\
ja
from the same point around a circle. If A can
R s

complete one round in 40 seconds and B in 50 (a) 5 (b) 6

seconds, how many seconds will they take to
a th

(c) 7 (d) 8
reach the starting point simultaneously?
ty a

Answer Key
di M

1.(b) 2.(b) 3.(c) 4.(a) 5.(a) 6.(a) 7.(b) 8.(b) 9.(d) 10.(a)

11.(b) 12.(b) 13.(a) 14.(c) 15.(a) 16.(b) 17.(b) 18.(c) 19.(a) 20.(d)

21.(c) 22.(c) 23.(d) 24.(b) 25.(c) 26.(d) 27.(c) 28.(c) 29.(b) 30.(c)

31.(d) 32.(d) 33.(a) 34.(b) 35.(c) 36.(a) 37.(c)

A

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CIRCULAR MOTION /o`Ùkh; xfr

(CLASSROOM SHEET)

CIRCULAR MOTION/ o`Ùkh; xfr Example :

A  5 m/s ; B  3 m/s; Track length  240 m If
What kind of questions are asked on Circular Track? they start simultaneously from the same point in
the same direction.
o`rh; iFk ij fdl rjg ds ç'u iwNs tkrs gSa\
;fn os ,d gh fn'kk dh vksj ,d gh fcUnq ls ,d lkFk nkSM+uk
• After how many seconds they will meet for the
'kq: djrs gSaA
first time?/fdrus lsdaM ds ckn os igyh ckj feysaxs\

r
(i) After how many seconds they will meet for the
• After how many seconds they will meet for the

si
first time?/fdrus lsdaM ds ckn os igyh ckj feysaxs\
first time at starting point?/'kq#vkrh fcanq ij os fdrus
lsdaM ds ckn feysaxs\
• an by
At how many points on the track they will
B  3 m/s

n
meet?/os VªSd ij fdrus fcUnqvksa ij feysaxs\ A  5 m/s
• When will be their nth meeting?/os n oha ckj dc
ja
R s
feysaxs\
• At what distance the n th meeting will take
a th

Track length
place?/os n oha ckj fdruh nwjh ij feysaxs\ 240m
Just imagine,
ty a

Two persons are running on circular track, when

they will meet for the first time?
A  5 m/s: B  3 m/s ; Track length  240 m
di M

nks O;fÙkQ xksykdkj VªSd ij nkSM+ jgs gSa] os igyh ckj dc feysaxs\
If they start simultaneously from the same point
in the same direction-
;fn os ,d gh fn'kk dh vksj ,d gh fcUnq ls ,d lkFk nkSM+uk
'kq: djrs gSaA
(ii) After how many seconds they will meet for the
first time at starting point?/'kq:vkrh fcUnq ij os
fdrus lsdaM ds ckn feysaxs\

B  3 m/s
A

A  5 m/s

For the first meeting the faster one has to travel

one round more than the slower one.
igyh ckj feyus ds fy, rst xfr ls nkSM+us okys dks /hes xfr ls Track length
nkSM+us okys ls ,d pDdj vf/d yxkuk iM+rk gSA 240m
Slow Fast
A B
X round (x + 1) round

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A  5 m/s ; B  3 m/s; Track length  240 m If 3. Sohan and Amit started a car race from the
they start simultaneously from the same point in same point in the same direction and at the
the same direction. same time on a circular track of length 1125
m with speeds of 36km/h and 54 km/h,
;fn os ,d gh fn'kk dh vksj ,d gh fcUnq ls ,d lkFk nkSM+uk respectively. After how much time (in seconds)
'kq: djrs gSaA will they meet for the first time since the start
of the race?
(iii) At how many points on the track they will
lksgu vkSj vfer us ,d gh foanq ls ,d gh fn'kk esa vkSj
meet?/ os VªSd ij fdrus fcUnqvksa ij feysaxs\
,d gh le; ij 1125 m yckbZ ds ,d o`Ùkkdkj VªSd ij

B  3 m/s
Øe'k%36 km/h vkSj54 km/h dh pky ls ,d dkj
jsl dh 'kq#vkr dhA jsl 'kq: gksus ds ckn ls fdrus le;
A  5 m/s
ckn (lsadM esa) os igyh okj feysaxs\
SSC CGL (PRE) 27/07/2023 (Shift-1)
(a) 220 (b) 215
Track length (c) 210 (d) 225
240m

r
4. Three persons P, Q, R run along a circular
track at speeds of 3 km/h, 4 km/h, 6 km/h,

si
respectively. If the length of the track is 36

EXERCISE
an by km, then after how much time will they meet
again at the starting point?

n
1. Ali and Badal start from the same position and rhu O;fÙkQP, Q, R ,d o`Ùkkdkj VªSd ij Øe'k% 3
at the same time in a 1200 m circular race, fdeh@?kaVk] 4 fdeh@?kaVk 6 fdeh@?kaVk dh pky l

ja
with speeds of 27 km/h and 45 km/h,
gSaA ;fn VªSd dh yackbZ 36 fdeh gS] rks os fiQ
R s
respectively. Find after how much time they
'kq#vkrh fcanq ij fdrus le; ckn feysaxs\
a th

will meet again on the track for the first time

when they are both running in the same SSC CPO 10/11/2022 (Shift-02)
direction. (a) 38 hours (b) 36 hours
ty a

vyh vkSj ckny ,d gh LFkku ls vkSj ,d gh le; esa1200 (c) 24 hours (d) 28 hours
4. In a circular race along a track 3600 m long, X
m o`Ùkkdkj nkSM+ eas 27Øe'k%
km/h vkSj45 km/h dh
and Y run at the speed of 27 km/h and 45 km/
di M

pky ls nkSM+uk vkjEHk djrs gSaA Kkr dhft, fd os fdrush respectively. Suppose they start walking at
le; ckn iqu% VSªd ij igyh ckj feysaxs tc os nksuksa ,d gh the same time and in the same direction, then
when will they meet again at the starting point?
fn'kk eas nkSM+ jgs gksA
3600 ehVj yacs VªSd ds vuqfn'k ,d o`Ùkkdkj nkSM+ x vkSj esa]
SSC CHSL 01/06/2022 (Shift- 2)
y Øe'k% 27 fdeh@?kaVk vkSj 45 fdeh@?kaVk dh xfr ls n
(a) 280 seconds (b) 240 seconds gSaA eku yhft, fd os ,d gh le; vkSj ,d gh fn'kk esa pyuk
(c) 250 seconds (d) 220 seconds 'kq: djrs gSa] rks os fiQj ls 'kq#vkrh fcanq ij dc feysaxs\
2. In a circular race of 1600 m, A and B start SSC PHASE XI 27/06/2023 (Shift-01)
from the same point and at the same time (a) 720 sec (b) 1440 sec
with speeds of 27 km/h and 45 km/h, (c) 2200 sec (d) 1200 sec
respectively. After how long will they meet
A

6. Two runners, Sony and Mony, start running on

again for the first time on the track when they a circular track of length 200 m at speeds of
are running in the same direction? 18 and 24 km/h, respectively, in the same
1600 m dh o`Ùkkdkj nkSM+ A vkSj
esa B leku fcanq ls direction. After how much time from the start
vkSj leku le; ij Øe'k% 27 km/h vkSj 45 km/h will they meet again at the starting point?
dh pky ls 'kq: djrs gSaA tc os leku fn'kk esa nkSM+ jgsnks /kfodk,a] lksuh vkSj eksuh] ,d gh fn'kk esa Øe'k%
gSa] rks fdrus le; ckn os VªSd ij igyh ckj fiQj feysaxs\ vkSj24 km/h, dh pky ls 200 m yackbZ ds ,d o`Ùkkdkj
SSC CGL TIER I 21/07/2023 (Shift-03) VªSd ij nkSM+uk 'kq: djrh gSaA vkjaHk ls fdrus le; ck
(a) 90 sec (b) 320 sec fiQj ls 'kq#vkrh fcanq ij feysaxh\
CGL PRE, 14/07/2023 (Shift-1)
(c) 240 sec (d) 180 sec

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Join Telegram- Maths by Aditya Ranjan Circular Motion

(a) 120 sec (b) 110 sec nks fe=k

P vkSjQ ,d lkFk ,d o`Ùkkdkj VªSd ij ,d gh fcanq
(c) 100 sec (d) 90 sec ls nkSM+uk 'kq: djrsgSaA os ,d gh fn'kk esa
P,nkSM+rs
6 m/ gS
7. In a race around a circular cycling track of 75 sec dh pky ls nkSM+rk gS Q, vkSj
b m/sec dh pky ls
km, two cyclists are riding at a speed of 30 nkSM+rk gSA ;fn os o`Ùkkdkj iFk ij Bhd nks fcanqvks
km/h and 25 km/h. After what time (in hours)
will they meet at the point from where they nwljs dks ikj djrs gSa vkSj
b ,d çkÑr la[;k gS] tks 6 ls
started their journey? de gS] rksb ds fdrus eku gks ldrs gSa\
75 km ds ,d o`Ùkkdkj lkbfdy VªSd ds ifjr% ,d nkSM+ esa CGL PRE, 14/07/2023 (Shift-3)
nks lkbfdy lokj 30 km/h vkSj25 km/h dh pky ls
(a) 2 (b) 1
lkbfdy pyk jgs gSaA fdrus le; (?kaVksa esa) ds ckn os ml
fcanq ij feysaxs] tgk¡ ls mUgksaus viuh ;k=kk 'kq: dh Fkh\
(c) 4 (d) 3
11. A, B and C run simultaneously, starting from
CGL PRE, 14/07/2023 (Shift-2)
a point, around a circular track of length
(a) 16 (b) 7
(c) 14 (d) 15 1200m, at respective speeds of 2m/s, 4m/s
and 6m/s. A and B run in the same direction,
8. Anjali and Babita are running on a circular track while C runs in the opposite direction to the

r
in opposite directions from same time at same other two. After how much time will they meet
point with speeds of 8 m/sec and 6 m/sec, for the first time?

si
respectively. If the length of the circular track A, B vkSjC ,d lkFk] ,d leku fcanq ls nkSM+uk 'kq: djrs
gSaA1200
os m yackbZ ds ,d o`Ùkkdkj VªSd ds ifjr% Øe'k%
will meet? an by
is 960 m, how many times distinct points they
2m/s, 4 m/s vkSj6 m/s dh pky ls nkSM+rsAgSaA vkSj

n
B ,d gh fn'kk esa nkSM+rs gSa]C tcfd
vU; nks ds foijhr
vatfy vkSj cchrk ,d o`Ùkkdkj VªSd ij ,d gh le; vkSj fn'kk esa nkSM+rk gSA os igyh ckj fdrus le; ds ckn feys

ja
,d gh fcUnq ls foijhr fn'kkvksa esa Øe'k%
8 m/sec vkSj6 SSC CGL TIER I 17/07/2023 (Shift-02)
R s
m/sec dh pky ls nkSM+ jgh gSaA ;fn o`Ùkkdkj VªSd dh
(a) 10 minutes (b) 9 minutes
a th

(c) 12 minutes (d) 11 minutes

yECkkbZ
960 m gS] rks os vyx&vyx feyu fcUnqvksa12.
ij A, B and C start running simultaneously on a
fdruh ckj feysaxh\ circular track of length 120 meters from the
same point with the speeds 2m/s, 3m/s and
ty a

SSC CHSL 09/06/2022 (Shift- 3)

6m/s respectively. A and C are running in anti-
(a) 7 times (b) 6 times clockwise direction and B is running in a
di M

(c) 12 times (d) 14 times clockwise direction. Answer the following

9. Two persons started running on a circular questions:
track at a speed of 20 m/s and 30 m/s in A, B vkSjC ,d gh fcanq ls 120 ehVj yacs o`Ùkkdkj VªSd ij
opposite directions. If the circumference of Øe'k%2m/s, 3m/s vkSj6m/s dh xfr ls nkSM+uk 'kq:
the circular track is 100 m, find at how many
distinct points they will cross each other?
djrs gSaA
A vkSj C okekorZ fn'kk esa nkSM+ jgsBgSa v

nks O;fDr ,d o`Ùkkdkj VªSd ij foijhr fn'kkvksa

20 esa
nf{k.kkorZ fn'kk esa nkSM+ jgk gSA fuEufyf•r loky
m/s vkSj 30 m/s dh pky ls nkSM+uk 'kq: djrs gSaA
tokc nsa%
;fn o`Ùkkdkj iFk dh ifjf/100 m gS] rks Kkr dhft, (i) After how much time from the start all three
will meet again at the starting point?
fd os ,d&nwljs dks fdrus vyx&vyx fcanqvksa ij ikj
djsaxs\ çkjaHk ls fdrus le; ckn rhuksa iqu% çkjafHkd fcanq ij fey
A

(a) 120 seconds (b) 60 seconds

SSC CGL TIER I 19/07/2023 (Shift-03)
(c) 75 seconds (d) 90 seconds
(a) 2 (b) 3
(ii) After how much time from the start all three
(c) 5 (d) 10
will meet for the firs t time anywhere on the
10. Two friends P and Q simultaneously start
track?
running from same point around a circular
track. They run in the same direction. P runs 'kq#vkr ds fdrus le; ckn rhuksa igyh ckj VªSd ij dgha
at 6 m/sec and Q runs at b m/sec. If they cross feysaxs\
each other at exactly two points on the circular (a) 150 seconds (b) 60 seconds
track and b is a natural number less than 6, (c) 75 seconds (d) 120 seconds
then how many values can b take?

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Join Telegram- Maths by Aditya Ranjan Circular Motion

13. A, B and C start running simultaneously from a 16. Ram and Shyam are racing along a circular
point on a circular track 600 m long with speeds track. The speed of Ram is thrice the speed of
of 40m/s, 70m/s, and 80m/s, respectively. A Shyam. The length of the circular track is 1440
and B are moving in a clockwise direction, while m. After the start of the race from the same
C is moving in an anticlockwise direction. After point simult-aneously, Ram meets Shyam for
how many seconds will all the three be together the first time at the end of the 8th minute. If
for the first time on the track? Ram and Shyam start the race again from the
A, B vkSjC 600 ehVj yacs o`Ùkkdkj VªSd ij ,d fcanq ls same starting point simultaneously, then the
Øe'k% 40 ehVj@lsdsaM] 70 ehVj@lsdsaM vkSj 80 ehVj@lsdsaM
time taken by Shyam to finish the race is:
(given that the length of the race is same as
dh xfr ls nkSM+uk 'kq: djrsAgSaA
vkSjB nf{k.kkorZ fn'kk the length of the track)
esa ?kwe jgs gSa]Ctcfd
okekorZ fn'kk esa ?kwe jgk gSA fdrusjke vkSj ';ke ,d o`Ùkkdkj iFk ij nkSM+ jgs gSaA jke dh p
lsdaM ckn rhuksa igyh ckj VªSd ij ,d lkFk gksaxs\ ';ke dh pky ls rhu xquh gSA o`Ùkkdkj iFk dh yackbZ 14
(a) 30 seconds (b) 60 seconds
(c) 75 seconds (d) 90 seconds
m gSA ,d gh fcanq ls ,d lkFk nkSM+ 'kq: gksus ds ckn]
14. Racer A and racer B run a race of 18 km on a 8osa feuV ds var esa igyh ckj ';ke ls feyrk gSA ;fn jke
circular track of length 800 m. Both complete vkSj ';ke ,d gh çkjafHkd fcanq ls ,d lkFk fiQj ls nkSM+ 'kq

r
one round in 200 sec and 250 sec, respectively. djrs gSa] rks nkSM+ lekIr djus esa ';ke }kjk fy;k x;k le;

si
After how much time from the start will the
gS (Kkr gS fd nkSM+ dh yackbZ iFk dh yackbZ ds leku
faster person meet the slower person for the
SSC CGL (PRE) 26/07/2023 (Shift-2)
last time?

an by
/kod A vkSjB, 800 m yackbZ ds ,d o`Ùkh; iFk18
km dh nkSM+ nkSM+rsa gSaA200 nksuksa
sec vkSj
ij
ozQe'k%
(a) 7.5 min
(c) 30 min
(b) 16 min
(d) 22.5 min

n
250
17. Joy and Kat run around a circular track of
sec esa ,d pDdj iwjk djrs gSaA nkSM+ vkjaHk gksus ds fdrus
le; ckn rst O;fDr /hes O;fDr ls vkf[kjh ckj feysxk\
ja length 1100 m in opposite directions with
R s
SSC CGL TIER I 17/07/2023 (Shift-04) initial speed of 6 m/sec and 4 m/sec,
a th

(a) 2700 sec (b) 4000 sec respectively. Starting from the same point
(c) 2250 sec (d) 1800 sec
whenever they meet, Joy's speed halves and
15. Having started from the same point and at the
same time, two runners - P and Q- are running Kat's speed doubles. After how much time from
ty a

around a circular track of length 500m in the beginning will they meet for the second
opposite directions with the speeds of 6 m and time?
di M

10 m, respectively. If they exchange their

speeds after meeting for the first time, who tkW; vkSj dSV
1100 m yackbZ ds ,d o`Ùkkdkj VSªd ds
will reach the starting point first?
ifjr% Øe'k%6 m/sec vkSj 4 m/sec dh izkjafHkd
,d gh fcanq ls vkSj ,d gh le; ij nkSM+uk 'kq: djds] nks
/kod & P vkSjQ & Øe'k%6 m/s vkSj10 m/s dh pky ls foijhr fn'kkvksa esa nkSM+rs gSaA tc Hkh os f
pky ls 500 m yacs ,d o`Ùkkdkj Vªsd ds ifjr% foijhr mlh fcUnq ls 'kq: djrs gq,] tkW; dh pky vk/h gks tkrh
fn'kkvksa esa nkSM+ jgs gSaA ;fn os igyh ckj feyus ds ckn viuh
gS vkSj dSV dh pky nksxquh gks tkrh gSA os 'kq:v
pky ijLij cny ysrs gSa] rks 'kq#vkrh fcanq ij lcls igys
fdrus le; ds ckn nwljh ckj feysaxs\
dkSu igqapsxk\
SSC Phase X 05/08/2022 (Shift- 03)
SSC CGL PRE, 25/07/2023 (Shift-4)
(a) Q (b) P (a) 220 sec (b) 210 sec
A

(c) Both P and Q will reach at the same time (c) 190 sec (d) 200 sec
(d) No one of the P and Q

Answer Key
1.(b) 2.(b) 3.(d) 4.(b) 5.(a) 6.(a) 7.(d) 8.(a) 9.(c) 10.(b)

11.(a) 12.i (a) 12.ii (d) 13.(b) 14.(b) 15.(c) 16.(b) 17.(b)

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 BOAT AND STREAM
(uko vkSj /kjk)
direction.
DEFINITION & FORMULAE ;g fo"k; ewy :i ls ikuh ds çokg ds lkFk ;k foijhr
There are a variety of subconcepts that are fn'kk esa cgus ij ikuh esa fdlh Hkh pht dh xfr dh x.kuk
related to answering questions based on boat and djus ls lacaf/r gSA
streams concept. Given below are the four terms
which are important for a candidate to know to Important Formulae : egRoiw.kZ lw=k
understand the concept of streams.
Given below are a few important formulas
uko vkSj /kjkvksa dh vo/kj.kk ij vk/kfjr ç'uksa dswith the help of which you can solve the
mÙkj nsus ls lacaf/r fofHkUu mi&vo/kj.kk,a gSaA uhps pkj 'kCn based on boat and streams.
questions
fn, x, gSa tks ,d ijh{kkFkhZ ds fy, /kjkvksa dh vo/kj.kk dks uhps dqN egRoiw.kZ lw=k fn, x, gSa ftudh lgk;rk ls
le>us ds fy, egRoiw.kZ gSaA vki uko vkSj ty/kjk ij vk/kfjr ç'uksa dks gy dj ldrs gSaA

r
 Stream//kjk : The moving water in a Candidates must learn these formulas by

si
river is called a stream. heart to ensure they are able to answer the simple
formula based questions correctly and do not end
unh esa cgrs ty dks /kjk dgrs gSaA
 an by
Upstream / ÅèoZizokg
: If the boat is
up losing marks for direct questions.
mEehnokjksa dks bu lw=kksa dks fny ls lh•uk pkfg, rkfd
;g lqfuf'pr gks lds fd os ljy lw=k vk/kfjr ç'uksa dk lgh

n
flowing in the opposite direction to the
stream, it is called upstream. In this case,
the net speed of boat is called upstream
mÙkj nsus esa l{ke gSa vkSj lh/s ç'uksa ds fy, vad ugha xaokrs g
speed.
ja Speed of boat in still water = B
R s
'kkar ty esa uko dh pky
;fn uko /kjk ds foijhr fn'kk esa cg jgh gS] rks bls
ÅèoZizokg dgk tkrk gSA bl fLFkfr esa uko dh dqy xfr of the stream = S
Speed
a th

dks ÅèoZizokg xfr dgrs gSaA /kjk dh pky

1. Downstream Speed of boat = (B + S)
 Downstream/vuqizokg
: If the boat is
flowing along the direction of the stream,
uko dh vuqizokg pky
ty a

it is called downstream. In this case, the 2. Upstream Speed of boat = (B – S)

net speed of boat is called downtream uko dh ÅèoZizokg pky
di M

speed. 3. Speed of boat in still water

;fn uko /kjk ds fn'kk esa cg jgh gS] rks bls vuqizokg 'kkar ty esa uko dh pky
dgk tkrk gSA bl fLFkfr esa uko dh dqy xfr dks
1
vuqizokg xfr dgrs gSaA = (Downstream speed + Upstream speed)
2
 Still Water / 'kkar ty: Under this 4. Speed of the stream//kjk dh pky
circumstance the water is considered to be
stationary and the speed of the water is 1
= (Downstream speed – Upstream speed)
zero. 2
,slh fLFkfr esa ty dks fLFkj ekuk tkrk gS vkSj ty dh
xfr 'kwU; gksrh gSA Points to Remember/Lej.kh; rF;
The questions from this topic may seem to 1. If the total time taken by the boat to row a
A

be confusing until a candidate is aware of the distance of D and reach back to its initial
above-mentioned terms and how they may be position is T then,
used for answering the questions. ;fn uko }kjk D dh nwjh r; djus vkSj viuh çkjafHkd
bl fo"k; ds ç'u rc rd Hkzfer djus okys çrhr gks fLFkfr esa okil vkus esa fy;k x;k dqy le;
T gS] rks
ldrs gSa tc rd fd dksbZ mEehnokj mi;ZqÙkQ 'krks± ls(a)voxr Distance
u between the two places is
gks vkSj ç'uksa dk mÙkj nsus ds fy, mudk mi;ksx dSls fd;k tknks LFkkuksa ds chp dh nwjh
ldrk gSA
This topic basically deals with calculating T B – S
2 2

D=
the speed of anything in the water when it flows 2B
along with the flow of water or in the opposite

[1]
 okil vkrh gS
(b) Average speed of the boat =
B 2
– S2 
Then, speed of man in Still water
2B
uko dh vkSlr pky rks] fLFkj ty esa euq"; dh xfr
2. If it takes T hours more to go to a point S  T2 + T1 
upstream than downstream for the same =
distance. Then,
 T2 – T1 
;fn leku nwjh ds fy, /kjk ds çfrdwy fdlh fcanq ij 4. If the time taken by the boat to row same
tkus esa /kjk ds vuqdwy tkus dh rqyuk
T ?kaVs
esa vf/d distance in downstream is T 1 and in
upstream is T2.
yxrs gSa] rks
;fn uko }kjk vuqçokg esa leku nwjh dks ikj djus esa
T B 2 – S 2  fy;k x;k le; T1 gS vkSj /kjk ds çfrdwy TesagSA
Distance/nwjh
= 2
2S Then, the ratio of speed of the boat to the
3. If a boat travels a distance downstream in speed of stream
T1 hours and returns the same distance rks] uko dh xfr dk /kjk dh xfr ls vuqikr
upstream in T2 hours.
;fn ,d uko /kjk ds vuqdwy ,d nwjhT1 ?kaVs esa r; B  T2 + T1 
= S= T –T
djrh gS vkSj leku nwjh /kjk ds çfrdwy
T2 ?kaVs esa

r
 2 1

si
PRACTICE SHEET
an by 3. A boat takes 48 minutes to cover 12 km

n
SOME BASICS QUESTIONS against the steam, if the speed of stream
is 2 km/hr then what will be the speed of
1.
ja
If the speed of a swimmer is 9 km/hr in
R s
the boat in still water?
still water and the speed of stream is 5 km/
,d uko /kjk dh foijhr fn'kk esa 48 feuV esa
a th

hr then find the speed of swimmer against

the stream and along the stream. 12 fdeh dh nwjh r; djrh gS] ;fn /kjk dh xfr
;fn 'kkar ty esa fdlh rSjkd dh pky 9 fdeh@#?kaVk 2 fdeh@?kaVk gks rks 'kkar ty esa uko dh xfr
o /kjk dh pky 5 fdeh@?kaVk gS rks /kjk ds izfrdwy fdruh gksaxh\
ty a

o /kjk ds vuqdwy rSjrs le; rSjkd dh pky Kkr (a) 17 km/h

di M

dhft,A (b) 15 km/h

(a) 4km/hr, 10 km/hr
(c) 13 km/h
(b) 4km/hr, 14 km/hr
(d) 1.25 km/h
(c) 14km/hr, 16 km/hr
(d) 14km/hr, 18 km/hr 4. A boat while travelling in the direction of
2. The speed fo a boat when travelling stream take 5 hours for 90 km, while
downstream is 32 km/hr, whereas when covering the same distance in the opposite
travelling upstream it is 28 km/hr. What direction of stream, it takes 6 hours then
is the speed of the boat in still water and the speed of stream is :
the speed of the stream?
,d uko /kjk dh fn'kk esa 90 fdehdh nwjh 5
A

/kjk dh fn'kk esa tkrs gq, uko dh pky 32 ?kaVs esa r; djrh gS tcfd /kjk dh foijhr fn'kk
fdeh@?kaVk gS tcfd /kjk ds foijhr uko dh pky esa ;gh nwjh 6 ?kaVs esa r; djrh gS] rks /kjk dh
28 fdeh@?kaVk gSA uko dh pky 'kkar ty esa vkSj
pky gS %
/kjk dh pky D;k gS\
(a) 2 km/hr
(a) 29 km/hr, 3 km/hr
(b) 2.5 km/hr
(b) 30 km/hr, 2 km/hr
(c) 30 km/hr, 8 km/hr (c) 1.5 km/hr
(d) 31 km/hr, 1 km/hr (d) 1 km/hr

[2]
Type-01 Type-02
5. A man rows down a river 15 km in 3 hrs. 9. If the speed of flow of river is 4 km/hr and
1 the speed of boat along the stream is 3
with the stream and returns in 7 hrs. times of the speed against the stream. Then
2
The rate at which he rows in still water is what will be the speed of boat?
: ;fn unh dk cgko 4 fdeh@?kaVk gS vkSj uko /kjk ds
,d O;fDr unh dh /kjk dh fn'kk esa 15 fdeh nwjh cgko ds foijhr fn'kk dh vis{kk /kjk ds lkFk rhu
1
3 ?kaVs esa r; djrk gS rFkk
7 ?kaVs esa og okil xquh jÝrkj ls tkrh gS rks uiko dh pky D;k gksxh\
2 (a) 12 km/hr (b) 16 km/hr
vk tkrk gS] rks 'kkar ty esa mldh xfr D;k gksxh\
(c) 8 km/hr (d) 10 km/hr
(a) 2.5 km/hr (b) 1.5 km/hr
10. The speed of boat in still water is thrice the
(c) 3.5 km/hr (d) 4.5 km/hr
speed of stream. If takes 6 hours to go 48
6. A swimmer walks 30 km along the flow of km against the steam then what is the speed
river in 3 hours 45 minutes and walks 15 of boat is still water in kilometer per hour?
km against the flow in 2 hours 30 min-

r
utes find the speed of boat in still water
'kkar ty esa uko dh pky] /kjk dh pky dk rhu
xquk gSA ;fn /kjk ds foijhr 48 fdeh tkus esa uko

si
and the speed of flow (in km/hr).
,d ukfod unh esa cgko dh vksj 3 ?kaVs 45 feuV dks 6 ?kaVs yxrs gksa] rks 'kkar ty esa uko dh pky
an by
esa 30 fdeh uko pykrk gS rFkk cgko ds fo:¼ 2
?kaVs 30 feuV esa 15 fdeh- uko pykrk gS] fLFkj
(fdyksehVj izfr ?kaVk) D;k gS\
(a) 10 (b) 8

n
ikuh esa uko dh xfr rFkk izokg dh xfr Kkr dhft,A (c) 12 (d) 14

(a) 8 and 1
ja
(b) 7 and 8
11. A man takes 2.2 times as long to row a
R s
distance in upstream as to row the same
(c) 7 and 1 (d) 9 and 10
distance in downstream. If he can row 55
a th

7. A boat moves downstream at the rate of km downstream in 2 hours 30 minutes,

1 km in 7½ minutes and upstream at the what is the speed of the boat in still water?
rate of 5 km an hour. What is the speed
,d O;fDr /kjk ds fo#¼ tkus esa] /kjk ds lkFk
ty a

of the boat in the still water?

tkus ls 2-2 xquk le; ysrk gSA ;fn og 55 fdeh /
,d uko 7-5 feuV esa 1 fdeh dh nj ls vuqçokg
kjk ds lkFk 2 ?kaVs 30 feuV esa uko pyk ldrk gS]
di M

esa pyrh gS vkSj 5 fdeh@?kaVk dh nj ls ÅèoZ çokg

rks 'kkar ty esa uko dh pky D;k gS\
esa pyrh gSA fLFkj ikuh esa uko dh xfr Kkr djsa\
(a) 40 km/hr (b) 8 km/hr
1 (c) 16 km/hr (d) 24 km/hr
(a) 2 km/hr (b) 6 km/hr
2
1
12. The speed of a boat in still water is 5 km/
1 3
(c) 4 km/hr (d) 3 km/hr
2 h. It is found that the boat takes thrice
8. A boat goes downstream in one third the as much time to row up than it does to
time it takes to go upstream. Then, the row down the same distance in the river
ratio between the speed of boat in still stream. Find the speed of the river stream.
A

water and that of the stream is : 1

'kkar ty eas ,d uko dh pky 5 km/h gSA ;g
,d uko ,d fuf'pr nwjh /kjk ds çfrdwy r; djus 3
esa fy, x, le; dh rqyuk esa /kjk ds vuqdwy leku ik;k gS fd uko dks /kjk dh foijhr fn'kk eas ,d
nwjh r; djus esa ,d frgkbZ le; ysrh gSA rks] fLFkj fuf'pr nwjh r; djus esa yxus okyk le;] /kjk
ikuh esa uko dh xfr vkSj /kjk dh xfr ds chp dk dh fn'kk eas ogh nwjh r; djus esa yxus okys le;
vuqikr Kkr djsaA dk rhu xquk gSA unh dh /kjk dh pky Kkr dhft,A
(a) 3 : 1 (b) 1 : 3 SSC CGL 05/12/2022 (Shift- 02)
(c) 1 : 2 (d) 2 : 1

[3]
 23 22 (a) 16 km (b) 18 km
(a) m/sec (b) m/sec
27 27 (c) 21 km (d) 25 km
16. Speed of a boat is 5 km/hr in still water
20 19
(c) m/sec (d) m/sec and the speed of the stream is 3 km/hr. If
27 27 the boat takes 3 hours to go a place and
come back, the distance of the place is:
Type-03
,d uko dh xfr fLFkj ikuh esa 5 fdeh@?kaVk gS vkSj
13. A swimmer run 3 km/hr against the stream èkkjk dh xfr 3 fdeh@?kaVk gSA ;fn uko dks ,d L?Fkku
and goes 1 km in 10 minutes along the
stream, then in how much time will be take
ij tkus vkSj okil vkus esa 3 ?kaVs yxrs gSa] rks ml
to cover 5 km in still water ? LFkku dh nwjh Kkr djsaA
,d ukfod /kjk ds foijhr 3 fdyksehVj ,d ?kaVs (a) 3.75 km (b) 4 km
esa tkrk gS rFkk /kjk dh fn'kk esa 1 fdyksehVj 10(c) 4.8 km (d) 4.25 km
feuV esa tkrk gS] rks fLFkj ikuh esa 5 fdyksehVj
17. The speed of the current is 5 km/hr. A
fdruh nsj esa tk,xk\ motorboat goes 10 km upstream and back

r
again to starting point in 50 minutes. The speed
1 (in km/hr) of the motorboat in still water is

si
(a) 1 hours (b) 1 hours
10 /kjk dh xfr 5 fdeh@?kaVk gSA ,d eksVj cksV 10 fdeh

(c) 1
1
9
hours an by
(d) 40 minutes
Å?oZ çokg esa tkus vkSj çkjafHkd fcanq ij okil vkus
esa 50 feuV dk le; ysrh gSA fLFkj ikuh esa eksVj cksV

n
14. A swimmer can swim 2 km in 15 minute dh xfr (fdeh@?kaVk esa) Kkr djsaA
in a lake in still water and he can swim 4
ja
km along the flow of river in 20 minutes.
(a) 20 (b) 26
R s
if a paper boat is put into river, then how (c) 25 (d) 28
a th

1 18. The speed of a boat in still water is thrice

far will it float in 2 hours?
2 the speed of the stream. If the boat
,d rSjkd >hy esa 'kkar ty esa 15 feuV esa 2 fdeh takes15.5 sec to go to a certain place
rd rSjdj tk ldrk gS rFkk og ,d unh esa /kjk downstream, then find the additional time
ty a

ds lkFk 20 feuV esa 4 fdeh dh nwjh rd rSj ldrk required to cover the same distance
gSA ;fn ml unh esa ,d dkxt dh uko j[k nh travelling upstream.
di M

1
tk,] rks og 2 ?kaVs esa fdruh nwj rd cgdj 'kkar ty eas ,d uko dh pky] /kjk dh dh rhu
2
pyh tk,xh\ xquh gSA ;fn uko /kjk dh fn'kk eas fuf'pr LFkku
(a) 18 km (b) 12 km rd tkus eas 15-5 lsad.M dk le; ysrh gS] rks /
(c) 8 km (d) 10 km kjk dh foijhr fn'kk eas ;k=kk djrs gq, mruh dh
nwjh r; djus ds fy, vko';d vfrfjDr le;
Type-04
Kkr dhft,A
15. A man goes downstream with a boat to
some destination and returns upstream to SSC CPO 11/09/2022 (Shift -02)
his original place in 5 hours. If the speed
(a) 15.5 sec (b) 29 sec
A

of the boat in still water and the stream are

10 km/hr and 4 km/hr respectively, the (c) 31 sec (d) 35 sec
distance of the destination from the
starting place is 3
,d vkneh uko ls fdlh xarO; rd tkus vkSj vius 19. A boat racer can row 21 2 km/h in still
ewy LFkku ij okil vkus esa 5 ?kaVs dk le; ysrk gSAwater. If the speed of river is 12.5 km/h,
;fn fLFkj ikuh esa uko dh xfr vkSj /kjk dh xfr it takes him 40 minutes to row to a place
Øe'k% 10 fdeh@?kaVk vkSj ”4 fdeh@?kaVk gS] rks çkjafHkd
and back, how far off is the place (consider
LFkku ls xarO; dh nwjh Kkr djsaA up to two decimals)?

[4]
 3 jfo fLFkj ty esa ,d uko dks 14 fdeh@?kaVk dh
,d cksV jslj fLFkj ty esa21 fdeh@?kaVk dh
2 pky ls ys tk ldrk gSA ;fn unh 2 fdeh@?kaVk dh
pky ls cksV pyk ldrk gSA ;fn12.5 fdeh@?kaVk pky ls izokfgr gS vkSj ujfo dks mlesa /kjk ds
dh pky ls pyus okyh unh esa] mls ,d LFkku rd foijhr ,d fuf'pr nwjh r; djus esa 3 ?kaVs yxrs gSa
tkus vkSj okil vkus esa
40 feuV dk le; yxrk rks mls /kjk dh fn'kk esa mruh gh nwjh r; djus esa
gS] rks og LFkku fdruh nwj gS (n'keyo ds nks fdruk le; yxsxk\
LFkku rd eku Kkr djsa)\ SSC CHSL 06/08/2021 (Shift- 01)
SSC CGL 06/12/2022 (Shift- 01) (a) 2 hr 20 min (b) 2 hr
(c) 2 hr 15 min (d) 2 hr 30 min
5 2 23. Sunil can row a boat 20 km upstream
(a) 5 km (b) 5 km
27 5 in 1 hour 15 minutes. If the speed of
the current of the river is 2 km/h, then
5 5
(c) 4 km (d) 3 km how much time will he take to row the baot
27 27
30 km downstream ?
20. A man rows to a place 48 km distant and
lquhy] uko dh /kjk ds foijhr 1 ?kaVs 15 feuV esa
comes back in 14 hours. He finds that he
can row 4 km with the stream in the same 20 fdeh rd ys tk ldrk gSA ;fn unh dh /kjk
time as 3 km against the stream. The dh pky 2 fdeh@?kaaVk gS rks /kjk dh fn'kk esa uko
speed of the stream is: dks 30 fdeh ys tkus esa mls dqy fdruk le; yxsxk\
,d vkneh 48 km nwj ,d LFkku ij uko pykdj SSC CHSL 10/08/2021 (Shift- 01)
tkrk gS vkSj 14 ?kaVs eas okil vkrk gSA og ikrk gS
(a) 1 hr 10 min
fd og /kjk ds lkFk 4 km dh nwjh r; dj ldrk (b) 1 hr 45 min
gS] tcfd mlh le; esa /kjk ds foijhr og 3 km
(c) 1 hr 30 min
dh nwjh r; dj ldrk gSA /kjk dh pky gSA
(d) 1 hr 20 min
SSC CGL 07/12/2022 (Shift- 02)
24. A boat can go 15 km downstream and 8km
(a) 1.5 km/h (b) 3.5 km/h upstream in 2 h. It can go 20 km
(b) 1.8 km/h (d) 1 km/h downstreamand 12km upstream in 2 h 50
m. What is the speed in km/h of the boat
21. A boat can travel with a speed of 19 km/
h in still water. If the speed of the stream while going downstream?
is 3 km/h, then what will be the total time dksbZ uko 2 ?kaVs esa /kjk dh fn'kk esa 15 fdeh vkSj
(in hours) taken by the boat to go 88 km
/kjk dh foijhr fn'kk esa 8 fdeh dh nwjh r; dj
downstream and 24 km upsteam ?
,d uko fLFkj ty esa 19 fdeh@?kaVk dh pky ls ldrh gSA ;g 2 ?kaVs 50 feuV esa /kjk dh fn'kk esa
py ldrh gSA ;fn /kjk dh pky 3 fdeh@?kaVk gS 20 fdeh vkSj /kjk dh foijhr fn'kk esa 12 fdeh
rks uko }kjk 88 fdeh /kjk dh fn'kk esa vkSj 24 dh nwjh r; dj ldrh gSA /kjk dh fn'kk esa tkrs
fdeh /kjk dh foijhr fn'kk esa tkus esa dqy fdruk le; uko dh pky (fdeh@?kaVk esa) Kkr djsaA
le; (?kaVs esa) yxsxk\ SSC CHSL 15/08/2021 (Shift- 01)
SSC CHSL 04/08/2021 (Shift- 01) (a) 16 (b) 15
(a) 4.5 (b) 5
(c) 20 (d) 18
(c) 4 (d) 5.5
22. Ravi can row a boat in still water in the 25. The speed of a boat downstream is 150%
speed of 14 km/h. If a river is flowing at more than its speed upstream. If the time
the speed of 2 km/h and Ravi takes 3 hours taken by the boat for going 80 km
to cover a certain distance upstrain, then downstream and 50 km upstream is 8.2
how much time will he take to cover the hours,then what is speed (in km/h) of
same distance downstream ? theboat downstream ?

[5]
 /kjk dh fn'kk esa] fdlh uko dh pky /kjk dh ,d ukSdk 8 ?kaVs esa /kjk dh foijhr fn'kk 25esa
foijhr fn'kk dh bldh pky ls 150» vf/d gSA km vkSj /kjk dh fn'kk esa39 km pyrh gSA ;g
;fn /kjk dh fn'kk esa 80 fdeh vkSj /kjk dh 11 ?kaVs esa /kjk dh foijhr fn'kk35esa
km vkSj
foijhr fn'kk esa 50 fdeh dh nwjh r; djus esa /kjk dh fn'kk esa52 km dh nwjh r; djrh gSA
yxk le; 8-2 ?kaVk gS] rks /kjk dh fn'kk esa uko ;fn ;g ,d leku pky ls ;k=kk djrh gS] rks /kjk
dhpky (fdeh@?kaVk esa) Kkr dhft,A dh pky crkb,A
SSC CHSL 12/08/2021 (Shift- 01) SSC CGL 12/12/2022 (Shift- 01)
(a) 16 (b) 30 (a) 4 km/h (b) 5 km/h
(c) 24 (d) 25 (c) 6 km/h (d) 3 km/h
29. A boat covers a certain distance against
26. A person rows upstream a distance of 55
the stream in 9 hours 36 min and it covers
km in 5 hours and rows downstream a
distance of 75 km in 3 hours. How much the same distance along the stream in 6
time will he take to too a distance of 96 hours. What is the ratio of the speed of
the boat in still water to that of the

r
km in still wates ?
stream?
dksbZ o;fDr /kjk dh foijhr fn'kk esa 55 fdeh dh

si
,d uko /kjk dh foijhr fn'kk esa] ,d fuf'pr
nwjh 5 ?kaVs esa r; djrk gS vkSj /kjk dh fn'kk esa
nwjh dks 9 ?kaVs 36 feuV eas r; djrh gSA vkSj ;g
an by
75 fdeh dh nwjh 3 ?kaVs esa r; djrk gSA mls fLFkj
ty esa 96 fdeh dh nwjh r; djus esa fdruk le;
/kjk dh fn'kk esa leku nwjh dks 6 ?kaVs esa r; djrh

n
gSA fLFkj ty esa uko dh pky vkSj /kjk dh pky
yxsxk\
dk vuqikr D;k gksxk\
ja
SSC CHSL 16/04/2021 (Shift- 01)
R s
(a) 4 hours 40 minutes SSC CGL 12/12/2022 (Shift- 02)
(a) 13 : 3 (b) 9 : 2
a th

(b) 5 hours 20 minutes

(c) 6 hours 10 minutes (c) 11 : 6 (d) 8 : 5
(d) 5 hours 45 minutes 30. A boat can go 40 km downstream and 25
27. X, Y are two points in a river. Points P and km upstream in 7 hours 30 minutes. It
ty a

Q divide the straight line XY into three can go48 km downstream and 36 km
equal parts. The river flows along XY and upstream in 10 hours. What is the speed
di M

the time taken by a boat to row from X to (in km/h) of theboat in still water?
Q and from Y to Q are in the ratio 4 : 5. The ,d uko 7 ?kaVs 30 feuV esa 40 fdeh /kjk dh
ratio of the speed of the boat downstream fn'kk esa vkSj 25 fdeh /kjk dh foijhr fn'kk esa
that of the river current is equal to:
tk ldrh gSA ;g 10 ?kaVs esa 48 fdeh /kjk dh
X vkSjY fdlh unh ij nks fcUnq gSaA P fcUnq
vkSjQ
fn'kk esa vkSj 36 fdeh /kjk dh foijhr fn'kk esa
lh/h js[kkXY dks rhu cjkcj Hkkxksa esa foHkkftr djrs
tk ldrh gSA 'kkar ty esa uko dh pky (fdeh@?kaVk
gSaA unh XY ds lekukarj cgrh gS vkSj fdlh uko
esa) fdruh gksxh\
}kjk X ls Q rd vkSj Q dh ;k=kk esa yxus okys
SSC CPO 09/11/2022 (Shift-03)
le; dk vuqikr 4 % 5 gSA /kjk dh fn'kk esa uko dh
(a) 6 (b) 12
A

pky vkSjunh dh /kjk dh pky dk vuqikr Kkr djsaA

(c) 9 (d) 15
SSC CGL 13/08/2021 (Shift- 01)
31. A boat covers a round trip journey between
(a) 3 : 10 (b) 3 : 4
two points A and B in a river in T hours.
(c) 10 : 3 (d) 4 : 3
If its speed in still water becomes 2 times,
28. A boat moves 25km upstream and 39km
80
downstream in 8 hours. It travels 35km it would take T hours for the same
161
upstream and 52km downstream in 11 journey. Find the ratio of its speed in still
hours. What is the speed of the stream if water to the speed of the river
it travels at a uniform speed?

[6]
 dksbZ uko fdlh unh esa nks fcUnqvksa
A vkSj B ds 1
,d uko 5 fdeh ÅèoZizokg vkSj
7 fdeh vuqizokg
chp jkmaM&fVªi ;k=kk okyh nwjh T ?kaVs
dks esa r; 2
45 feuV esa tk ldrh gSA og 25 feuV esa 5 fdeh
djrh gSA ;fn fLFkj ty esa bldh pky nqxquh gks
vuqizokg vkSj 2-5 fdeh ÅèoZizokg ij Hkh tk ldrh
80
tkrh gS] rksbls mlh nwjh dks r; djus esa T gSA 6 fdeh ÅèoZizokg tkus esa fdruk le; (feuVksa
161
?kaVs yxsaxsA fLFkj ty esa bldh pky dk] unh dhesa) yxsxk\
SSC CGL Tier-II (18/11/2020)
pky ls vuqikr Kkr djsaA
(a) 30 (b) 24
SSC CGL 23/08/2021 (Shift- 01)
(c) 36 (d) 32
(a) 11 : 1 (b) 161 : 40 35. A swimmer swims from a point P against
(c) 1 : 11 (d) 2 : 1 the current for 6 min and then swims back
32. Abhi rows upstream a distance of 28 km in along the current for next 6 min and
4 hours and rows downstream a distance of reaches at a point Q. If the distance
50 km in 2 hours. To row a distance of between P and Q is 120 m then the speed
44.8 km in still water, he will take : of the current (in km/h) is:
vfHk /kjk ds izfrdwy 28 fdeh 4 ?kaVs esa tkrk gS rFkk,d rSjkd ,d fcUnq P ls /kjk ds foijhr 6 feuV
/kjk ds vuqdwy 50 fdeh 2 ?kaVs esa r; djrk gSA fLFkjrd rSjrk gS vkSj fiQj vxys 6 feuV ds fy, /kjk

r
ty esa 44-8 fdeh dh nwjh r; djus esa mls fdruk ds lkFk rSjrk gS vkSj ,d fcUnq
Q ij igq¡prk gSA

si
le; yxsxk\ ;fn P vkSj Q ds chp dh nwjh120 m gS] rks /
an by
SSC CGL Tier-II (11/09/2019)
(a) 2.8 hours (b) 3.2 hours
kjk dh pky (km/h esa
) gSA
SSC CGL 01/12/2022 (Shift- 03)

n
(c) 2.4 hours (d) 2.2 hours (a) 0.4 (b) 0.2
33. The speed of boat in still water is 18 km/ (c) 1 (d) 0.6

ja
h and the speed of the current is 6 km/
36. A boat can go 2.4 km upstream in 16
R s
h. In how much time (in hours) will the
minutes. The ratio of the speed of the boat
boat travel a distance of 90 km upstream
a th

in still water to the speed of the stream

and the same distance downstream ? is 8 : 3. How much time (in hours) will the
fLFkj ty esa ,d uko dh pky 18 fdeh@?kaVk gS boat take to go 21.6 km in still water and
rFkk /kjk dh pky 6 fdeh@?kaVk gSA ;g uko /kjk 33 km downstream?
ty a

ds izfrdwy 90 fdeh rFkk bruh gh nwjh /kjk ds ,d uko /kjk ds foijhr 2.4 km dh nwjh16
vuqdwy fdrus le; (?kaVk esa) esa r; djsxh\ feuV esa r; dj ldrh gSA fLFkj ty esa uko dh
di M

SSC CGL Tier-II (12/09/2019) pky vkSj /kjk dh pky dk vuqikr 8 : 3 gSA uko
1 1 dks fLFkj ty esa
21.6 km vkSj /kjk dh fn'kk esa
(a) 9 (b) 11 33 km tkus esa fdruk le; (?kaVksa esa) yxsxk\
2 4
(c) 12 (d) 10 ICAR Assistant 29/07/2022 (Shift- 03)
1
34. A boat can go 5 km upstream 7 km 5 19
2 (a) (b)
downstream in 45 2 minutes. It can also 2 6
go 5 km downstream and 2.5km upstream
in 25 minutes. How much time ( in 17 13
(c) (d)
minutes) will it take to go 6 km upstream ? 6 6
A

Answer Key
1.(b) 2.(b) 3.(a) 4.(c) 5.(c) 6.(c) 7.(b) 8.(d) 9.(c) 10.(c)

11.(c) 12.(b) 13.(c) 14.(d) 15.(c) 16.(c) 17.(c) 18.(a) 19.(a) 20.(d)

21.(d) 22.(c) 23.(c) 24.(b) 25.(d) 26.(b) 27.(c) 28.(a) 29.(a) 30.(c)

31.(a) 32.(a) 33.(b) 34.(c) 35.(d) 36.(b)

[7]
Join Telegram- Maths by Aditya Ranjan Boat & Stream

Boat & Stream/uko vkSj /kjk

(Practice Sheet With Solution)
1. A boat takes 19 hours for travelling 5. A boat goes 4 km upstream and 4 km
downstream from point A to point B and downstream in 1 hour. The same boat goes 5
coming back to a point C which is at midway km downstream and 3 km upstream in 55
between A and B. If the velocity of the stream minutes. What is the speed (in km/hr) of boat
is 4 kmph and the speed of the boat in still in still water?
water is 14 km/h, what is the distance ,d uko 1 ?kaVs esa /kjk ds çfrdwy 4 fdeh vkSj /kjk ds
between A and B?
vuqdwy 4 fdeh tkrh gSA ogh uko 55 feuV esa /kjk ds
,d uko fcanqA ls fcanqB rd /kjk ds vuqdwy ;k=kk vuqdwy 5 fdeh vkSj /kjk ds çfrdwy 3 fdeh tkrh gSA
djus vkSj fcanq
C ij okil vkus esa 19 ?kaVs dk le; ysrh
'kkar ty esa uko dh xfr (fdeh@?kaVk esa) D;k gS\

r
gS] tks fcanq
A vkSjB ds chp esa gSA ;fn /kjk dh xfr 4
(a) 6.5 (b) 7.75
fdeh çfr ?kaVs gS vkSj fLFkj ty esa uko dh xfr 14 (c) 9

si
(d) 10.5
fdeh@?kaVkA gS]
vkSjB ds chp dh nwjh fdruh gS\ 6. Mahesh rows to the place 80 km away and back
an by
(a) 180 km (b) 160 km in 20 hours. He finds that he can row 8 km
(c) 140 km (d) 120 km downstream in the same time as 4 km upstream.

n
2. Ajay kumar can row a boat d km upstream and The speed of the boat in still water is.
the same distance downstream in 5 hours 15 egs'k uko ls 80 fdeh dh nwjh r; djrk gS vkSj 20 ?kaVs
ja
minutes. Also, he can row the boat 2d km
esa okil vkrk gSA og ikrk gS fd og /kjk ds vuqdwy 8
R s

upstream in 7 hours. How long will it take to row

the same distance 2d km downstream for ajay? fdeh dh nwjh mrus gh le; esa r; dj ldrk gS ftruh
a th

vt; dqekj 5 ?kaVs 15 feuV esa ,d uko dks /kjk ds fd /kjk ds çfrdwy 4 fdeh dh nwjh r; djus esaA fLFkj
çfrdwy d fdeh vkSj /kjk ds vuqdwy leku nwjh r; dj ty esa uko dh xfr gSA
ldrk gSA lkFk gh] og 7 ?kaVs esa uko dks /kjk ds çfrdwy(a) 9 km/h (b) 7 km/h
ty a

(c) 2 km/h (d) 5 km/h

2d fdeh rd pyk ldrk gSA vt; dks leku nwjh 2 d
7. A boat can travel 20 km downstream in 24
fdeh /kjk ds vuqdwy r; djus esa fdruk le; yxsxk\ min. The ratio of the speed of the boat in still
di M

(a) 4 hrs 10 min (b) 3 hrs 15 min water to the speed of the stream is 4 : 1. How
(c) 3 hrs 30 min (d) 4 hrs 1 min much time will the boat take to cover 15 km
3. A boat whose speed in still water is 9 kmph, upstream?
goes 12 km downstream and comes back in 3
hrs. Find the speed of the stream?
,d uko 24 feuV esa /kjk ds vuqdwy 20 fdeh dh ;k=kk
,d uko ftldh 'kkar ty esa xfr 9 fdeh çfr ?kaVs gS] dj ldrh gSA fLFkj ty esa uko dh xfr dk /kjk dh xfr
/kjk ds vuqdwy 12 fdeh tkrh gS vkSj 3 ?kaVs esa okil ls vuqikr 4 % 1 gSA uko dks /kjk ds çfrdwy 15 fdeh
vkrh gSA /kjk dh xfr Kkr dhft;s\ dh nwjh r; djus esa fdruk le; yxsxk\
(a) 20 mins (b) 22 mins
(a) 1 km/h (b) 3 km/h
(c) 5 km/h (d) 4 km/h (c) 25 mins (d) 30 mins
4. A steamer moves with a speed of 4.5 km/h in 8. If the upstream speed of a boat is 50% less
than the downstream speed of the boat and if
A

still water to a certain upstream point and

comes back to the starting point in a river a object is thrown in the river it covers 100m
which flows at 1.5 km/h The average speed of in 50 sec, then how much distance boat can
steamer for the total journey is. cover in still water in 5 hours?
,d LVhej fLFkj ikuh esa 4-5 fdeh@?kaVk dh xfr ls /kjk ;fn ,d uko dh /kjk ds çfrdwy xfr uko dh /kjk ds
ds çfrdwy ,d fuf'pr fcanq rd tkrk gS vkSj 1-5 vuqdwy xfr ls 50» de gS vkSj ;fn dksbZ oLrq unh esa iQs
fdeh@?kaVk dh xfr ls cgus okyh unh esa çkjafHkd fcanqtkrh
ij gS rks og 50 lsdaM esa 100 ehVj dh nwjh r; djrh gS
okil vkrk gSA iwjh ;k=kk ds fy, LVhej dh vkSlr xfr gSA rks 'kkar ty esa uko 5 ?kaVs esa fdruh nwjh r; dj ldrh gS\
(a) 12 km/h (b) 10 km/h (a) 900 km (b) 100 km
(c) 6 km/h (d) 4 km/h (c) 120 km (d) 108 km

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9. The ratio of the speed of boat in still water to ,d O;fÙkQ dks /kjk dh fn'kk16 esakm tkus esa 15 feuV
the speed of stream is 16 : 5. A boat goes 16.5
yxrs gSa] tks /kjk ds foijhr fn'kk esa leku nwjh r; djus es
km in 45 minute upstream, find the time
taken by boat to cover the distance of 17.5 km fy, x, le; ls 25» de gSA O;fÙkQ fLFkj ty esa ,d ?kaVs esa
downstream. fdrus fdyksehVj uko pyk ldrk gS\ (fudVre iw.kZ la[;k
'kkar ty esa uko dh xfr dk /kjk dh xfr ls vuqikr 16 % 5 rd iw.kkZafdr)
gSA ,d uko /kjk ds çfrdwy 45 feuV esa 16-5 fdeh CGL PRE, 14/07/2023 (Shift-4)
tkrh gS] /kjk ds vuqdwy 17-5 fdeh dh nwjh r; djus esa (a) 56 (b) 60
uko }kjk fy;k x;k le; Kkr dhft,A (c) 58 (d) 54
(a) 30 minutes (b) 25 minutes 14. The speed of boat a down the stream is 125%
(c) 50 minutes (d) 45 minutes of the speed in still water. If the boat takes
10. A boat covers 24 km upstream and 36 km 30 minutes to cover 20 km in still water, then
downstream in 6 hours while it covers 36 how much time (in hours) will it take to cover
1 15 km upstream?
km upstream and 24 km downstream in 6
2 /kjk dh fn'kk esa uko dh pky] fLFkj ty esa uko dh
pky dh 125» gSA ;fn fLFkj ty esa uko dks
20 km dh

r
hours. The velocity of the current is:
,d uko /kjk ds çfrdwy 24 fdeh vkSj /kjk ds vuqdwy nwjh r; djus esa 30 feuV dk le; yxrk gS] rks crkb,

si
36 fdeh 6 ?kaVs esa r; djrh gS tcfd ;g 36 fdeh /kjk fd mls /kjk ds foijhr fn'kk esa15 km dh nwjh r;
djus esa fdruk le; (?kaVksa esa) yxsxk\
an by
1
ds çfrdwy vkSj 24 fdeh /kjk ds vuqdwy
6 ?kaVs esa
2 SSC CGL TIER I 19/07/2023 (Shift-03)
r; djrh gSA /kjk dk osx gS%

n
3 1
(a) 1 km/hr (b) 1.5 km/hr (a) (b)
4 2
ja
(c) 2 km/hr (d) 2.5 km/h
1
R s

11. In a fixed time, a boy swims double the distance (c) (d) 1
4
along the current that he swims against the
a th

15. A boat can go 60 km downstream and 40 km

current. If the speed of the current is 3 km/
hr, the speed of the boy in still water is. upstream in 12 hours 30 minutes. It can go 84
km downstream and 63 km upstream in 18
,d fuf'pr le; esa] ,d yM+dk /kjk ds lkFk nqxquh nwjh hours 54 minutes. What is the speed (in km/h,
ty a

rSjrk gS ftruh nwjh og /kjk ds foijhr rSjrk gSA ;fn /kjk to the nearest integer) of the boat in still water?
dh xfr 3 fdeh@?kaVk gS] rks fLFkj ty esa yM+ds dh xfr gSA,d uko 12 ?kaVs 30 feuV esa /kjk ds vuqdwy
60 km
di M

(a) 6 km/hr (b) 9 km/hr

vkSj /kjk ds çfrdwy40 km tk ldrh gSA ;g 18 ?kaVs
(c) 10 km/hr (d) 12 km/hr
12. The speed of the stream is 4 km/h. The time
54 feuV esa /kjk ds vuqdwy
84 km vkSj /kjk ds çfrdwy
taken by a boat to cover a certain distance 63 km tk ldrh gSA 'kkar ty esa uko dh pky (km/
upstream is equal to 2.5 of the time taken by h esa] fudVre iw.kkZad rd) fdruh gS\
it to cover the same distance downstream.
SSC CGL TIER I 20/07/2023 (Shift-01)
What is the speed (in km/h) of the boat in still
water? (a) 7 (b) 8
(c) 9 (d) 10
/kjk dh xfr 4 fdeh@?kaVk gSA ,d uko }kjk /kjk ds çfrdwy
,d fuf'pr nwjh r; djus esa fy;k x;k le;] /kjk ds vuqdwy 16. A boat's speed in still water is 45 km/h, while
the river is flowing at a speed of 15 km/h. The
leku nwjh r; djus esa fy, x, le; ds 2-5 ds cjkcj gSA time taken to cover a certain distance
'kkar ty esa uko dh xfr (fdeh@?kaVk esa) D;k gS\
A

upstream is 9 h more than the time taken to

(a) 8 (b) 10 cover the same distance downstream. Find the
1 1 distance (in km).
(c) 7 (d) 9
2 3 'kkar ty esa ,d uko dh pky 45 km/h gS] tcfd unh
13. A man takes 15 minutes to row 16 km 15 km/h dh pky ls cg jgh gSA /kjk ds foijhr fn'kk
downstream, which is 25% less than the time esa ,d fuf'pr nwjh r; djus esa yxk le;] /kjk ds fn'kk
he takes to row the same distance upstream.
How many kilometres can the man row in an
esa leku nwjh r; djus esa yxs le; ls 9 ?kaVs vf/d gSA
hour in still water? (Rounded off to nearest nwjhkm( esa) dh x.kuk djsaA
whole number) SSC CGL TIER I 20/07/2023 (Shift-04)

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(a) 540 (b) 320 21. A boat takes 4 hours to travel from P to Q
(c) 480 (d) 450 downstream and from Q to P upstream. What
17. A boat can cover 120 km upstream and back is the speed (in km/h) of the boat in still
in a total of 30 hours, and 25 km upstream water, if the distance between P to Q is 6 km
and 40 km downstream in a total of 7 hours. and speed of the river is 2 km/h?
How much distance will the boat cover in 16 ,d uko /kjk ds vuqdwyP ls Q rd vkSj /kjk ds izfrdwy
hours in still water? Q ls P rd tkus esa4 ?kaVs dk le; ysrh gSAP;fn
ls Q ds
,d uko }kjk /kjk dh foijhr fn'kk esa120 km tkus vkSj chp dh nwjh6 fdeh- gS vkSj unh ds izokg dh xfr 2
okil vkus esa dqy30 ?kaVs dk le; yxrk gS] vkSj ml uko fdeh@?kaVk gS] rks 'kkar ty esa uko dh pky (fdeh@?ka
dks /kjk dh foijhr fn'kk esa
25 km rFkk /kjk dh fn'kk esa fdruh gksxh\
40 km tkus esa dqy 7 ?kaVs dk le; yxrk gSA og uko 'kkar ICAR Mains, 08/07/2023 (Shift-1)
ty esa 16 ?kaVs esa fdruh nwjh r; dj ysxh\ (a) 3 (b) 4
SSC CGL (PRE) 24/07/2023 (Shift-1) (c) 6 (d) 2
(a) 200 km (b) 180 km 22. Speed of stream is 4 km/hr and the speed of
(c) 175 km (d) 225 km the boat is 11 km/hr. In how much time will

r
18. A boat covers a distance of 80 km downstream in the boat cover a distance of 21 km upstream

si
8 h while it takes 10 h to cover the same distance and 45 km downstream?
upstream. What is the speed (in km/h) of the boat /kjk dh pky 4 fd-eh-@?kaVk gS vkSj uko dh pky 11 fd-eh
an by
in still water? @?kaVk gSA uko /kjk ds izfrdwy 21 fd-eh- vkSj /kj
,d uko /kjk dh fn'kk esa80 km dh nwjh 8 ?kaVs esa r; vuqdwy 45 fd-eh- dh nwjh fdrus le; esa r; djsxh\

n
djrh gS] tcfd /kjk dh foijhr fn'kk esa leku nwjh r; SSC CHSL 13/03/2023 (Shift-01)
djus esa 10 ?kaVs dk le; ysrh gSA 'kkar ty esa uko dh pky (a) 6 hours (b) 3 hours
ja
( km/h esa) dh x.kuk djsaA
R s

(c) 4 hours (d) 7 hours

SSC CGL PRE, 24/07/2023 (Shift-4) 23. A boat can travel 104 km downstream in 8
a th

(a) 18 (b) 12 hours. If the speed of the stream is 2 km/h,

(c) 9 (d) 16 then find in what time will it be able to cover
13 km upstream?
19. Dharmendra can row 80 km upstream and 110
,d uko 8 ?kaVs esa /kjk dh fn'kk eas 104 fdeh dh nw
ty a

km downstream in 13 hours. Also, he can row

60 km upstream and 88 km downstream in 10 r; dj ldrh gSA ;fn /kjk dh pky 2 fdeh@?kaVk gS]
di M

hours. What is the speed (in km/h) of the rks Kkr dhft, fd og uko /kjk dh foijhr fn'kk esa
current?
13 fdeh dh nwjh fdrus le; esa r; dj ik,xh\
/eZsanz 13 ?kaVs esa /kjk ds foijhr fn'kk
kmesavkSj
80/kjk
SSC CPO 09/11/2022 (Shift-02)
ds fn'kk esa 110
km uko pyk ldrk gSA lkFk gh] og 10
?kaVs esa /kjk ds foijhr fn'kk esa
km 60
vkSj /kjk ds fn'kk 2 4
(a) 2 hours (b) 1 hours
3 9
esa 88km uko pyk ldrk gSA /kjk dh pky (km/h esa)
Kkr djsaA 1 2
(c) 2 hours (d) 1 hours
SSC CGL PRE, 24/07/2023 (Shift-4) 2 3
(a) 6 (b) 16 24. A boat can go 40 km downstream and 25 km
(c) 10 (d) 12 upstream in 7 hours 30 minutes. It can go
A

20. A boat covers a distance of 12 km in 1 hour 48 km downstream and 36 km upstram in 10

upstream and in 45 minutes downstream. Find hours. What is the speed (in km/h) of the boat
the speed of the boat and the stream (in km/h). in still water?
,d uko /kjk ds çfrdwy 1 ?kaVs esa vkSj èkkjk ds vuqdwy 45,d uko 7 ?kaVs 30 feuV esa 40 fdeh /kjk dh fn'kk esa
feuV esa 12km dh nwjh r; djrh gSA uko vkSj /kjk dh vkSj 25 fdeh /kjk dh foijhr fn'kk esa tk ldrh gSA
pky ( km/h esa) Kkr dhft, A ;g 10 ?kaV esa 48 fdeh /kjk dh fn'kk esa vkSj 36
SSC CGL (PRE) 25/07/2023 (Shift-2) fdeh /kjk dh foijhr fn'kk esa tk ldrh gSA 'kkar ty
(a) 16 : 4 (b) 16 ; 2 esa uko dh pky (fdeh@?kaVk esa) fdruh gksxh\
(c) 14 ; 2 (d) 12 ; 4 SSC CPO 09/11/2022 (Shift-03)

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(a) 6 (b) 12 ,d O;fÙkQ Bgjs gq, ikuhxesa fdeh @?kaVk dh pky ls uko
(c) 9 (d) 15 •s ldrk gSA ;fn ,d /kjk (unh)] tks y fdeh@?kaVk dh
25. The speed of a boat in still water is thrice xfr ls cg jgh gS] esa ,d LFkku ls fdlh nwljs LFkku rd uko
the speed of the stream. If the boat takes 15.5
ls tkus vkSj okil vkus (ykSVus esa) ml O;fÙkQ z ?kaVs
dks
sec to go to a certain place downstream, then
find the additional time required to cover the yxrs gSa] rks nksuksa LFkkuksa ds chp dh nwjh D;k gS
same distance travelling upstream. UPSC CDS-1 2018
'kkar ty esa ,d uko dh pky] /kjk dh pky dh rhu
z x 2 – y2
  z x 2 – y2
 
xquh gSA ;fn uko /kjk dh fn'kk esa fuf'pr LFkku rd (a) (b)
2y 2x
tkus esa 15-5 lsadM dk le; ysrh gS] rks /kjk dh foijhr
fn'kk esa ;k=kk djrs gq, mruh gh nwjh r; djus ds fy, 2
– y2 z x 2 – y2
vko';d vfrfjDr le; Kkr dhft,A (c)
x  (d)
 
2zx x
SSC CPO 11/11/2022 (Shift-02)
27. A man rows downstream 32 km and 14 km
(a) 15.5 sec (b) 29 sec
upstream, and he takes 6 hours to cover each
(c) 31 sec (d) 35 sec

r
distance. What is the speed of the current?
26. A man can row at a speed of x km/hr in still
,d O;fDr 32 fdeh /kjk dh fn'kk esa rFkk
14 fdeh /kjk

si
water. If in a stream which is flowing at a speed
of y km/hr it takes him z hours to row to a dh foijhr fn'kk esa uko [ksrk gS vkSj mls izR;sd nwjh dk
djus esa6 ?kaVs yxrs gSaA /kjk dh pky D;k gS\
an by
place and back, then what is the distance.
between the two places? UPSC CDS 2015 (1)

n
(a) 0.5 km/hr (b) 1 km/hr
(c) 1.5 km/hr (d) 2 km/hr
ja
R s

Answer Key
a th

1.(a) 2.(c) 3.(b) 4.(d) 5.(c) 6.(a) 7.(d) 8.(d) 9.(b) 10.(c)
ty a

11.(b) 12.(d) 13.(a) 14.(b) 15.(c) 16.(a) 17.(a) 18.(c) 19.(a) 20.(c)
di M

21.(b) 22.(a) 23.(b) 24.(c) 25.(a) 26.(b) 27.(c)

A

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Ratio/ vuqikr
(CLASSROOM SHEET)
1. In a bag, black tablet covers and white 6. Which of the following ratios is the
tablet covers are in the ratio 5 : 9. If there smallest?
are 450 white tablet covers, how many 3 : 4, 1 : 2 , 2 : 5, 1 : 3
black tablet covers are there in the bag? fuEufyf[kr esa ls dkSu&lk vuqikr lcls NksVk gS\
,d cSx esa] dkys VScysV doj vkSj lisQn VScysV3 : 4, 1 : 2 , 2 : 5, 1 : 3
doj 5 % 9 ds vuqikr esa gSaA ;fn mlesa 450 lisQn SSC CHSL 07/06/2022 (Shift 02)
VScysV doj gSa] rks cSx esa dkys VScysV dolZ dh
(a) 1 : 3 (b) 2 : 5
la[;k fdruh gksxh\ (c) 3 : 4 (d) 1 : 2

r
SSC CHSL 30/05/2022 (Shift- 01)
7. If a : b = 2 : 3 and b : c = 6 : 8, then find

si
(a) 200 (b) 275 a : b : c.
(c) 225 an by (d) 250 ;fn a : b = 2 : 3 vkSj b : c = 6 : 8 gS] rksa :
2. A sum of Rs.2002 is divided among A, B
b : c Kkr djsaA
and C in the ratio 3 : 4 : 6. Find the share

n
of B in that? SSC CHSL 31/05/2022 (Shift- 01)

2002 #i;s dh jkf'k dks 3%4 %6 ds vuqikr esa

ja (a) 2 : 3 : 5 (b) 2 : 3 : 4
R s
A, B vkSjC ds chp foHkkftr fd;k tkrk gSA blesa (c) 1 : 2 : 3 (d) 2 : 3 : 6
B dk fgLlk Kkr dhft,A 8. If a : b = 5 : 8 and c : b = 4 : 3 . Then a : b : c
a th

(a) Rs.616 (b) Rs.610 is equal to :

(c) Rs.462 (d) Rs.1510 ;fn a : b = 5 : 8 vkSjc : b = 4 : 3 gS] rks
a:b:
3. If x : y = 1 : 2, find the value of (2x + 4y ) : c cjkcj gS %
ty a

(x + 4y). SSC CGL 11/06/2019 (Shift-01)

;fn x : y = 1 : 2 gS] rks(2x + 4y ) : (x + 4y)
di M

(a) 15 : 24 : 28 (b) 5 : 6 : 8
dk eku Kkr dhft,A (c) 15 : 24 : 32 (d) 5 : 8 : 6
SSC CHSL 26/05/2022 (Shift- 02) 9. If 3x = 5y = 4z then x : y : z is equal to:
(a) 10 : 9 (b) 8 : 7 ;fn 3x = 5y = 4z gS] rks
x : y : z cjkcj gS %
(c) 5 : 4 (d) 9 : 8 (a) 9 : 12 : 16 (b) 15 : 10 : 9
4. If a : b = 2 : 3, then find (5a + 3b) : (6a – (c) 20 : 12 : 15 (d) 8 : 5 : 3
2b) 10. A sum of Rs x is divided among A, B and
;fn a : b = 2 : 3 gS] rks
(5a + 3b) : (6a – 2b) C such that the ratio of shares of A and
B is 7:12 and that of B and C is 8 : 5. If
dk eku Kkr djsaA
the difference in the share of A and C is
SSC CGL 12/06/2019
Rs 214, then the value of x is.
A

(a) 19 : 6 (b) 3 : 2
x #i;s dh jkf'k dks A, B vkSj C esa bl izdkj
(c) 17 : 5 (d) 10 : 7
foHkkftr fd;k tkrk gS fdA vkSjB ds 'ks;jksa dk
5. If (5x + 2y) : (10x + 3y) = 5 : 9, then
(2x2 + 3y2) : (4x2 + 9y2) = ? vuqikr 7 % 12 gS vkSj B vkSj C ds 'ks;jksa dk
;fn (5x + 2y) : (10x + 3y) = 5 : 9 gS] rks
(2x2 vuqikr 8 % 5 gSA ;fn A vkSj C ds fgLls dk
+ 3y2) : (4x2 + 9y2) = ? varj 214 #i;s gS] rksx dk ewY; gS %
SSC CGL Tier II 2018 SSC CGL Tier I 2018
(a) 31 : 87 (b) 10 : 27 (a) Rs.11556 (b) Rs.11128
(c) 16 : 47 (d) 1 : 3 (c) Rs.11770 (d) Rs.11342

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16. The seats for Mathematics, English and

4 5 9
11. Three numbers are in the ratio : : Chemistry in a school are in the ratio of
5 6 10 6 : 4 : 7. If these seats are increased by
The difference between the smallest and 20%, 40% and 60%, respectively, the ratio
the greatest numbers is 12. Find the of the increased seats is:
number which is NEITHER the smallest ,d Ldwy esa xf.kr] vaxzsth vkSj jlk;u foKku dh
NOR the greatest.
lhVksa dk vuqikr 6 % 4 % 7 gSA ;fn bu lhVksa
4 5 9 Øe'k% 20»] 40» vkSj 60» dh o`f¼ dh tkrh gS] rks
rhu la[;k : : ds vuqikr esa gSA lcls NksVh
5 6 10 c<+h gqbZ lhVksa dk vuqikr D;k gksxk\
vkSj lcls cM+h la[;k ds chp dk varj
12 gSA og la[;k SSC CGL TIER I 19/07/2023 (Shift-02)
Kkr djsa tks u rks lcls NksVh gS vkSj u gh lcls cM+hA
(a) 9 : 7 : 8 (b) 9 : 7 : 14
SSC CGL (PRE) 24/07/2023 (Shift-2) (c) 1 : 2 : 3 (d) 7 : 9 : 14
(a) 96 (b) 108
17. If a : b = 2 : 3, b : c = 4 : 5 and
(c) 100 (d) 104
c : d = 6 : 7. Find a : b : c : d.
12. If P : Q = 10 : 11 and Q : R = 11 : 12,
;fn a : b = 2 : 3, b : c = 4 : 5 vkSjc : d = 6 :

r
then P + Q : Q + R : R + P is:
;fn P : Q = 10 : 11 vkSj Q : R = 11 : 12 gS] 7 gS] rksa : b : c : d dk eku Kkr dhft,A

si
rksP + Q : Q + R : R + P D;k gS\ (a) 16 : 24 : 30 : 31 (b) 16 : 24 : 30 : 35

(a) 21 : 23 : 22
an by
SSC CHSL 26/05/2022 (Shift- 01)
(b) 22 : 21 : 23 18.
(c) 72 : 54 : 15 : 32 (d) 8 : 32 : 50 : 71
If x : y = 6 : 5, y : z = 9 : 4 and

n
(c) 11 : 12 : 10 (d) 23 : 22 : 21 z : w = 2 : 3, then what is the value of
13. If (a + b) : (b + c) : (c + a) = 7 : 6 : 5 and a x:z:w?
ja
+ b + c = 27 , then what will be the value
;fn x : y = 6 : 5, y : z = 9 : 4 vk S j
R s
1 1 1
of : : ? z : w = 2 : 3 gS] rks
x : z : w dk eku D;k gS\
a th

a b c
(a) 6: 2 : 3 (b) 27 : 10 : 15
;fn (a + b) : (b + c) : (c + a) = 7 : 6 : 5 vkSj
(c) 7 : 6 : 9 (d) 9 : 4 : 6
1 1 1 19. The ratio of the prices of A and B is 5 : 9
ty a

a + b + c = 27 gS] rks : : dk eku D;k and prices of C and D is 24 : 13. The price
a b c
of C is ` 1500 more than the price of B, and
gksxk\
di M

the price of D is ` l300. Find the price of A.

SSC CGL Tier II 2018
(a) 3 : 6 : 4 (b) 3 : 2 : 4
A vkSjB ds dherksa dk vuqikr
5 : 9 vkSjC rFkkD ds
(c) 4 : 3 : 6 (d) 3 : 4 : 2 dherksa dk vuqikr
24 : 13 gSA
C dh dher B dh dher
14. If a, b and c are positive numbers such ls ` 1500 C vf/d gS vkSj D C dh dher ` l300 C
that (a2 + b2): (b2 + c2) : (c2 + a2) = 34 : 61 gSAA dk ewY; Kkr djsaA
: 45, then b – a : c – b : c – a = ______. SSC CHSL 15/03/2023 (Shift-03)
;fn a, b vkSjc rhu ,slh /ukRed la[;k,a gSa fd (a) ` 2,400 (b) ` 900
(a2 + b2): (b2 + c2) : (c2 + a2) = 34 : 61 : 45 (c) ` 1,000 (d) ` 500
gS] rks b – a : c – b : c – a = ______| 20. The ratio of incomes of P and Q is 1 : 2.
SSC CGL MAINS 29/06/2022 Ratio of income of Q and R is 3 : 2. If one-
A

(a) 1 : 2 : 3 (b) 2 : 1 : 3 third of P's income is ` 4400 less than the

(c) 3 : 1 : 2 (d) 3 : 2 : 1 half of P's income, then what is the Q's
15. If A : B : C = 2 : 3 : 4, then what will be income'?
the value of (A/B): (B/C): (C/A)? P vkSjQ ds vk; dk vuqikr 1 : 2 gSA
Q vkSjR ds vk;
;fn A : B : C = 2 : 3 : 4 gS] rks(A/B): (B/C): dk vuqikr3 : 2 gSA ;fnP ds vk; dk ,d&frgkbZ]P ds
(C/A) dk eku D;k gksxk\ vk; ds vk/s ls ` 4400 de gS] rksQ dh vk; D;k gS\
SSC MTS 14/06/2023 (Shift-03) SSC CHSL 14/03/2023 (Shift-02)
(a) 9:5:36 (b) 8:7:25 (a) ` 56600 (b) ` 52800
(c) 8:9:24 (d) 12:10:13 (c) ` 46600 (d) ` 41200

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21. A sum of Rs 2,310 is divided between A, B (a) 6500 (b) 7000

and C such that the ratio of the shares of (c) 5000 (d) 6000
B and C is 3 : 5 and the ratio of the shares 24. A sum of Rs 7,410 is divided between A,
of C and A is 4 : 9. What is the difference B and C such that the ratio of the share
(in Rs) between the shares of A and C? of A to the combined share of B and C is
2]310 #i;s dh jkf'k A, B vkSj C ds chp bl 9:17 and the ratio of the share of C to the
combined share of A and B is 5 : 8. What
çdkj foHkkftr dh tkrh gS fdB vkSjC ds 'ks;jksa
is the ratio of the shares of B and C?
dk vuqikr 3% 5 gS vkSj C vkSj A ds 'ks;jksa dk
7]410 #i;s dh jkf'k dksA, B vkSj C ds chp bl
vuqikr 4% 9 gSAA vkSj C ds 'ks;jksa ds chp varj
çdkj foHkkftr fd;k tkrk gS fd A ds fgLls dk B
(#i;s esa) D;k gS\
vkSjC ds la;qÙkQ fgLls ls vuqikr 9 % 17 gS C vkSj
SSC Phase IX 2022
ds fgLls dkA vkSjB ds la;qÙkQ fgLls ls vuqikr 5
(a) 240 (b) 750
(c) 450 (d) 990
% 8 gSAB vkSjC ds 'ks;jksa dk vuqikr D;k gS\
SSC Phase IX 2022
22. A sum of 6,300 is divided among A, B, C

r
and D such that the ratio of the combined (a) 13 : 17 (b) 7 : 10
share of A and D to the combined share (c) 9 : 10 (d) 8 : 9

si
of B and C is 11 : 10 and the ratio of the 25. A, B and C divide an amount of Rs 10,500
an by
shares of B and D is 8 : 9. If C receives amongst themselves in the ratio 5 : 7 :
Rs 1,560, then what is the difference (in 9, respectively. If each one gets Rs 500
more, then what will be the ratio of the

n
Rs) between the shares of A and B ?
6]300 dh jkf'k dksA, B, C vkSj D esa bl çdkj amounts with A, B and C?
ja
foHkkftr fd;k tkrk gS fd A vkSj D ds la;qÙkQ A, B vkSj C rhuksa #- 10]500 dh jkf'k dks vkil
R s
fgLls dk B vkSj C ds la;qÙkQ fgLls ls vuqikr esa Øe'k% 5%7%9 ds vuqikr esa foHkkftr djrs g
;fn çR;sd dks #- 500 vf/d feyrs gS] rksA, B
a th

11%10 gS vkSjB vkSj D ds 'ks;jksa dk vuqikr 8 %

9 gSA ;fnC dks 1]560 #i;s feyrs gSa] rks
A vkSj vkSjC dh jkf'k;ksa dk vuqikr D;k gksxk\
SSC CGL 20/04/2022 (Shift- 02)
B ds 'ks;jksa ds chp dk varj (# esa) D;k gS\
ty a

(a) 3 : 4 : 5 (b) 5 : 6 : 7
SSC Phase IX 2022
(c) 5 : 7 : 9 (d) 7 : 9 : 11
(a) 180 (b) 240
26. ` 13000 is divided among X, Y and Z such
di M

(c) 120 (d) 160 that 2 times of X's share is equal to 3 times
23. A sum of Rs 46,800 is divided among A, of Y's share which is equal to 4 times of Z's
B, C and D in such a way that the ratio of share. What is the share Y ?
the combined share of A and D to the ` 13000 dksX, Y vkSjZ esa bl izdkj foHkkftr fd;k
combined share of B and C is 8 : 5. The x;k gS fd X ds fgLls dk 2 xquk Y ds fgLls ds 3 xquk
ratio of the share of B to that of C is 5: 4. ds cjkcj gS tksZ ds fgLls ds 4 xquk ds cjkcj gSA
Y dk
A receives Rs 18,400. If x is the difference fgLlk fdruk gS\
between the shares of A and B and y is the SSC CHSL 17/03/2023 (Shift-01)
difference between the shares of C and D,
(a) ` 3200 (b) ` 4800
then what is the value of (x – y) (in Rs)? (c) ` 5600 (d) ` 4000
46,800 :i;s dh jkf'k dks] A, B, C vkSjD esa
A

p r t 2
bl izdkj foHkkftr fd;k tkrk gS fd A vkSjD ds 27. If q  s  u  5 , then what is the value of
la;qDr fgLls dk] B vkSjC ds la;qDr fgLls ls (4p + 3r + 7t) : (4q + 3s + 7u)?
vuqikr 8 : 5 gSA B ds fgLls dk]C ds fgLls ls p r t 2
vuqikr 5 : 4 gSA A dks18,400 :i;s feyrs gSaA ;fn q  s  u  5 gS] rks
(4p + 3r + 7t) : (4q +

;fn A vkSjB ds fgLlksa ds chp dk varjx gS vkSj 3s + 7u) dk eku D;k gS\
C vkSjD ds fgLlksa ds chp dk varj y gS] rks SSC CHSL 09/03/2023 (Shift-01)
(x – y) dk eku (:i;s esa) fdruk gS\ (a) 4 : 11 (b) 3 : 7
SSC CGL MAINS 29 Jan 2022 (c) 2 : 5 (d) 5 : 9

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28. If a : b = c : d = e : f = 1 : 2, then 34. Atul purchased Bread costing Rs 20 and gave

(pa + qc + re) : (pb + qd + rf) is a 100 rupee note to the shopkeeper.
Shopkeeper gave the balance gave the
;fn a : b = c : d = e : f = 1 : 2, gS] rks
(pa +
balance money in coins of denomination Rs
qc + re) : (pb + qd + rf) = ? 2, Rs 5 and Rs 10. If these coins are in the
(a) 1 : 2 (b) 4 : 3 ratio 5:4:1, then how many Rs 5 coins did
(c) 2 : 1 (d) 1 : 1 the shopkeeper give?
29. If a : (b + c) = 5 : 7 , b : (c + a) = 7 : 9,
then find c : (a + b). vrqy 20 #i;s Ø; ewY; okyk czsM [kjhnrk gS vksj
;fn a : (b + c) = 5 : 7 , b : (c + a) = 7 : 9 nqdkunkj dks 100 :i;s dk uksV nsrk gSA nqdkunk
gS] rks
c : (a + b) dk eku Kkr djsaA 2 #i;s] 5 #i;s vkSj 10 #i;s ewY; oxZ ds flDdksa
(a) 4 : 41 (b) 20 : 41 esa 'ks"k /u nsrk gSA ;fn bu flDdksa dk vuqikr 5 % 4
(c) 21 : 41 (d) 7 : 41 % 1 gS] rks nqdkunkj 5 #i;s ds fdrus flDds nsrk gS\
30. If a : (b + c) = 1 : 3 , c : (a + b) = 5 : 7,
then find b : (a + c). SSC CGL 13/08/2021(Shift 03)

;fn a : (b + c) = 1 : 3 , c : (a + b) = 5 : 7 (a) 5 (b) 6

r
gS] rks
b : (a + c) dk eku Kkr djsaA
(c) 8 (d) 4

si
(a) 1 : 2 (b) 2 : 5
(c) 1 : 3 (d) 3 : 4 35. In a bag there are coins of Rs.5, Rs.10 and
31.
an by
If (a + b + c) : d = 17 : 3 , (a + c + d)
: b = 3 : 1 , (a + b + d) : c = 3 : 2, then
Rs.20 denominations. The total number
of coins in the bag is 240. If the number

n
find (b + c + d) : a. of coins of Rs.5, Rs.10 and Rs.20
denominations are in the ratio of 2 : 3 :
;fn (a + b + c) : d = 17 : 3 , (a + c + d) : b = 3
ja 5, then what is the total amount of money
: 1 , (a + b + d) : c = 3 : 2 gS] rks
R s
(b + c + d)
in the bag?
: a dk eku Kkr djsaA
a th

(a) 1 : 2 (b) 2 : 5 ,d cSx esa 5 :i;s] 10 :i;s vkSj 20 :i;s ewY;oxZ

(c) 3 : 1 (d) 4 : 1 ds flDds gSaA cSx esa flDdksa dh dqy la[;k 240 g
;fn 5 :i;s] 10 :i;s vkSj 20 :i;s ewY;oxZ ds
Questions Based on Coins
ty a

flDdksa dh la[;k 2 % 3 % 5 ds vuqikr esa gS] rks

32. In a wallet, there are coins of Rs 1, Rs 2 cSx eas dqy fdruk /ujkf'k gS\
di M

and Rs 5 in the ratio of 2 : 5 : 3

SSC MTS 12/07/2022 (Shift- 02)
respectively. If there is Rs 54 in all, then
how many Rs 5 coins are there? (a) Rs.3540
,d cVq, esa Øe'k% 2% 5% 3 ds vuqikr esa 1 #i;s] 2 (b) Rs.4600
#i;s vkSj 5 #i;s ds flDds gSaA ;fn dqy 54 #i;s gSa (c) Rs.4620
rks 5 #i;s ds fdrus flDds gSa\
(d) Rs.3360
SSC MTS 09/05/2023 (Shift-02)
36. A bag contains Rs. 840 in the form of 2
(a) 20 (b) 10 rupee, 5 rupee and 10 rupee coins. The
(c) 4 (d) 6 number of coins of 2 rupee. 5 rupee and
33. In a bag, the ratio of the number of Rs.2, 10 rupee are in the ratio of 5 : 7 : 6. What
A

Rs.1 and 50 paise coins is 3 : 4 : 5. If the is the total number of coins in the bag?
total amount in the bag is Rs 250, then ,d cSx esa #i;s gSa- 840 #i;s 2 #i;s] 5 #i;s vkSj
how many ` 1 coins are there ?
10 #i;s ds flDdksa ds :i esaA 2 #i;s ds flDdksa dh
,d cSax esa` 2] ` 1 vkSj 50 iSls ds flDds dh la[;k- 5 #i;s vkSj 10 #i;s dk vuqikr 5 % 7 % 6
la[;k dk vuqikr 3 %4 %5 gSA ;fn cSax dqy esa gSA cSx esa flDdksa dh dqy la[;k fdruh gS\
jkf'k ` 250 gS] rks cSx`esa
1 ds fdrus flDds gSa\
SSC MTS 19/05/2023 (Shift-01)
SSC CGL MTS 2018
(a) 70 (b) 100 (a) 158 (b) 132
(c) 60 (d) 80 (c) 102 (d) 144

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41. The ratio of number of boys and girls in a

Questions Based on Addition college is 3 : 2. If 40 boys leave the college
or Subtraction and 40 girls join the college, the their ratio
will becomes 2 : 3. What is the initial
37. Two numbers are in the ratio 9 : 16. If both number of boys in the college?
numbers are increased by 40, then their ,d dkWyst esa yM+dksa vkSj yM+fd;ksa dh la[;k
ratio becomes 2 : 3. What is the difference vuqikr 3 : 2 gS ;fn 40 yM+ds dkWyst NksM+ nsrs gSa
between the two number's? 40 yM+fd;k¡ dkWyst esa HkrhZ gks tkrh gS] rks
nks la[;k,¡ 9 % 16 ds vuqikr esa gSA ;fn nksuksa la[;kvksa
vuqikr 2 : 3 gks tk,xkA dkWyst esa yM+dksa dh izkja
esa 40 dh o`f¼ dj nh tk,] rks mudk vuqikr 2 % 3 gks la[;k fdruh gS\
tkrk gSA nksuksa la[;kvksa ds chp dk varj D;k gS\ SSC CHSL 10/03/2023 (Shift-04)
SSC CHSL 16/03/2023 (Shift-02) (a) 120 (b) 150
(a) 64 (b) 60 (c) 225 (d) 75
42. On a tree, there are some parrots and some
(c) 48 (d) 56
pigeons in the ratio of 7 : 9, respectively.
38. The ratio of two numbers A and B is 5 :

r
After an hour, 8 parrots fly away, and 6
8. If 5 is added to each of A and B, then
pigeons and 10 sparrows come and sit on

si
the ratio of A and B becomes 2 : 3. The
the tree. The ratio of the parrots and the
sum of A and B is:
an by pigeons on the tree now is 1 : 4. What is
AvkSjB nks la[;kvksa dk vuqikr 5 % 8 gSA ;fn the ratio of the parrots and the sparrows
AvkSjB esa ls izR;sd esa 5 tksM+k tkrk AgS] rks that are now on the tree?

n
vkSjB dk vuqikr 2 % 3 gks tkrk gSA
A vkSjB dk ,d isM+ ij dqN rksrs vkSj dqN dcwrj Øe'k% 7 %
;ksxiQy Kkr djsaA ja 9 ds vuqikr esa cSBs gSaA ,d ?kaVs ckn 8 rksrs
R s
SSC CGL 13/08/2021(Shift 02) tkrs gSa vkSj 6 dcwrj vkSj 10 xkSjS;k vkdj isM+ i
cSB tkrs gSaA vc isM+ ij rksrs vkSj dcwrjksa dk vu
a th

(a) 42 (b) 78
(c) 65 (d) 91 1 % 4 gSA vc isM+ ij rksrs vkSj xkSjS;ksa dk vu
39. Two numbers are in the ratio 7 : 5. On Kkr dhft,A
ty a

diminishing each of them by 40, the ratio SSC MTS 20/07/2022 (Shift- 2)
becomes 27 : 17. The sum of the numbers is: (a) 1 : 1 (b) 1 : 2
di M

nks la[;k,¡ 7%5 ds vuqikr esa gSA muesa ls izR;sd(c) 3 : 5 (d) 4 : 5

dks 40 ls de djus ij vuqikr 27 %17 gks tkrk 43. Two numbers are in the ratio
gSA la[;kvksa dk ;ksx gS % 3 : 5. If 13 is subtracted from each, the
new numbers are in the ratio 10 : 21. If
SSC CHSL 2018
5 is added to each of the original numbers,
(a) 300 (b) 240 then the ratio becomes:
(c) 325 (d) 275 nks la[;k,¡ 3%5 ds vuqikr esa gSA ;fn izR;sd esa ls
40. Two numbers A and B are in the ratio 5 : 13 ?kVk;k tkrk gS] rks ubZ la[;k,¡
%2110ds vuqikr
2 . If 4 is added to each number then the
ratio becomes 9 : 4. If 5 is subtracted from
esa gksrh gSA ;fn izR;sd ewy la[;kesda 5 tksM+
each of the original numbers, then the tk, rks vuqikr gks tkrk gS %
A

ratio of A and B will be: SSC CGL Tier II 2018

nks la[;k,¡A vkSj B 5 %2 ds vuqikr esa gSaA ;fn (a) 5 : 7 (b) 23 : 33
(c) 4 : 5 (d) 19 : 30
izR;sd la[;k esa 4 tksM+ fn;k tk, rks vuqikr
%4 9
44. In a school library, the ratio of Science to
gks tkrk gSA ;fn izR;sd ewy la[;k esa ls 5 ?kVkEnglish books is 10:13. If there are 400
fn;k tk, rks A vkSjB dk vuqikr gksxk % Science books and due to increase demand
SSC CHSL 2018 of Science books, few Science books are
added by school authority and the ratio
(a) 3 : 1 (b) 8 : 3 becomes 25:26. What is the number of
(c) 7 : 2 (d) 4 : 1 Science books added?

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,d Ldwy iqLrdky; esa foKku vkSj vaxzsth iqLrdksa dk Income & Expenditure
vuqikr 10 % 13 gSA ;fn 400 foKku dh fdrkcsa gSa
vkSj foKku dh fdrkcksa dh c<+rh ekax ds dkj.k] Ldwy Based Questions
çkf/dj.k }kjk dqN foKku dh fdrkcsa tksM+ nh tkrh gSa
48. Avinash's monthly salary is Rs.50,000 and
vkSj vuqikr 25 % 26 gks tkrk gSA foKku dh tksM+h xbZ
his monthly expenditure is Rs.18,000.
iqLrdksa dh la[;k fdruh gS\ Radha's monthly salary is Rs.60,000 and
SSC MTS 09/05/2023 (Shift-02) her monthly expenditure is Rs.24,000.
(a) 1.50 (b) 100 Find the ratio of Radha's savings to
(c) 120 (d) 80 Avinash's saving's.
45. Monthly salaries of Anil and Kumud are vfouk'k dk ekfld osru #- 50]000 gS vkSj mldk
in the ratio 19:17. If Anil and Kumud get ekfld O;; #- 18]000 gSA jk/k dk ekfld osru #-
salary hike of Rs. 2000 and Rs. 1000 60]000 gS vkSj mldk ekfld O;; #-24]000 gSA jk/k
respectively, then the ratio in their salaries dh cp r vkSj vfouk'k dh cpr dk vuqikr Kkr djsaA
become 8:7. What is the present salary of
SSC CGL (PRE) 27/07/2023 (Shift-3)
Kumud after increased (in Rs.)?

r
(a) 9 : 8 (b) 9 : 7
vfuy vkSj dqeqn dk ekfld osru 19 % 17 ds

si
(c) 6 : 5 (d) 8 : 7
vuqikr esa gSA ;fn vfuy vkSj dqeqn ds osru esa
49. The expenditure and savings of a person
Øe'k% 2000 :i;s vkSj 1000 :i;s dh o`f¼ gksrh
an by are in ratio of 4 : 3. His savings increase by
gS] rks muds osru dk vuqikr 8 % 7 gks tkrk gSA 1

n
dqeqn dk orZeku osru (:i;s esa) D;k gS\ 5
of his income and income remains the
SSC CGL 24/08/2021(Shift 02) same.What is the new ratio of his
ja expenditure and savings?
R s
(a) 38000 (b) 18000
(c) 34000 (d) 35000 ,d O;fDr dk O;; vkSj cpr 4 % 3 ds vuqikr esa gSA
a th

46. The students in three classes are in a ratio 1

of 3 : 7 : 8. If 6 students are increased in mldh cpr mldh vk; ds ds cjkcj c<+ tkrh gS
5
each class, the ratio changes to 11 : 23 :
vkSj vk; leku jgrh gSA mlds O;; vkSj cpr dk u;k
ty a

26. Find the total number of students in

the three classes before the increase. vuqikr D;k gS\
rhu d{kkvksa esa Nk=kksa dk vuqikr 3 % 7 % 8 gSA ;fn SSC CHSL 10/03/2023 (Shift-01)
di M

çR;sd d{kk esa 6 Nk=k c<+ tkrs gSa] rks vuqikr 11%
(a) 12 : 17 (b) 14 : 17
23% 26 esa cny tkrk gSA o`f¼ ls igys rhu d{kkvksa(c) 13 : 22 (d) 15 : 13
esa Nk=kksa dh dqy la[;k Kkr dhft,A 50. The ratio of the expenditure and savings
of a person is 4 : 3. His expenditure
SSC MTS 17/05/2023 (Shift-01)
(a) 162 (b) 112 1
(c) 90 (d) 144 increases by of his initial savings and
4
47. The students in three batches of a dance
his income increases by Rs 300. If his
class are in the ratio of 2 : 3 : 5. If 20
savings remains the same, then what is his
students increase in each batch the ratio
changes to 4 : 5 : 7. Find the total number initial expenditure?
A

of students in the three batches before the fdlh O;fÙkQ ds O;; vkSj cpr dk vuqikr 4% 3 gSA
increase.
1
,d u`R; d{kk ds rhu cSpksa esa Nk=kksa dk vuqikr 2%3mldk
% 5 O;; mldh çkjafHkd cpr dk 4 c<+ tkrk gS
gSA ;fn çR;sd cSp esa 20 Nk=k c<+rs gSa rks vuqikr
vkSj mldh vk; 300 #i;s c<+ tkrh gSA ;fn mldh
cnydj 4 % 5 % 7 gks tkrk gSA o`f¼ ls igys rhuksa cSpksa
cpr leku jgrh gS] rks mldk çkjafHkd O;; D;k gS\
esa Nk=kksa dh dqy la[;k Kkr dhft,A
SSC MTS 10/05/2023 (Shift-01)
SSC PHASE XI 27/06/2023 (Shift-01)
(a) 120 (b) 100 (a) Rs.1600 (b) Rs.20000
(c) 150 (d) 80 (c) Rs.10000 (d) Rs.12000

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51. The ratio of income of Jitendra, and 55. The ratio of income of A to that of B is
Narendra is 4 : 7 and the ratio of their
5
expenditure is 6 : 5 respectively. If Jitendra 4 : 3. The expenditure of A is of his
saves Rs. 400 out of Rs. 2,800 income, then 12
find the savings of Narendra. 7
ftrsUnz vkSj ujsUnz dh vk; dk vuqikr 4 % 7 gS rFkkincome and the expenditure of B is 15
mlds [kpZ dk vuqikr Øe'k% 6 % 5 gSA ;fn ftrsUnz
` of his income, The difference between
2800 dh vk; esa ls` 400 cpkrk gS] rks ujsUnz dh cpr their expenditures is Rs. 4,500. Find the
Kkr dhft,A income of B.
SSC CHSL 13/03/2023 (Shift-02) A vkSj B dh vk; dk vuqikr 4 % 3 gSAA dk
(a) ` 2,900 (b) ` 2,000
5
(c) ` 4,900 (d) ` 3,900 O;; mldh vk; dk gS vkSjB dk O;; mldh
12
52. The annual incomes of Anand and Bharath
are in the ratio 3: 5 and their annual 7
expenses are in the ratio 1 : 3. If each of vk; dk gSA muds O;; dk varj #- 4]500 gSA
15
them saves Rs 10,000 at the end of the year,

r
then the annual income of Bharath is: B dh vk; Kkr dhft,A

si
vkuan vkSj Hkjr dh okf"kZd vk; 3 % 5 ds vuqikr esa gS SSC CHSL 25/05/2022 (Shift- 03)
vkSj mudk okf"kZd O;; 1 % 3 ds vuqikr esa gSA ;fn muesa
(a) Rs. 49,625 (b) Rs. 48,625
an by
ls izR;sd O;fDr o"kZ ds var esa :i;s 10]000 dh cpr
djrk gS] rks Hkjr dh okf"kZd vk; D;k gS\
(c) Rs. 51,625 (d) Rs. 50,625

n
SSC PHASE XI 28/06/2023 (Shift-01) 56. 2
The income of A is of B's income and
(a) Rs 25,000 (b) Rs 12,000 3
ja
R s
(c) Rs 15,000 (d) Rs 30,000 3
53. Ratio of monthly incomes of A and B is the expenditure of A is of B's
4
a th

4 : 5 respectively. Ratio of monthly savings

of A and B is 14 : 19 respectively. If the 1
expenditure. If of the income of B is
monthly expenditure of A and B is Rs.1200 3
each, then what is the difference between equal to the expenditure of A, then the
ty a

the monthly incomes of A and B? ratio of the savings of A to those of B is:

A rFkkB dh ekfld vk; dk vuqikr Øe'k% 4 :
di M

2
5 gSA A rFkkB dh ekfld cpr dk vuqikr Øe'k% A dh vk; B dh vk; dh gS vkSj
A dk O;;]
3
14 % 19 gSA ;fn A rFkkB eas ls izR;sd dk ekfld
O;; 1200 #i;s gks] rksA rFkkB dh ekfld vk; 3 1
B ds O;; dk gSA ;fnB dh vk; dk A ds
4 3
ds chp fdruk varj gS\
SSC CGL Mains (08/08/2022)
O;; ds cjkcj gS] rksA dh cpr dk B dh cpr
(a) Rs.2000 (b) Rs.5000 ls vuqikr Kkr djsaA
(c) Rs.4000 (d) Rs.1000 SSC CGL MAINS 29/06/2022
54. The ratio of monthly incomes of A and B (a) 5 : 3
is 4 : 5 and that of their monthly
expenditure is 3 : 8. If the income of A (b) 3 : 5
is equal to the expenditure of B, then what (c) 4 : 3
A

is the ratio of savings of A and B? (d) 3 : 4

A vkSj B dh ekfld vk; dk vuqikr 4%5 gS vkSj
57. The ratio of the incomes of A and B in
muds ekfld O;; dk vuqikr 3 % 8 gSA ;fn
A dh the last year was 4: 3. The ratios of their
vk; B ds O;; ds cjkcj gS] rksA vkSj B dh individual incomes in the last year and the
cpr dk vuqikr D;k gS\ present year are 3 : 4 and 5 : 6, respectively.
SSC CGL 20/08/2021(Shift 02) If their total income in the present year is
Rs 24.12 lakhs, then the sum of the income
(a) 8 : 3 (b) 2 : 5 (in Rs lakhs) of A in the last year and that
(c) 5 : 2 (d) 3 : 8 of B in the present year is:

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fiNys o"kZ AesavkSjB dh vk; dk vuqikr 4 % 3 A, B vkSj C viuh vk; dk Øe'k% 80»] 85»
FkkA fiNys o"kZ vkSj orZeku o"kZ esa mudh O;fDrxrvkSj 75» [kpZ djrs gSaA ;fn mudh cpr %98%20
vk; dk vuqikr Øe'k% 3 % 4 vkSj 5 % 6 gSA ds vuqikr esa gS vkSj A vkSj C dh vk; ds chp
;fn orZeku o"kZ esa mudh dqy vk; :i;s 24-12 dk varj 18]000 #i;s gS] rksB dh vk; gS %
yk[k gS] rks fiNys o"kZ A dh
esavk; vkSj orZeku SSC CGL TIER II 2018
o"kZ esa
B dh vk; (:i;s yk[k esa) dk ;ksx Kkr djsaA
(a) Rs.24000 (b) Rs.27000
SSC CGL MAINS 29/06/2022
(c) Rs.30000 (d) Rs.36000
(a) 22.17 (b) 21.28
Miscellaneous Questions
(c) 10.98 (d) 20.52
58. The ratio of the incomes of A and B in 2020 61. If (x – 2y + 8z) : (y – 3z + 4w) : (4x + 5z – 7w)
was 5 : 4. The ratios of their individual 6 x + 2 y  17 w
incomes in 2020 and 2021 were 4 : 5 and = 3 : 4 : 7 then find =?
w
2: 3, respectively. If the total income of

r
A and B in 2021 was 7,05,600, then what ;fn (x – 2y + 8z) : (y – 3z + 4w) : (4x + 5z –
was the income (in Rs) of B in 2021?

si
6 x + 2 y  17 w
o"kZ 2020 esa]
A vkSjB dh vk; dk vuqikr 5 % 4 7w) = 3 : 4 : 7 gS] rks =?
an by
FkkA o"kZ 2020 vkSj 2021 esa] mudh O;fDrxr vk;
ds vuqikr Øe'k% 4 % 5 vkSj 2 % 3 FksA ;fn 2021 (a) 5 (b) 6
w

n
esaA vkSjB dh vk; 705600 Fkh rksB dk vk; (c) 7 (d) 8
2021 (:i;s esa) fdruh Fkh\
ja 62. The ratio of the number of employees
R s
SSC CGL MAINS 03/02/2022 (male and female) in offices A and B is 2
: 3. The ratio of the female employees in
a th

(a) 3,45,600 (b) 2,79,700 A and B is 1 : 2, and the ratio of the female
(c) 3,60,000 (d) 4,25,900 employees in A to the total employees in
A is 1:3. What is the ratio of the male
59. The ratio of last year income of A, B
ty a

employees in A and B?
and C is 3 : 4 : 5. While the ratio of
their last year income to current year dk;kZy;ksa
A vkSjB esa deZpkfj;ksa (iq#"k vkSj efgyk)
di M

income is 4 : 5, 2 : 3 and 3 : 4. If their dh la[;k dk vuqikr 2 % 3 gSA

A vkSj B esa efgyk
total current year income is Rs. 98,500, deZpkfj;ksa dk vuqikr 1 % 2 gS] AvkSjesa efgyk
then find out the present income of deZpkfj;ksa dk dqy deZpkfj;ksa ls vuqikr
A esa 1 % 3
(B + C). gSA
A vkSjB esa iq#"k deZpkfj;ksa dk vuqikr fdruk gS\
A, B vkSj C dh fiNys o"kZ dh vk; dk vuqikr SSC Phase IX 2022

3 %4 %5 gS] tcfd mudh fiNys o"kZ dh vk; (a) 6 : 7 (b) 5 : 6

dk orZeku o"kZ dh vk; ls vuqikr Øe'k% %5]
4 (c) 4 : 5 (d) 3 : 2
2 %3 vkSj 3%4 gSA ;fn mudh orZeku o"kZ 63. dh On the whole surface of earth the ratio
of land and water is 3 : 5. The land and
dqy vk; 98]500 #i;s gS rks(B + C) dh orZeku water in northern hemisphere is 7 : 9. Then
A

vk; Kkr djsaA what is the ratio of land and water in

southern hemisphere?
(a) Rs.72000 (b) Rs.74000
i`Foh dh iwjh lrg ij Hkwfe vkSj ty dk vuqikr
(c) Rs.76000 (d) Rs.78000
3 %5 gSA mÙkjh xksyk¼Z esa Hkwfe%vkSj9 gSAikuh 7
60. A , B and C spend 80% , 85% and 75% of
fiQj nf{k.kh xksyk¼Z esa Hkwfe vkSj ikuh dk vu
their income respectively. If their savings
D;k gS\
are in the ratio 8 : 9 : 20 and the difference
between the incomes of A and C is (a) 6 : 7 (b) 5 : 11
Rs.18000, then the income of B is: (c) 9 : 2 (d) 3 : 2

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64. The expenses of a family on wheat, fdlh iRFkj dk eku mlds Hkkj ds oxZ ds lekuqikrh
vegetables and oil are in the ratio 12 : 8
gksrk gSA :i;s 1]20]000 ewY; ds ,d iRFkj dks 2
: 5. The prices of these items increased
by 50%, 25% and 40%, respectively. The % 3 ds vuqikr esa nks VqdM+ksa esa rksM+k tk
total expenses of the family on these items NksVs iRFkjksa dk dqy ewY; fdruk gS\
increased by: SSC MTS 07/07/2022 (Shift- 01)
,d ifjokj dk xsagw] lfCt;ksa vkSj rsy ij O;; 12 % (a) Rs. 68,400 (b) Rs. 62,400
8 % 5 ds vuqikr eas gSA bu oLrqvksa ds ewY; esa Øe'k% (c) Rs. 66,500 (d) Rs. 65,400
50»] 25» vkSj 40» dh o`f¼ gks xbZA bu oLrqvksa 68. The cost of a diamond is directly
ij ifjokj ds O;; esa fdrus izfr'kr dh o`f¼ gksxh\ proportional to the square of its weight.The
cost of a 14 gm diamond is Rs.2560. This
SSC CHSL 02/06/2022 (Shift- 01)
diamond got broken down into two pieces
(a) 40% (b) 38% in the ratio of 5 : 9. How much loss percent
(c) 44% (d) 42% is incurred due to this breakage? (Correct
65. Salaries of B, C, D and E are in the ratio to two decimal places)

r
of 2 : 3 : 4 : 5 respectively. Their salaries ,d ghjs dk ewY; mlds Hkkj ds oxZ ds vuqØekuqikrh
are increased by 20 percent, 30 percent, gSA ,d 14 gm ds ghjs dk ewY; #i;s 2560 gSA

si
40 percent and 50 percent respectively.
an by
If the increased salary of D is Rs.560, then
;g ghjk 5 % 9 ds vuqikr esa nks VqdM+ksa esa
what is the sum of the original salaries tkrk gSA blds VwVus ds dkj.k fdrus izfr'kr dh
gkfu gqbZ gS\

n
of B , C, D and E?
B, C, D vkSjE ds osru Øe'k%2 : 3 : 4 : 5 ds (n'keyo ds nks LFkkuksa rd lgh mÙkj nhft,)
ja
vuqikr eas gSA muds osru esa Øe'k% 20 izfr'kr] 30 SSC CGL Mains (08/08/2022)
R s
izfr'kr] 40 izfr'kr vkSj 50 izfr'kr dh o`f¼ dh (a) 53.47 percent (b) 49.71 percent
a th

xbZ gSA ;fn D dk c<+k gqvk osru #Ik;s 560 gks] (c) 55.41 percent (d) 45.92 percent
rksB, C, D vkSjE ds ewy osruksa dk ;ksx fdruk gS\
69. In an examination, the success to failure
ratio was 5 : 2. Had the number of failures
SSC CGL Mains (08/08/2022)
been 14 more, then the success to failure
ty a

(a) Rs.1260 (b) Rs.1820

ratio would have been 9 : 5. The total
(c) Rs.1560 (d) Rs.1400 number of candidates who appeared for the
di M

66. The Price of a semi-precious stone examination was:

weighing 48 g, is Rs 2,30,400. It is broken ,d ijh{kk esa] liQyrk vkSj vliQyrk dk vuqikr
into two pieces whose weights are in the
ration of 5 : 7. If the price is proportional
5 %2 FkkA ;fn vliQy vH;FkhZ dh la[;k 14 vf/
to the square of the weight, then the loss d gksrh] rks liQyrk vkSj vliQyrk dk vuqikr
(in Rs) incurred, is: 9 %5 gksrkA bl ijh{kk esa dqy fdrus vH;FkhZ 'kkfe
48 xzke otu okys ,d v¼Z dherh iRFkj dh dher gq, Fks\
2]30]400 #i;s gSA bls nks VqdM+ksa esa foHkkftr (a)
fd;k121 (b) 196
x;k gS] ftudk otu 5% 7 ds vuqikr esa gSA ;fn (c) 126 (d) 128
70.
dher otu ds oxZ ds lekuqikrh gS] rks gqbZ gkfu In an examination, the number of students
A

who passed and the number of students who

(#i;s esa) gS% failed were in the ratio 25: 4. If one more
SSC CGL MTS 2020 student had appeared and passed and the
(a) 112000 (b) 40000 number of failed students was 3 less than
(c) 118400 (d) 78400 earlier, the ratio of passed students to failed
67. The value of a stone is proportional to the students would have become 22: 3. What
square of its weight. A stone worth Rs. is the difference between the number of
Rs.1,20,000 is broken into two pieces in students who, initially, passed the
the ratio of 2 : 3. What is the total price examination and the number of students
of the two small stones? who failed the examination?

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,d ijh{kk esa] mÙkh.kZ gksus okys Nk=kksa dhdkla[;kvuqikr yky jax ds yksxksa dh la[;k 35%76 gS] rk
iq#"kksa
vkSj vuqÙkh.kZ gksus okys Nk=kksa dh la[;k dk vuqikr dh la[;k dk efgykvksa dh la[;k ls vuqikr
25 % 4 FkkA ;fn ,d vkSj Nk=k mifLFkr gq, vkSjD;k gS\
mÙkh.kZ gq, vkSj vuqÙkh.kZ Nk=kksa dh la[;k igys dh SSC MTS 04/05/2023 (Shift-01)
rqyuk esa 3 de Fkh] rks mÙkh.kZ Nk=kksa dk vuqikr
(a) 47:51 (b) 40:43
vuqÙkh.kZ Nk=kksa dh la[;k 22%3 gks tkrhA çkjaHk esa
(c) 62:57 (d) 52:59
ijh{kk mÙkh.kZ djus okys fo|kfFkZ;ksa dh la[;k vkSj
73. Find the compound ratio of the following
1 : 2 and 3 : 5
ijh{kk esa vuqÙkh.kZ gksus okys fo|kfFkZ;ksa dh la[;k
1 : 2 rFkk3 : 5 dk feJ vuqikr crk,¡A
dk varj fdruk gS\
(a) 3 : 10 (b) 3 : 5
SSC CGL MAINS 03/02/2022
(c) 10 : 3 (d) 5 : 3
(a) 132 (b) 126
(c) 174 (d) 150 74. Find the mixed ratio of the following 1 : 2,
3 : 5 and 5 : 9.
71. In an election four candidates were there
in the fray, out of which three were 1 : 2, 3 : 5 vkSj5 : 9 dk feJ vuqikr crk,¡A

r
nominated from the three national parties (a) 1 : 6 (b) 1 : 5

si
and they got votes in a ratio of 2 : 3 : 4. (c) 1 : 3 (d) 1 : 18
The total votes polled were 1,89,000 and 75. Find the compound ratio of the following
an by
the fourth candidate got 18,000 votes. The
votes obtained by the three candidates of 0.45 : 0.55 and
1 4
:
9 5
.

n
the national parties are respectively:
1 4
(assuming all votes valid) 0.45 : 0.55 rFkk :dk feJ vuqikr crk,¡A
ja 9 5
,d pquko esa pkj mEehnokj eSnku esa Fks] ftuesa (a) ls 5 : 41
R s
(b) 5 : 44
rhu dks rhu jk"Vªh; nyksa }kjk ukekafdr fd;k x;k Fkk(c) 44 : 5 (d) 41 : 5
a th

vkSj mUgsa 2 % 3 % 4 ds vuqikr esa oksV feys76. FksA dqy

Find the duplicate ratio of 14 : 17.
oksV 1]89]000 Fks vkSj pkSFks mEehnokj dks 18]000 14 : 17 dk oxkZuqikr crk,¡A
oksV feys FksA jk"Vªh; nyksa ds rhuksa mEehnokjksa(a)dsk196
fdrus
: 289 (b) 169 : 256
ty a

fdrus oksV feys\ (lHkh oksVksa dks oS| ekfu,) (c) 197 : 729 (d) 576 : 729
SSC CHSL 06/06/2022 (Shift- 02) 77. Find the duplicate ratio of 0.04 : 0.005.
di M

(a) 38,000, 57,000 and 76,000

0.04 : 0.005 dk oxkZuqikr crk,¡A
(a) 1 : 64 (b) 64 : 1
(b) 34,000, 51,000 and 68,000
(c) 16 : 25 (d) 25 : 16
(c) 36,000, 54,000 and 72,000
78. Find the subduplicate ratio of
(d) 40,000, 60,000 and 80,000 16 : 25.
72. In a party hall, there are people in blue and 16 : 25 dk oxkZewykuqikr crk,¡A
red dresses. The ratio of number of men (a) 4 : 5 (b) 5 : 4
in blue to the number of women in red is (c) 256 : 625 (d) 625 : 256
3: 7. The ratio of men in red to the number 79. Find the subduplicate ratio of
1 1
of women in blue is 2 : 1. If the ratio of : .
A

number of people in blue to the number of 0 .2 2 5 0 .2 5 6

1 1
people in red is 35: 76, then what is the : dk oxkZewykuqikr crk,¡A
ratio of number of men to the number of 0 .2 2 5 0 .2 5 6
(a) 16 : 15 (b) 15 : 16
women?
(c) 225 : 256 (d) 256 : 225
,d ikVhZ gkWy esa uhys vkSj yky jax dh iks'kkdsa
80. igus
Find the triplicate ratio of 3 : 5.
yksx gSaA uhys jax esa iq#"kksa dh la[;k vkSj yky jax
3 : esa
5 dk ?kukuqikr crk,¡A
efgykvksa dh la[;k dk vuqikr 3% 7 gSA yky jax esa (a) 27 : 125 (b) 9 : 25
iq#"kksa dh la[;k vkSj uhys jax esa efgykvksa dh la[;k 1 1
dk vuqikr 2% 1 gSA ;fn uhys jax esa yksxksa dh la[;k
(c) 3 3 : 5 3 (d) 125 : 27

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1 1 1 1
81. Find the triplicate ratio of : . : dk çfrykse vuqikr crk,¡A
0 .4 9 0 .3 4 3 6 4 5 12
(a) 8 : 1 (b) 1 : 8
1 1 (c) 64 : 1 (d) 1 : 64
: dk ?kukuqikr crk,¡A
0 .4 9 0 .3 4 3 86. If P varies directly to R and Q varies inversely
(a) 7 : 10 to R, which of the following is NOT correct?
(b) 10 : 7 ;fn P, R ls lh/s fHkUu gksrk gSQ,vkSj
R ls O;qRØekuqikrh
(c) 343 : 1000 gksrk gS] rks fuEu esa ls dkSu lk lgh ugha gS\
(d) 1000 : 343
CRPF HCM 27/02/2023 (Shift - 01)
82. Find the subtriplicate ratio of 512 : 729.
(a) PQ = constant
512 : 729 dk ?kuewykuqikr crk,¡A
(a) 8 : 9 (b) 8 : 7 1
(b) P  R and Q 
(c) 7 : 8 (d) 7 : 9 R
83. Find the subtriplicate ratio of
P
1 1 (c) = constant × R2
: Q

r
.
0 .3 4 3 0 .5 1 2

si
1 1 1
: dk ?kuewykuqikr crk,¡A (d) (P + Q) 
R
0 .3 4 3 0 .5 1 2 an by
(a) 7 : 8 (b) 8 : 7 87. x varies directly y and inversely as z. When
(c) 6 : 7 (d) 7 : 6 y = 1.8 and z = 4.5, then x = 2.5. What is

n
84. Find the inverse ratio of 5 : 8. the value of x when y = 4.2 and z = 1.25?
5 : 8 dk çfrykse vuqikr crk,¡A x, y ds lekuqikrh rFkk
z ds O;qRØekuqikrh gSA
y = tc
ja 1.8 vkSjz = 4.5, rksx = 2.5gks] rks
x dk eku D;k
R s
(a) 8 : 5 (b) 16 : 25
(c) 64 : 25 (d) 25 : 64 gksxk tcy = 4.2 vkSjz = 1.25 gks\
a th

1 1 ICAR MAINS, 07/07/2023 (Shift-1)

85. Find the inverse ratio of : .
64 512 (a) 21 (b) 20
(c) 10.5 (d) 10
ty a

ANSWER KEY
di M

1. (d) 2.(a) 3. (a) 4. (a) 5. (a) 6. (a) 7. (b) 8. (c) 9. (c) 10. (d)

11.(c) 12.(a) 13.(c) 14.(b) 15.(c) 16.(b) 17.(b) 18.(b) 19.(d) 20.(b)

21.(b) 22.(b) 23.(d) 24.(b) 25.(a) 26.(d) 27.(c) 28.(a) 29.(d) 30.(a)

31.(d) 32.(d) 33.(d) 34.(c) 35.(a) 36.(d) 37.(d) 38.(c) 39.(a) 40.(a)
A

41. (a) 42.(c) 43. (d) 44. (b) 45. (d) 46. (a) 47. (b) 48. (a) 49. (c) 50. (a)

51.(a) 52.(a) 53.(d) 54.(c) 55.(d) 56.(b) 57.(d) 58. (a) 59. (c) 60. (b)

61. (a) 62.(c) 63. (b) 64. (a) 65. (d) 66.(a) 67.(b) 68.(d) 69.(b) 70.(c)

71.(a) 72.(d) 73. (a) 74.(a) 75. (b) 76. (a) 77. (b) 78. (a) 79. (a) 80. (a)

81. (c) 82. (a) 83.(b) 84.(a) 85.(b) 86.(d) 87.(a)

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Ratio/vuqikr
(Practice Sheet With Solution)
1. If (a + b) : (b + c) : (c + a) = 7 : 6 : 5 and a + b + 7. 22,500 is to be divided among A, B, C, D as
follows. that the sum of the shares of A and C
1 1 1
c = 27, then what is the value of : : ?
a b c 3
is of the sum of the shares of B and D. B's
2
;fn (a + b) : (b + c) : (c + a) = 7 : 6 : 5 vkSja + b
1 1 1 5
+ c = 27 gS] rks: : dk eku D;k gS\ share is
4
of D's share. And the share of A is

r
a b c
3 times that of C, then tell the share of D.
(a) 3 : 6 : 4 (b) 3 : 4 : 2

si
(c) 3 : 2 : 4 (d) 4 : 3 : 6 22]500 #i;s dksA, B, C, D esa bl izdkj ck¡Vk tkrk gSA
2. If 6A = 4B = 9C, what is A : B : C? fd A vkSj C ds fgLls dk ;ksxB vkSj D ds fgLls ds

an by
;fn 6A = 4B = 9C rksA : B : C D;k gS\ 3 5
;ksx dk Hkkx gSA
B dk fgLlk D ds fgLls dk gSA

n
(a) 6 : 4 : 9 (b) 4 : 6 : 9 2 4
(c) 6 : 9 : 4 (d) 4 : 9 : 6 vkSjA dk fgLlk C dk 3 xquk gS rks
D dk fgLlk crkvksA

ja
3. If A : B = 6 : 7 Then what is the value of
3A²  4B
R s (a) 5,000 (b) 10,125
expression (c) 3,375 (d) 4,000
a th
3A² – 4B
8. Four numbers are in proportion. The sum of
the squares of the four No. is 50 and the sum
;fn A : B = 6 : 7 rks O;atd 3A²  4B dk eku D;k gS\ of means is 5. The ratio of two terms is 1 : 3
3A² – 4B
ty a

what is the average of four numbers?

(a) 17 : 20 (b) 20 : 17
(c) 10 : 13 (d) C.N.D pkj la[;k,¡ lekuqikr esa gSaA pkj la[;kvksa ds oxks± dk ;
di M

50 gS vkSj ekè;ksa dk ;ksx 5 gSA nks inksa dk vuqikr 1

a c e 2a²  3c²  4e²
4. If = = = 3 find
2b²  3d²  4f ²
gS] pkj la[;kvksa dk vkSlr D;k gS\
b d f
(a) 9 (b) 4 (a) 2 (b) 3
(c) 3 (d) 2 (c) 5 (d) 6
5. If w1 : w2 = 2 : 3 and w1 : w3 = 1 : 2 the find 9. The Ratio of income of Anil and Mukesh is 2 : 3
w22 : w32. The sum of their expenditure is 8,000 and the
;fn w1 : w2 = 2 : 3 vkSj w1 : w3 = 1 : 2 Kkr djsa amount of savings of Anil is equal to amount of
expenditure of Mukesh. What is the sum of their
w22 : w32.
savings?
(a) 3 : 4 (b) 9 : 16
(c) 4 : 3 (d) 16 : 9 vfuy vkSj eqds'k dh vk; dk vuqikr 2 % 3 gSA muds
O;; dk ;ksx 8]000 gS vkSj vfuy dh cpr dh jkf'k
A

6. The volume of gold is proportional to the

square of its weight. A person breaks a piece eqds'k ds O;; dh jkf'k ds cjkcj gSA mudh cpr dk ;ksx
of gold in the form of 3 : 2 : 1 then he has a D;k gS\
loss of Rs 4620 then tell the initial price of
gold. (a) 22,000 (b) 4,000
lksus dk ewY; mlds Hkkj
(weight) ds oxZ ds lekuqikrh gSA (c) 16,000 (d) 12,000
,d O;fDr lksus ds VqdM+s dks 3 % 2 % 1 ds :i esa rksM+
10. A naughty student breaks the pencil in such
a way that the ratio of two broken parts is
nsrk gS rks mls #i;s 4620 dh gkfu gksrh gS rks lksus dk
same as that of the original length of the
izkjfEHkd ewY; crkvksA
d pencil to one of the larger part of the pencil.
(a) 7460 (b) 7560 The ratio of the other part to the original
(c) 9450 (d) 10800 length of pencil is:

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,d 'kjkjrh Nk=k isafly dks bl rjg ls rksM+rk gS fd nks 1 1 1 1

usg: th ds ikl 'n' pkdysV FkhA mlus mUgsa
VwVs gq, fgLlksa dk vuqikr ogh gS tks isafly dh ewy yackbZ : : :
2 3 5 8
vkSj isafly ds ,d cM+s fgLls dk gSA nwljs Hkkx dk isafly
ds vuqikr esa4 cPpksa esa ckaV fn;kA ;fn og muesa ls
dh ewy yackbZ ls vuqikr gS% çR;sd dks ,d iwjh pkWdysV nsrk gS] rks U;wure la[;kA m
(a) 1 : 2 5 (b) 2 : (3  5) ikl tks pkWdysV Fkh%
(a) 139 (b) 240
(c) 2 : 5 (d) Can't be determined (c) 278 (d) None of these
11. If a³ + b³ : a³ – b3 = 133 : 117; find a : b: 16. Equal quantities of three mixtures of Alcohol
and water are mixed in the ratio of 1 : 2, 2 : 3
;fn a³ + b³ : a³ – b3 = 133 : 117 rksa : b: and 3 : 4. The ratio of water and Alcohol in the
(a) 2 : 3 (b) 5 : 4 mixture is:
(c) 5 : 2 (d) None of these vYdksgy vkSj ikuh ds rhu feJ.kksa dh leku ek=kk dks
12. A child has three different kinds of chocolates 1 % 2] 2 % 3 vkSj 3 % 4 ds vuqikr esa feyk;k tkrk gSA

r
costing Rs 2, Rs 5 and Rs 10. He spends total feJ.k esa ikuh vkSj vYdksgy dk vuqikr gS%
Rs 120 on the chocolates. What is the minimum

si
(a) 193 : 122 (b) 122 : 193
possible number of chocolates, he can buy, if
(c) 61 : 97 (d) 137 : 178
there must be at least one chocolate of each

an by
kind? 17. The ratio of age of P and Q is 8 : 9 and the

,d cPps ds ikl 2 #i;s] 5 #i;s vkSj 10 #i;s dh dher 2 9

n
age of Q is of R's age and age of R is
okyh rhu vyx&vyx rjg dh pkWdysV gSaA og dqy 120 3 13
#i;s •pZ djrk gSA og de ls de fdruh pkWdysV •jhn times the age of S. If the age of Q is 18 years

ja
then the age of R is:
R s
ldrk gS] ;fn çR;sd çdkj dh de ls de ,d pkWdysV
P vkSjQ dh vk;q dk vuqikr 8 % 9 gS vkSj
Q dh vk;q
gksuh pkfg,\
a th
2
(a) 22 (b) 19 R dh vk;q dk gS vkSjR dh vk;q S dh vk;q dk
3
(c) 17 (d) 15
9
ty a

13. In the previous problem (no. 8) what is the xquk gSA ;fn
Q dh vk;q 18 o"kZ gS rks dh vk;q
R gS%
maximum possible no. of chocolates? 13
fiNyh leL;k (la[;k 8) pkWdysV dh vf/dre la[;k
di M

(a) 36 yrs. (b) 39 yrs.

laHko la[;k D;k gS\ (c) 27 yrs. (d) 54 yrs.
(a) 52 (b) 53 18. A and B are two alloys of Iron and tin prepared
by mixing the respective metals in the ratio
(c) 55 (d) 60 of 5 : 3 and 5 : 11 respectively. If the alloys A
14. In the Ruchika's wallet there are only Rs. 16, and B are mixed to form a third alloy C with
consisting of 10 paise, 20 paise and Rs. 1 an equal proportion of Iron and tin, what is the
coins. The ratio of no. of coins of 10 paise and ratio of alloys A and B in the new alloy C?
20 paise is 6 : 1. The minimum no. of Rs. 1 A vkSj B yksgs vkSj fVu dh nks feJ/krq gSa ftUgsa Øe'k
coin is:
5 % 3 vkSj 5 % 11 ds vuqikr esa lacaf/r /krqvksa dk
#fpdk ds cVq, esa ek=k 16] #i;s ftlesa 10 iSls] 20 iSls feykdj rS;kj fd;k x;k gSA ;fn feJ/krqA vkSj B dks
vkSj 1 #i;s flDds gSA ;fn 10 iSls vkSj 20 iSls ds flDdksa feykdj ,d rhljh feJ/krq C cukbZ tkrh gS ftlesa vkW;ju
A

dh la[;k dk vuqikr 6 % 1 gSA 1 #i;s flDdksa dh de ls vkSj fVu dk leku vuqikr gksrk gS] rks ubZ feJ/krq
C esa
de la[;k ckrkvksaA feJ/krq A vkSjB dk vuqikr D;k gS\
(a) 5 (b) 12 (a) 3 : 5 (b) 4 : 5
(c) 4 (d) 8 (c) 3 : 2 (d) 2 : 3
15. Nehru Ji had 'n' chocolates. He distributed 19. The ratio of third proportional to 21 and 42
them among 4 children in the ratio of and mean proportional to 16 and 49 is:

1 1 1 1
21 vkSj 42 ds rhljs vkuqikfrd vkSj 16 vkSj 49 ds
: : : . If he gave them each one a
2 3 5 8 eè;kuqikfrd dk vuqikr gS%
complete chocolate, the minimum no. of (a) 3 : 1 (b) 2 : 3
chocolates that he had: (c) 4 : 3 (d) 1 : 3

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p²  q²
S, T vkSjU dh jkf'k 3 : 4 : 5 ds vuqikr esa gSA igys
20. Find the value of , if p : q :: r : s. 1 1 1
r²  s² T, S dks nsrk gS vkSj U dks ] S dks nsrk gSA
4 4 6
p²  q² S, T vkSj U dh jkf'k dk vafre vuqikr Kkr dhft,A
dk eku Kkr dhft,] ;fn p : q :: r : s. Øe'k%
r²  s²
(a) 4 : 3 : 5 (b) 5 : 4 : 3
1 1 (c) 6 : 4 : 2 (d) 5 : 2 : 5
(a) (b) 25. A three digit number is such that this number
4 9
itself is divisible by the sum of its digits. The
ps  p – q 2 sum of hundreds and unit digit is 6 while the
(c) rq (d)  
 sum of the tens and unit digit is 5. What is the
r – s 
ratio of unit and tens digit:
21. A rabit takes 22 leaps for every 17 leaps of cat ,d rhu vadksa dh la[;k ,slh gS fd ;g la[;k Lo;a vius
and 22 leaps of a rabit are equal to 17 leaps of vadksa ds ;ksx ls foHkkT; gSA lSdM+s vkSj bdkbZ ds v

r
the cat. What is the ratio of the speeds of rabit
;ksx 6 gS tcfd ngkbZ vkSj bdkbZ ds vad dk ;ksx 5 gSA
and cat?
bdkbZ vkSj ngkbZ ds vad dk vuqikr D;k gS\

si
,d •jxks'k fcYyh dh çR;sd 17 Nykax ds fy, 22 Nykax (a) 1 : 2 (b) 2 : 3
yxkrk gS vkSj ,d •jxks'k dh 22 Nykax fcYyh dh 17

an by
(c) 3 : 4 (d) 2 : 7
Nykax ds cjkcj gksrh gSA •jxks'k vkSj fcYyh dh xfr dk
26. Ram bought 1.5 kg. fresh grapes. The ratio of
vuqikr D;k gS\

n
water is to pulp was 4 : 1. When his naughty
(a) 1 : 1 (b) 484 : 289 child crushed these grapes, then some water

ja
R s get wasted. Now the ratio of water is to pulp
(c) 17 : 22 (d) None of these is 3 : 2. What is the total amount of the
crushed grapes?
1
a th
22. 10 yrs. ago the age of Radha was
3
rd of the jke us 1-5 fdxzk rktk vaxwj •jhnsaA ikuh vkSj xwns dk vuq
age of Mamta. 14 year hence the ratio of ages 4 % 1 FkkA tc mUgsa uV•V cPps us bu vaxwjksa dks d
of Radha and Mamta will be 5 : 9. Find the rks dqN ikuh cckZn gks x;kA vc ikuh dk xwns ls vuqik
ty a

ratio of their present ages: 3 % 2 gSA dqpys gq, vaxwj dh dqy ek=kk fdruh gS\
(a) 0.5 kg. (b) 1 kg.
1
di M

10 o"kZ igys jk/k dh vk;q eerk dh vk;q dk FkhA 14 (c) 0.75 kg. (d) None of these
3
o"kZ ckn jk/k vkSj eerk dh vk;q dk vuqikr 5 % 9 gksxkA
27. If m =
4pq
, then the value of
m  2p m  2q
 :
mudh orZeku vk;q dk vuqikr Kkr dhft,% p q m – 2p m – 2q

(a) 13 : 29 (b) 11 : 27 4pq m  2p m  2q

(a);fn m = ] rks  dk eku
(c) 29 : 17 (d) 13 : 25 pq m – 2p m – 2q
23. x varies directly as (y² + z²) At y = 1 and z = 2, (a) 2 (b) 4
the value of x is 15. Find the value of z, when 2mpq
x = 39 and y = 2: (c) (d) None of these
(p q)
x lh/s (y² + z²) ds :i esa fHkUu gksrk ygS]
= 1 vkSj 28. Three cats are roaming in a zoo in such a way
z = 2 ij] x dk eku 15 gSA z dk eku Kkr dhft,] tc
A

that when cat A takes 5 steps, B takes 6 steps

x = 39 vkSjy = 2: and cat C takes 7 steps. But the 6 steps of A
re equal to the 7 steps of B and 8 steps of C.
(a) 2 (b) 3
What is the ratio of their speeds:
(c) 4 (d) 6 ,d fpfM+;k?kj esa rhu fcfYy;k¡ bl çdkj ?kwe jgh gSa fd
24. S, T and U have amounts in the ratio of 3 : 4 : tc fcYyh A 5 dne pyrh gS] B 6 dne pyrh gS vkSj
1 1 fcYyhC 7 dne pyrh gSA ysfdu A ds 6 pj.k B ds 7
5. First T gives th to S and th to U gives
4 4 pj.kksa vkSj
C ds 8 pj.kksa ds cjkcj gSaA mudh xfr dk
1 vuqikr D;k gS%
th S. Find the final ratio of amount of S, T (a) 140 : 144 : 147 (b) 40 : 44 : 47
6
and U, respectively: (c) 15 : 21 : 28 (d) 252 : 245 : 240

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29. Find the value of x if (14x – 4) : (8x – 1) = (3x + 8) 34. Ratanlal sells rasgullas (a favorite Indian
: (9x + 5): sweets) at Rs. 15 per kg. A rasgulla is madeup
x dk eku Kkr dhft, ;fn (14x – 4) : (8x – 1) = (3x + of flour and sugar in the ratio of 5 : 3. The ratio
8) : (9x + 5): of price of sugar and flour is 7 : 3 (per kg). Thus

1 2
he earns 66 % profit. What is the cost price
(a) 1 (b) 3
2
of sugar?
3
(c)
4
(d) None of these jruyky 15 #i;s izfr fdxzk dh nj ls jlxqYys (,d ilanhnk
30. Pooja, Shipra and Monika are three sisters. Hkkjrh; feBkbZ) #i;s esa csprk gSaA ,d jlxqYyk 5 % 3 d
Pooja and Shipra are twins. The ratio of sum vuqikr esa vkVs vkSj phuh ls cuk gSA phuh vkSj vkVs
of the ages of Pooja and Shipra is same as that dher dk vuqikr 7 % 3 (çfr fdyks) gSA bl çdkj og
of Monika alone. Three yrs earlier the ratio of
2
age of Pooja and Monika was 2 : 7. What will 66 % ykHk vftZr djrk gSA phuh dk Ø; ewY; D;k
be the age of Shipra 3 yrs hence? 3

r
gS\
iwtk] f'kçk vkSj eksfudk rhu cgusa gSaA iwtk vkSj f'kçk tqM+oka

si
gSaA iwtk vkSj f'kçk dh vk;q ds ;ksx dk vuqikr vdsys(a) Rs. 10/kg. (b) Rs. 9/kg.
eksfudk dh vk;q ds leku gSA rhu lky igys iwtk vkSj (c) Rs. 18/kg. (d) Rs. 14/kg.

an by
eksfudk dh vk;q dk vuqikr 2 % 7 FkkA f'kçk dh 35. vk;q A company make a profit of Rs. 9,00,000, 20%
3 o"kZ ckn D;k gksxhA of which is paid as taxes. If the rest is divided

n
among the partners P, Q and R in the ratio of
(a) 21 yrs. (b) 16 yrs.
1

ja
(c) 8 yrs. (d) 12 yrs. 1:1 : 2 , then the shares of P, Q and R are
R s
31. In two alloys the ratio of Iron and copper is 4 : 3 2
and 6 : 1 respectively. If 14 kg of the first alloy respectively:
a th
and 42 kg of the second alloy are mixed
,d daiuh 9]00]000 #i;s dk ykHk dekrh gSA ftldk 20»
together to form a new alloy, then what will
be the ratio of copper to iron in the new alloy: dj ds :i esa Hkqxrku fd;k tkrk gSA ;fn 'ks"k dks Hkkxhnkj
nks feJ/krqvksa esa vk;ju vkSj dkWij dk vuqikr Øe'k% 1
ty a

P] Q vkSjR esa1 : 1 : 2 ds vuqikr esa foHkkftr fd;k

4 % 3 vkSj 6 % 1 gSA ;fn 14 fdxzk igyh feJ /krq vkSj 2
42 fdxzk nwljh feJ/krq dks feykdj ,d ubZ feJ/krq cukbZ tkrh tkrk gS] rks
P] Q vkSjR ds fgLls Øe'k% gSa%
di M

gS] rks ubZ feJ/krq

dkWij
esadk vk;ju ls vuqikr D;k gksxk\ (a) 2,40,000; 3,20,000; 1,60,000
(a) 11 : 3 (b) 11 : 8 (b) 3,20,000; 2,40,000; 1,60,000
(c) 8 : 11 (d) None of these (c) 1,60,000; 3,20,000; 2,40,000
32. In a zoo, there are rabbits and pigeons. If heads (d) 1,60,000; 2,40,000; 3,20,000
are counted, there are 340 heads and if legs
36. Four milkmen rented a pasture to graze 16
are counted there are 1060 legs. How many
cows for 3 months, B 20 cows for 4 months, C
pigeons are there?
18 cows for 6 months and D 42 cows for 2
,d fpfM+;k?kj esa •jxks'k vkSj dcwrj gSaA ;fn flj fxusmonths. If A's share of rent be Rs. 2400, the
tk,a rks 340 flj vkSj ;fn iSj fxus tk,a rks 1060 iSj gksrs rent paid by C is:
gSaA fdrus dcwrj gSa\ pkj nwf/;ksa us ,d pkjkxkg fdjk, ij fy;kAA us 16
A

(a) 120 (b) 150 xk;ksa dks 3 eghus]

B us 20 xk;ksa dks 4 eghus]
C us 18
(c) 180 (d) 170 xk;ksa dks 6 eghus DvkSj
42 xk;ksa dks 2 eghus rd pjk;kA
33. The number of oranges in three baskets are in ;fn fdjk, esa A dk fgLlk #i;s 2400] C }kjk Hkqxrku
the ratio of 3 : 4 : 5. In which ratio the no. of
oranges in first two baskets must be increased
fd;k x;k fdjk;k gS%
so that the new ratio becomes 5 : 4 : 3? (a) Rs. 3,200 (b) Rs. 4,200
rhu Vksdfj;ksa esa larjs dh la[;k 3 % 4 % 5 ds vuqikr esa
(c) Rs. 4,000 (d) Rs. 5,400
gSA igyh nks Vksdfj;ksa esa larjs dh la[;k c<+kuh gksxh
37. The rkfdvalue of a coin varies directly to the square
u;k vuqikr 5 % 4 % 3 gks tk,\ of its radius, when its thickness is constant.
The radius of a coin is 1.5 cm. and its value is
(a) 1 : 3 (b) 2 : 1
Rs. 2. What will be the radius of a coin if its
(c) 3 : 4 (d) 2 : 3 value is Rs. 5?

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,d flDds dk ewY; lh/s mldh f=kT;k ds oxZ ds cjkcj42. Raju and Lalita had marbles in the ratio 4 : 9.
gksrk gS] tc mldh eksVkbZ fLFkj gksrh gSA ,d flDds Lalita
dh gave some of her marbles to Raju as a
result. The ratio of number of marbles with
f=kT;k 1-5 lseh gSA vkSj bldk ewY; 2 #i;s gSA ,d flDdsRaju to that with Lalita became 5 : 6. What
dh f=kT;k D;k gksxh ;fn mldk ewY; 5 #i;s gks\ fraction of her original number of marbles was
(a) 2 (b) 4 given by Lalita to Raju.
(c) 2.4 (d) 3 jktw vkSj yfyrk ds ikl 4 % 9 ds vuqikr esa daps FksA
38. A cat takes 7 steps for every 5 steps of a dog, blds ifj.kkeLo:i yfyrk us vius dqN daps jktw dks ns
but 5 steps of a dog are equal to 6 steps of cat. fn,A jktw ds dapksa dh la[;k dk yfyrk ds lkFk dapksa dh
What is the ratio of speed of cat to that of dog?
la[;k ls vuqikr 5 % 6 gks tkrk gSA yfyrk }kjk jktw dks
,d fcYyh dqÙks ds gj 5 dne ds fy, 7 dne pyrh gS] dapksa dh okLrfod la[;k dk fdruk fHkUu fn;k x;k FkkA
ysfdu ,d dqÙks ds 5 dne fcYyh ds 6 dne ds cjkcj gksrs
7 21
gSaA fcYyh dh xfr dk dqÙks dh xfr ls vuqikr fdruk gS\ (a) (b)
11 31
(a) 7 : 6 (b) 7 : 5

r
7 1
(c) 6 : 7 (d) 5 : 7 (c) (d)
33 3

si
39. The Income of A, B & C are in the ratio 7 : 9 : 12
43. The salaries of Ramesh, Ganesh & Rajesh were
and their spending are in the ratio 8 : 9 : 15.
in the ratio 6 : 5 : 7 in 2010, and in the ratio

an by
1 3 : 4 : 3 in 2015. If Ramesh's salary increased
If A saves th of his income then the saving
4 by 25% during 2010-15, then the percentage

n
of A, B & C are in the ratio of? increase in Rajesh's salary during this period
is closed to.
A] B vkSj C dh vk; 7 % 9 % 12 ds vuqikr esa gS vkSj

ja
jes'k] x.ks'k vkSj jkts'k dk osru 2010 esa 6 % 5 % 7 ds
R s
mudk •pZ 8 % 9 % 15 ds vuqikr esa gSA A ;fn
viuh
vuqikr esa Fkk] vkSj 2015 esa 3 % 4 % 3 ds vuqikr esa FkkA
a th
1
vk; dk oka Hkkx cpkrk gSA]rks
B vkSj C dh cpr 2010&15 ds nkSjku jes'k ds osru esa 25» dh o`f¼ gqbZ] rks
4
vof/ ds nkSjku jkts'k ds osru esa yxHkx çfr'kr o`f¼ gqbZA
dk vuqikr gS dk\
(a) 10 (b) 7
ty a

(a) 56 : 99 : 69 (b) 69 : 56 : 99 (c) 9 (d) 8

(c) 99 : 56 : 69 (d) 99 : 69 : 56 44. If the ratio of sides of angels of a triangle is
di M

40. 16 years ago my grandfather's age was 9 times 1 : 1 : 2 Then the ratio of square of the
of my age. After 8 years from now his age will greatest side to sum of the squares of other
be 3 times of my age. What was the ratio of two sides is:
my age and my grandfather's age 8 years ago ;fn ,d f=kHkqt ds dks.kksa dh Hkqtkvksa dk
1:1vuqikr
: 2
respectively? gS% rks lcls cM+h Hkqtk dk oxZ vU; nks Hkqtkvksa ds
16 o"kZ igys esjs nknk dh vk;q esjh vk;q dk 9 xquk FkhA
;ksx ls vuqikr gS%
vc ls 8 o"kZ ckn mudh vk;q esjh vk;q dk 3 xquk gksxhA(a) 3 : 4 (b) 2 : 1
8 o"kZ igys esjh vk;q vkSj esjs nknk dh vk;q dk vuqikr(c) 1 : 1 (d) 1 : 2
Øe'k% fdruk FkkA 45. A student took five papers in an examination,
where the full marks were the same for each
(a) 3 : 8 (b) 1 : 5 paper. His marks in these papers were in the
(c) 1 : 2 (d) 11 : 53
A

proportion of 6 : 7 : 8 : 9 : 10. in all papers

41. If a, b, c are three positive integers such that together. The candidate obtained 60% of total
a & b are in the ratio 3 : 4 while b & c are in marks. Then the number of papers in which
the ratio 2 : 1, then which one of the following he got more than 50% marks is:
is a possible value of (a + b + c)? ,d Nk=k us ,d ijh{kk esa ik¡p isij fn,] tgk¡ çR;sd isij
;fn a, b, c rhu /ukRed iw.kkZad bl çdkj gSaa fd
vkSj ds fy, iwjs vad leku FksA bu isijksa esa mlds vad lHkh
b dk vuqikr 3 % 4 gS tcfd b vkSj c dk vuqikr isijksa esa feykdj 6 % 7 % 8 % 9 % 10 ds vuqikr esa F
2 % 1 gS] rks fuEufyf•r esa ls dkSu
(a lk
+ b + c) ,d mEehnokj us dqy vadksa dk 60» çkIr fd;kA rks fdrus isij
laHkkfor eku gS\ esa mls 50» ls vf/d vad feys gSa%
(a) 201 (b) 205 (a) 2 (b) 3
(c) 207 (d) 210 (c) 4 (d) 5

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46. To get the ratio p : q (for pq). What must add fouksn vkSj olw }kjk çkIr vadksa dk vuqikr 6 % 5 gSA ;
to each term of the ratio x : y? muds çfr'kr dk la;qDr vkSlr 68-75 gS vkSj muds vadksa
vuqikr p : q ( pq ds fy,) çkIr djus ds fy,A vuqikr dk ;ksx 275 gS] rks dqy vad Kkr dhft, ftlds fy,
x : y ds çR;sd in esa D;k tksM+k tkuk pkfg,\ ijh{kk vk;ksftr dh xbZ FkhA
px  qy qx – py (a) 150 (b) 400
(a) p–q (b) p–q (c) 200 (d) None of these
49. The ratio of A two-digit natural number to a
px – qy py – qx number formed by reversing its digit is 4 : 7.
(c) p–q (d) p–q Which of following is the sum of all the
numbers of all such pairs?
47. The monthly incomes of A & B are in the ratio
,d nks vadksa dh çkÑfrd la[;k dk mlds vad dks myV
4 : 5. Their expenses are in the ratio 5 : 6. If
'A' saves Rs. 25 per month, and 'B' saves Rs. 50 dj cukbZ xbZ la[;k ls vuqikr 4 % 7 gSA fuEufyf•r esa ls
permonth, what are their respective incomes. dkSu lk ,sls lHkh tksM+s dh lHkh la[;kvksa dk ;ksx gS\

r
A vkSj B dh ekfld vk; 4 % 5 ds vuqikr esa gSA muds (a) 99 (b) 198

si
O;; 5 % 6 ds vuqikr esa gSaA'A';fn25 #i;s izfrekg (c) 330 (d) 132
cpkrk gSA vkSj
'B' 50 #i;s izfrekg cpkrk gSA mudh lacafèkr

an by
50. The ratio of expenditure to savings of a woman
vk; D;k gSaA is 5:1. If her income and expenditure are

n
(a) 400,500 (b) 240,300 increased by 10% and 20%, respectively, then
find the percentage change in her savings.
(c) 440,550 (d) 320,440
,d efgyk dk O;; vkSj cpr dk vuqikr 5 % 1 gSA ;fn

ja
R s
48. The ratio of marks obtained by Vino d and
Vasu is 6 : 5. If the combined Average of their mldh vk; vkSj O;; esa Øe'k% 10» vkSj 20» dh o`f¼ dh
tkrh gS] rks mldh cpr eas izfr'kr ifjorZu Kkr dhft,A
a th
percentage is 68.75 and Their sum of the
marks is 275 Find the total marks for which (a) 55% (b) 60%
exam was conducted. (c) 50% (d) 40%
ty a

Answer Key
di M

1.(d) 2.(c) 3.(d) 4.(a) 5.(b) 6.(b) 7.(d) 8.(b) 9.(d) 10.(b)

11.(c) 12.(c) 13.(b) 14.(c) 15.(a) 16.(a) 17.(c) 18.(c) 19.(a) 20.(c)

21.(a) 22.(a) 23.(b) 24.(d) 25.(b) 26.(c) 27.(a) 28.(a) 29.(b) 30.(c)

31.(d) 32.(b) 33.(b) 34.(d) 35.(d) 36.(d) 37.(c) 38.(a) 39.(a) 40.(b)

41.(c) 42.(c) 43.(b) 44.(c) 45.(b) 46.(b) 47.(a) 48.(b) 49.(c) 50.(d)
A

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 PROPORTION/lekuqikr
(CLASSROOM SHEET)
5. The fourth proportional to the numbers 5, 6
WHEN THREE NUMBERS and 8 is:
ARE GIVEN. la[;kvksa 5] 6 vkSj 8 dk prqFkkZuqikrh D;k gS\
SSC CHSL 24/05/2022 (Shift- 03)
(a) 9.8 (b) 9.6
FIRST PROPORTION (c) 9 (d) 9.5
(izFke vuqikr) 6. The fourth proportional to 5, 8 and 30 is:
5] 8 vkSj 30 dk pkSFkk lekuqikrh D;k gksxk\

r
1. The first proportional of three numbers 6,
SSC CHSL 27/05/2022 (Shift- 01)

si
12 and 24 is :
(a) 50 (b) 60
rhu la[;k,¡ 6] 12 vkSj 24 dk çFke vuqikr D;k
gksxk\ an by 7.
(c) 48 (d) 90
What is the ratio of the fourth proportional

n
(a) 3 (b) 4 of 2, 5, 6 and the fourth proportional of 6,
(c) 7 (d) 6 8, 9?

ja 2, 5, 6 ds
prqFkkZuqikrh6,vkSj
8, 9 ds prqFkkZuqikrh
R s
SECOND PROPORTION
dk vuqikr D;k gS\
(f}rh; vuqikr)
a th

SSC CGL 02/12/2022 (Shift- 03)

2. The second proportional of three numbers (a) 3 : 2 (b) 5 : 3
28, 4 and 5 is : (c) 3 : 4 (d) 5 : 4
ty a

rhu la[;k,¡ 28] 4 vkSj 5 dk f}rh; vuqikr D;k 8. What is the fourth proportional of
gksxk\ 1 1 1
di M

, , ?
(a) 39 (b) 48 72 168 150
(c) 35 (d) 40 1 1 1
, , dk prqFkkZuqikrh D;k gS\
THIRD PROPORTION 72 168 150

(r`rh; vuqikr) SSC Phase X 02/08/2022 (Shift- 02)

3. The third proportional of three numbers 1 1

(a) (b)
2, 3 and 15 is : 250 275
rhu la[;k,¡ 2] 3 vkSj 15 dk r`rh; vuqikr D;k 1 1
gksxk\ (c) (d)
375 350
A

(a) 10 (b) 20
When Two Numbers are Given
(c) 30 (d) 40

FOURTH PROPORTION FIRST PROPORTION

(prqFkZuqikr)
v (izFke vuqikr)
4. The fourth proportional to 7, 16, 21 is:
9. The first proportional of two numbers 3
7, 16, 21 dk prqFkkZuqikrh ------------- gSA and 5 is :
ICAR MAINS, 10/07/2023 (Shift-1) nks la[;k,¡ 3 vkSj 5 dk izFke vuqikr D;k gksxk\
(a) 54 (b) 48 (a) 1.6 (b) 1.8
(c) 45 (d) 51 (c) 1.2 (d) 1.4

[1]
 15. What is the third proportion to 15 and 24?
MEAN PROPORTION
15 vkSj24 dk r`rh;kuqikr D;k gS\
(eè; vuqikr) SSC CHSL 24/05/2022 (Shift- 01)

10. Find the mean proportion of 3 and 27. 4 2

(a) 38 (b) 37
3 vkSj 27 dk eè;kuqikrh
(mean proportion) 5 5
Kkr dhft,A
2 4
SSC CHSL 24/05/2022 (Shift- 02) (c) 38 (d) 37
5 5
(a) 5 (b) 10
16. If the third proportion of 3 and x is 27 and
(c) 6 (d) 9
the third proportion of 2 and y is 8, then
11. Find the mean proportional between 144 find x : y.
and 225. ;fn 3 vkSj x dk r`rh; vuqikr 27 gS vkSj 2 vkSj
y
144 vkSj 225 ds chp dk eè;kuqikrh Kkr dhft,A dk r`rh; vuqikr 8 gS] rks
x %y Kkr djsaA
SSC CHSL 31/05/2022 (Shift- 02)

r
SSC MTS 03/05/2023 (Shift-02)
4 27 (a) 7 : 9 (b) 4 : 5

si
(a) (b) (c) 3 : 7 (d) 9 : 4
5 2
SOME MIX TCS QUESTIONS
(c) 180
an by (d)
5
4
17. The fourth porportion to 12 , 24 and 27

n
is the same as the third proportion to A
and 36. What is the value of A?
a3 + b3
12. Find the mean proportion of and 12, 24 vkSj 27 dk prqFkkZuqikr]
A vkSj 36 ds
ja a–b
R s
r`rh;kuqikr ds cjkcj gSA
A dk eku Kkr dhft,A
a 2 – b2 SSC CGL 05/12/2022 (Shift- 03)
a th

.
a – ab + b2
2
(a) 22 (b) 24
(c) 26 (d) 20
a3 + b3 a 2 – b2
vkSj dk eè;kuqikrh Kkr 18. If p is the third proportional to 8, 20 and
ty a

a–b a 2 – ab + b2
q is the fourth proportional to 3, 5, 24 ,
dhft,A then find the value of (2p + q).
di M

SSC CGL 06/12/2022 (Shift- 03) ;fn 8] 20 dk r`rh;kuqikrhp gS vkSj 3] 5] 24 dk

(a) 1 (b) a + b
prqFkkZuqikrh
q gS] rks
( 2p + q) dk eku Kkr dhft,A
a+b SSC CGL 11/04/2022 (Shift- 03)
(c) (d) a + b
a–b (a) 140 (b) 126
13. If A is the mean proportion of 24 and 6. B (c) 90 (d) 104
is the mean proportion of 81 and 9. Find 19. What is the difference in the mean
the value of 3A – B. proportional between 1.8 and 3.2 and the
;fn A] 24 vkSj 6 dk ekè; vuqikr gSA
B] 81 vkSj third proportional to 5 and 3?
9 dk ekè; vuqikr gSAA3& B dk eku Kkr dhft,A 1-8 vkSj 3-2 ds chp eè;kuqikr vkSj 5 vkSj 3 ds
SSC MTS 09/05/2023 (Shift-03) r`rh;kuqikr esa varj Kkr djsaA
A

(a) 33 (b) 32 SSC CGL 17/08/2021(Shift- 02)

(c) 63 (d) 55 (a) 0.6 (b) 0.4
(c) 0.5 (d) 0.7
THIRD PROPORTION
20. Find the ratio between the fourth
(r`rh; vuqikr) proportional of 12, 16, 6 and the third
proportional of 4, 6.
14. The third proportional to 32 and 40 is: 12] 16] 6 ds prqFkkZuqikr vkSj 4] 6 ds r`rh;kuqikr
32 vkSj 40 dk rhljk lekuqikrh fdruk gksxk\ ds eè; vuqikr Kkr djsaA
ICAR MAINS, 10/07/2023 (Shift-2) SSC CGL 18/08/2021(Shift- 01)
(a) 56 (b) 48 (a) 11 : 5 (b) 3 : 2
(c) 42 (d) 50 (c) 4 : 3 (d) 8 : 9

[2]
21. If the third proportion to 2y – 1 and 6 is la[;kvksa
27, 31, 29 vkSj37 esa ls izR;sd ls dkSu&lh
12 and the fourth proportion to 2x + 7, 5 la[;k ?kVkbZ tk, fd izkIr 'ks"k la[;k,a lekuqikrh gks
and 39 is 15, then find the value of x + 2y.
ICAR MAINS, 08/07/2023 (Shift-2)
;fn 2y – 1 vkSj 6 dk rhljk vuqikr 12 gS vkSj
(a) 25 (b) 27
2x + 7] 5 vkSj 39 dk pkSFkk vuqikr 15 gS]
x+rks
2y dk eku Kkr dhft,A (c) 30 (d) 20
27. If x is subtracted from each of 24, 40, 33 and
CRPF HCM 01/03/2023 (Shift - 02)
57, the numbers, so obtained are in proportion.
(a) 3 (b) 5 The ratio of (5x + 12) to (4x+15) is
(c) 7 (d) 4 20] 40] 30 vkSj 57 esa ls izR;sd xls?kVkus ij
22. If the four numbers, 39, 117, 17 and y are izkIr la[;k,a lekuqikr esa (5x
gSaA+ 12) vkSj (4x
in proportion, then find the value of y
+ 15) dk vuqikr Kkr djsaA
;fn pkj la[;k,¡] 39] 117] 17 vkSj y lekuqikr esa gSa]
SSC CGL 23/08/2021(Shift- 02)

r
rksy dk eku Kkr dhft,A
(a) 4 : 3 (b) 14 : 13

si
CGL PRE, 14/07/2023 (Shift-1)
(c) 7 : 4 (d) 7 : 5
(a) 49 (b) 51
(c) 57 an by (d) 85
28. When x is subtracted from each of the
numbers 54, 49, 22 and 21, the numbers
so obtained are in proportion. The ratio

n
PROPORTION AFTER of (8x – 25) to (7x – 26) is:
ADDITION OR SUBTRACTION la[;kvksa 54] 49] 22 vkSj 21 esa ls izR;sd
x dks
ls
ja
R s
23. Which number should be added in 4, 10, ?kVkus ij izkIr la[;k,a lekuqikr eas(8xgSaA
–25)
12 and 24 each to make these numbers vkSj(7x – 26) dk vuqikr Kkr djsaA
a th

in proportion.
SSC CGL 23/08/2021(Shift- 03)
4, 10, 12, 24 esa izR;sd esa dkSu lh la[;k tksM+h
(a) 29 : 24 (b) 15 : 13
tkuh pkfg, ftlls ifj.kkeh la[;k,¡ lekuqikfrd gks\
ty a

(c) 27 : 26 (d) 5 : 4
(a) 9 (b) 3
29. When x is added to each of 2, 3, 30 and
di M

(c) 6 (d) 4 35, then the numbers obtained in this

24. Which number when added to each of the order, are in proportion. What is the mean
numbers 6, 7, 15, 17 will make the proportional between (x + 7) and (x – 2)?
resulting numbers proportional. tc x dks 2] 3] 30 vkSj 35 esa tksM+k tkrk gS rks bl
fdl la[;k dks 6, 7, 15, 17 ds izR;sd la[;k esa Øe esa izkIr gksus okyh la[;k,¡ lekuqikr (x
esa+ gSA
tksM+k tk, dh pkjksa la[;k,¡n lekuqikfrd gks tk,\ 7) rFkk(x + 2) ds chp eè; lekuqikrh Kkr djsaA
(a) 5 (b) 3 SSC CGL, Tier II 11/09/2019
(c) 6 (d) 4 (a) 7 (b) 4
25. What is the least number subtracted from (c) 6 (d) 5
A

14, 36, 20 and 54 so that these numbers 30. What number must be added to each of
become proportional? the number 8, 13, 26 and 40 so that the
14, 36, 20, 54 esa izR;sd in esa ls de&ls&de number obtained in this order are in
proportion?
D;k ?kVk;k tk, fd ;s la[;k,¡ lekuqikrh gks tk,\
(a) 3 (b) 2
fdl la[;k dks 8] 13] 26 vkSj 40 esa tksM+k tkuk
pkfg, rkfd bl Øe esa izkIr la[;k,¡ lekuqikr esa gks\
(c) 4 (d) 5
26. What number should be subtracted from SSC CHSL,16/10/2020 (Shift- 02)
each of the numbers 27, 31, 29 and 37 (a) 2 (b) 3
so that the remainders are proportional? (c) 1 (d) 4

[3]
 Answer Key
1. (a) 2.(c) 3. (a) 4. (b) 5. (b) 6. (c) 7. (d) 8. (c) 9. (b) 10. (d)

11.(c) 12.(b) 13.(c) 14.(d) 15.(c) 16.(d) 17.(b) 18.(c) 19.(a) 20.(d)

21.(c) 22.(b) 23.(d) 24.(b) 25.(a) 26.(a) 27.(b) 28.(a) 29.(c) 30.(a)

r
si
an by
n
ja
R s
a th
ty a
di M
A

[4]
Join Telegram- Maths by Aditya Ranjan Proportion

Proportion@lekuqikr
(Practice Sheet With Solution)
1. What is the fourth proportional to 3, 7, 15. 7. x varies directly as (y² + z²). At y = 2 and z =
3] 7] 15 dk prqFkZ lekuqikrh D;k gS\ 3, then value of x is 26. Find the value of x,
when z = 1, and y = 5.
(a) 20 (b) 30
x lh/s (y² + z²) ds :i esa fHkUu gksrkygSA
= 2 vkSjz
(c) 35 (d) 45
2. What is the mean proportion between 8 and 32.
=3 ij] rc x dk eku 26 gSA dk eku Kkr dhft,]
x
tc z = 1] vkSjy = 5 gksA
8 vkSj 32 ds chp eè; vuqikr D;k gS\
(a) 50 (b) 55

r
(a) 2 (b) 4
(c) 52 (d) 60

si
(c) 16 (d) 32
8. If 80 is the fourth proportional to 10, 16 and
3. What is the sub-duplicate ratio of 16 : 25. x, then the value of x is:

an by
16%25 dk lc&MqfIydsV vuqikr D;k gS\ ;fn 10] 16 vkSj x dk prqFkkZuqikrh 80 gS]
x dkrks
eku
(a) 2 : 3 (b) 4 : 5 Kkr dhft,A

n
(c) 3 : 7 (d) None (a) 128 (b) 2
4. Given that both x and y vary directly from

ja
(c) 50 (d) 108
R s
each other. If x = 10 and y = 15, which of the 9. What is the fourth proportional to 0.6, 0.12,
following pairs is not possible with respect to 0.04?
a th
the value of x and y? 0.6, 0.12, 0.04 dk prqFkkZuqikrh D;k gS\
fn;k x;k gS fd x vkSj y nksuksa ,d nwljs ls lh/s fHkUu (a) 0.1 (b) 0.098
gksrs gSaAx;fn
¾ 10 vkSjy ¾ 15] fuEufyf•r esa ls dkSu (c) 0.008 (d) 0.68
ty a

lk ;qXex vkSjy ds eku ds laca/ esa laHko ugha gS\ 10. What is the ratio of the mean proportional
(a) x = 2 and y = 3 (b) x = 8 and y = 12 between 4.8 and 10.8 and the third
di M

proportional to 0.4 and 2.4?

(c) x = 15 and y = 20 (d) x = 25 and y = 37.5
4-8 vkSj 10-8 ds chp eè; vkuqikfrd vkSj 0-4 vkSj 2-4
5. If p, q, r and s are proportional then the mean
proportion between p² + r² and q² + s² is ds chp r`rh; vkuqikfrd dk vuqikr D;k gS\
(a) 2 : 3 (b) 1 : 2
;fn p, q, r vkSjs vkuqikfrd gSa rks
p² + r² vkSjq² +
(c) 3 : 2 (d) 2 : 1
s² ds chp vkSlr vuqikr gS
11. What is the difference in the mean
pr proportional between 1.8 and 3.2 and the third
(a) (b) pq  rs proportional to 5 and 3?
qs
1-8 vkSj 3-2 ds chp eè;kuqikr vkSj 5 vkSj 3 ds rqrh;kuqikr
p s 2
p r2
eas varj Kkr djsaA
(c) + (d) 
A

q r q2 s2 (a) 0.6 (b) 0.4

(c) 0.5 (d) 0.7
6. At constant temperature, pressure of a definite
12. Find the ratio between the fourth proportional
mass of gas is inversely proportional to the
of 12, 16, 6 and the third proportional of 4, 6.
volume. If the pressure is reduced by 20%, find
the respective change in volume. 12] 16] 6 ds prqFkkZuqikr vkSj 4] 6 ds r`rh;kuqikr ds
fLFkj rkieku ij] xSl ds ,d fuf'pr æO;eku dk ncko eè; vuqikr Kkr djsaA
(a) 11 : 5 (b) 3 : 2
vk;ru ds O;qRØekuqikrh gksrk gSA ;fn nkc dks 20» de
(c) 4 : 3 (d) 8 : 9
dj fn;k tk,] rks vk;ru esa lacaf/r ifjorZu Kkr dhft,A 13. Fourth proportion to 12, 18 and 6 is same as
(a) –16.66% (b) +25% the third proportion to k and 6. What is the
(c) –25% (d) +16.66 value of k?

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12] 18 vkSj 6 dk prqFkkZuqikr

k vkSj 6 ds r`rh;uqikr ds la[;kvksa 54] 49] 22 vkSj 21 esa ls izR;sd
x dks
ls ?kVkus
cjkcj gSA
k dk eku Kkr djsaA ij izkIr la[;k,a lekuqikr esa gSA
(8x – 25) vkSj(7x –
(a) 363 (b) 13.5 26) dk vuqikr Kkr djsaA
(c) 4 (d) 3 (a) 29 : 24 (b) 15 : 13
14. What number should be added to each of the (c) 27 : 26 (d) 5 : 4
number 103, 135, 110 and 144 so that the 20. If b is the mean proportion to a and c with a
resulting numbers are in proportion?
2
103] 135] 110 vkSj 144 esa izR;sd la[;k esa dkSu lh common ratio 3 3 , then (a – b)3 : (b – c)3 is
la[;k tksM+h tkuh pkfg, fd ftlds ifj.kkeLo:i izkIr
;fn a vkSjc dk eè;kuqikrhb gS vkSj bldk nksuksa ds
la[;k,a lekuqikr esa gksa\
(a) 12 (b) 15 2
lkFk mHk;fu"B vuqikr
3
gS rks
(a – b)3 : (b – c)3 dk
(c) 9 (d) 6 3
15. If 2x + 1, x + 2, 2 and 5 are in proportion, then eku Kkr dhft,A
what is the mean proportional between 3.5(1

r
(a) 3 : 2 (b) 1 : 1
– x) and 8(1 + x)? (c) 2 : 3 (d) 1 : 2

si
;fn 2x + 1, x + 2, 2 vkSj5 lekuqikr esa gS]3.5(1
rks 21. A gold broke into three parts, the ratio of
– x) vkSj8(1 + x) dk eè;kuqikrh D;k gS\ weight of three part is 3:4:5. The price of gold

an by
is directly proportional to its square weight.
(a) 5.5 (b) 4.25
If there is loss of Rs 23500 after breaking gold
(c) 5.25 (d) 4.5

n
then what was the starting price of gold?
16. When x is added to each of 9, 15, 21 and 31,
,d lksuk rhu fgLls esa VwV x;kA bu rhuks fgLls ds otu
the numbers so obtained are in proportion.
dk vuqikr 3 % 4 % 5 gSA lksus dh dher blds otu ds

ja
What is the mean proportional between the
R s
numbers (3x – 2) and (5x + 4)? oxZ ds vuqØekuqikrh gSA ;fn ;s lksuk VwVus ij 235
tc x dks 9] 15] 21 vkSj 31 esa ls izR;sd esa tksM+k tkrk :i;s dk uqdlku gqvkA lksus dh ewy dher D;k Fkh\
a th
gS] rks izkIr la[;k,¡ lekuqikr esa gksrh gSaA
(3x –la[;k
2) (a) 30,000 (b) 36,000
(c) 40,000 (d) 46,000
vkSj(5x + 4) ds chp eè;kuqikr Kkr dhft,A 22. If x is the mean proportional between 12.8 and
ty a

(a) 35 (b) 20 64.8 and y is the third proportional to 38.4

(c) 30 (d) 42 and 57.6, then 2x : y is equal to:
;fn x, 12.8 vkSj64.8 dk eè;kuqikrh gS vkSjy, 38.4 vkSj
di M

17. When x is added to each of 2, 3, 30 and 35,

then the numbers obtained in this order, are 57.6 dk r`rh;kuqikrh in gS] 2x
rks: y____ds cjkcj gksxk\
in proportion. What is the mean proportional
(a) 1 : 2 (b) 2 : 3
between (x + 7) and (x – 2)?
(c) 3 : 4 (d) 4 : 5
tc 2] 3] 30 vkSj 35 esa ls izR;sd esa
x tksM+k tkrk gS] 23.
rks The fourth proportional to 0.12, 0.21 and 8 is
bl Øe esa izkIr la[;k,a] lekuqikfrd gksrh(xgS
+ 7) vkSj 0-12] 0-21 vkSj 8 dk pkSFkk lekuqikfrd gS
(x – 2) ds chp dk eè; vkuqikfrd D;k gksxk\ (a) 8.9 (b) 14
(a) 7 (b) 4 (c) 17 (d) 56
(c) 5 (d) 6 24. The mean proportional between (3 + 2) and
(12 – 32) is
18. If x is subtracted from each of the numbers
20, 37, 54 and 105, then the numbers so (3 + 2) vkSj(12 – 32) ds chp ekè; lekuqikfrd gS
obtained in this order are in proportion. What (a) 7 (b) 27
A

is the mean proportional between (7x – 5) and

15 – 3 2
(x + 1)? (c) 6 (d)
2
tc 20] 37] 54 vkSj 105 esa ls izR;sd xesa?kVk;k tkrk
25. When a particular number is subtracted from
gS rks bl Øe esa izkIr la[;k,a] vuqikr esa gksrh
(7x –gS each of 7, 9, 11 and 15 the resulting numbers are
5) vkSj(x + 1) dk eè;kuqikr Kkr dhft,A in proportion. The number to be subtracted is
(a) 8 (b) 9 tc ,d fo'ks"k la[;k dks 7] 9] 11 vkSj 15 çR;sd esa ls
(c) 6 (d) 12 ?kVk;k tkrk gS rks ifj.kkeh la[;k,¡ lekuqikr esa gksrh g
19. When x is subtracted from each of the ?kVkbZ tkus okyh la[;k gS
numbers 54, 49, 22 and 21, the numbers so (a) 1 (b) 2
obtained are in proportion. The ratio of (8x –
(c) 3 (d) 5
25) to (7x – 26) is:

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26. If 2x + 1, x + 2, 2 and 5 are proportion then 29. The mean proportional between 45 and a
find (x + 3) : (x – 2) ? certain number is three times the mean
;fn 2x + 1, x + 2, 2 vkSj 5 lekuqikr gSa](xrks+ 3) : proportional between 5 and 22. The number is:
(x – 2) Kkr dhft,A
45 vkSj ,d fuf'pr la[;k ds chp dk eè;kuqikr 5 vkSj 22
(a) 23 : – 17 (b) 23 : 17
(c) 23 : 16 (d) – 23 : 17
ds chp ds eè;kuqikr dk rhu xquk gSA la[;k gS%
27. What is the mean proportional of (15 + 200) (a) 56 (b) 22
and (27 – 648)? (c) 43 (d) 65
(15 + 200) vkSj(27 – 648) dk vkSlr vuqikr D;k gS\ 30. What number should be added to each of the
(a) 35 (b) 820 numbers 94, 24, 100 and 26, so that the
(c) 37 (d) 73 resulting numbers are in continued
x y proportion?
28. What is the third proportional of y  x , x ²  y² .
94] 24] 100 vkSj 26 la[;kvksa esa ls izR;sd la[;k esa fdl

r
x y la[;k dk ;ksx fd;k tkuk pkfg,] rkfd ifj.kkeh la[;k

y x, x ²  y² dk rhljk lekuqikrh D;k gS\
fujarj vuqikr eas gks\

si
(a) xy (b) x
(a) 10 (b) 9

an by
(c) 2 (d) x²y²
(c) 11 (d) 8

n
ja
Answer Key
R s
1.(c) 2.(c) 3.(b) 4.(c) 5.(b) 6.(b) 7.(c) 8.(c) 9.(c) 10.(b)
a th
11.(a) 12.(d) 13.(c) 14.(c) 15.(c) 16.(a) 17.(d) 18.(a) 19.(a) 20.(c)
ty a

21.(b) 22.(b) 23.(b) 24.(b) 25.(c) 26.(a) 27.(a) 28.(a) 29.(b) 30.(c)
di M
A

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QUESTIONS BASED ON AGE/ vk;q ij vk/kfjr iz'u

[CLASSROOM SHEET]
1. The present age of Rahim is five times the firk vkSj iq=k dh vk;q esa 15 o"kZ dk varj gSA 5 o"kZ
present age of his daughter, Savita. Seven iwoZ firk dh vk;q] vius iq=k dh vk;q dh 2 xquh FkhA
years from now, Rahim will be three times
mu nksuksa dh orZeku vk;q Kkr dhft,A
as old as Savita. What is the present age (in
years) of Rahim? SSC CHSL TIER II 26/06/2023
jghe dh orZeku vk;q] mldh iq=kh lfork dh orZeku (a) 45 yrs, 30 yrs (b) 40 yrs, 25 yrs
vk;q dh ik¡p xquk gSA vc ls lkr o"kZ ckn jghe dh (c) 30 yrs, 15 yrs (d) 35 yrs, 20 yrs

r
vk;q] lfork dh vk;q dh rhu xquh gksxhA jghe 5.dh The ratio between the present ages of A
orZeku vk;q (o"kZ esa) D;k gS\

si
and B is 3:5. If the ratio of their ages five
years hence becomes 13:20, then the
CGL PRE, 14/07/2023 (Shift-2)
(a) 45 an by (b) 35
present age of B is :
A vkSj B dh orZeku vk;q dk vuqikr 3%5 gSA ;fn

n
(c) 40 (d) 30 ikap o"kZ ckn mudh vk;q dk vuqikr 13%20 gks tkrk
2. Ratio of the present age of a mother to gS] rks
B dh orZeku vk;q gS%

ja
that of the daughter is 7 : 1. After 5 years
R s
CGL 2019 Tier-II (18-11-2020)
the ratio will become 4 : 1. What is the (a) 32 Years (b) 35 Years
a th

difference (in years) in their present ages?

(c) 30 Years (d) 40 Years
,d ek¡ vksj mldh csVh dh orZeku vk;q dk vuqikr
6. Eight year ago, the ratio of ages of A and
7 % 1 gSA 5 o"kZ ckn ;g vuqikr 4 % 1 gks tk,xkA B was 5 : 4. The ratio of their present ages
ty a

mudh orZeku vk;q esa varj (o"kZ esa) Kkr djsaA is 6 : 5. What will be the sum (in years) of
the ages of A and B after 7 years from now?
SSC CGL 16/08/2021 (Shift-01)
di M

vkB o"kZ igys]

A vkSjB dh vk;q dk vuqikr 5 % 4
(a) 30 (b) 28
FkkA mudh orZeku vk;q dk vuqikr 6 % 5 gSA vc ls
(c) 29 (d) 31 7 o"kZ ckn]
A vkSj B dh vk;q dk ;ksx (o"kksZa esa)
3. The ratio of present ages of A and B is 7 : fdruk gksxk\
8. After 6 years from now, the ratio of their SSC CGL MAINS 29 JAN 2022
ages will be 8 : 9. If C's present age is 10
(a) 80 (b) 112
years more than the present age of A, then
(c) 112 (d) 102
the present age (in years) of C is:
7. Mother told her daughter, "Seven years
A vkSjB dh orZeku vk;q dk vuqikr 7 % 8 gSA vc ago, I was seven times as old as you were
ls Ng o"kZ ckn] mudh vk;q dk vuqikr 8 % 9 gksxkAthen. Also, three years from now, I shall be
;fn C dh orZeku vk;q]A dh orZeku vk;q ls 10
A

three times as old as you will be". Find the

o"kZ vf/d gS] rks
C dh orZeku vk;q (o"kZ esa) Kkr present ages of the mother and the
djsaA daughter, respectively.

SSC CGL 17/08/2021 (Shift-03) ek¡ us viuh iq=kh ls dgk] ¶lkr lky igys] esjh vk;q
rqEgkjh rc dh vk;q dh lkr xquk FkhA vc ls rhu o"kZ
(a) 56 (b) 52
ckn esjh vk;q rqEgkjh rc dh vk;q dh rhu xquh gks
(c) 59 (d) 45 tk,xhA ek¡ vkSj iq=kh dh Øe'k% orZeku vk;q Kkr dhft,A
4. The difference between the ages of father
SSC CGL TIER I 19/07/2023 (Shift-03)
and son is 15 years. 5 years ago the age of
the father was twice the age of his son. (a) 45; 15 (b) 40; 10
Find the present age of both of them. (c) 42; 12 (d) 50; 20

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8. The ratio of the age of Ram and Rahim 10 13. The ages of Fatima and Ahmed are in the
years ago was 1 : 3. The ratio of their age ratio of 3:8. The sum of their present ages
five years hence will be 2 : 3. Then the ra- is 44 years. The difference of their ages is:
tio of their present age is
iQkfrek vkSj vgen dh vk;q dk vuqikr 3%8 gSA mudh
10 o"kZ iwoZ jke vkSj jghe dh vk;q dk vuqikr 1%3 orZeku vk;q dk ;ksx 44 o"kZ gSA mudh vk;q dk varj gS%
FkkA ikap o"kZ ckn mudh vk;q dk vuqikr 2%3 gksxkA SSC CHSL 26/10/2020 (Shift-03)
rks mudh orZeku vk;q dk vuqikr gS
(a) 30 years (b) 11 years
(a) 1 : 2 (b) 3 : 5
(c) 24 years (d) 20 years
(c) 3 : 4 (d) 2 : 5
9. The ratio of present ages of two brothers 14. The ratio of present ages (in years) of a fa-
is 1 : 2 and 5 years back the ratio was 1 : ther and son is 15 : 8. Six years ago, the
3. What will be the ratio of their age after ratio of their ages was 13 : 6. What is the
5 years ? father's present age?
,d firk vkSj iq=k dh orZeku vk;q (o"kks± esa) dk
nks Hkkb;ksa dh orZeku vk;q dk vuqikr 1 % 2 gS vkSj

r
vuqikr 15%8 gSA Ng o"kZ igys] mudh vk;q dk vuqikr
5 o"kZ iwoZ vuqikr 1 % 3 FkkA 5 o"kZ ckn mudh vk;q

si
dk vuqikr D;k gksxk\ 13%6 FkkA firk dh orZeku vk;q D;k gS\
SSC CHSL 19/10/2020 (Shift-03)
(a) 1 : 4
(c) 3 : 5 an by (b) 2 : 3
(d) 5 : 6 (a) 65 years (b) 58 years

n
10. The ratio of the ages of A and B is 3 : 4. (c) 45 years (d) 78 years
Four years ago, the ratio of their ages was 15. Six years ago, the average of the ages of

ja
5 : 7. What will be the ratio of the ages of
R s
Ravi, Mohan and Govind was 32 years. If
A and B four years from now?
Shyam joins them now, the average of the
a th

A vkSjB dh vk;q dk vuqikr 3%4 gSA pkj o"kZ igys] ages of all four of them is 36 years. The
mudh vk;q dk vuqikr 5%7 FkkA vc ls pkj o"kZ ckn present age of Shyam is:
A vkSjB dh vk;q dk vuqikr D;k gksxk\
Ng o"kZ igys] jfo] eksgu vkSj xksfoan dh vk;q dk
ty a

SSC PHASE IX 10/02/2022 (Shift-03)

vkSlr 32 o"kZ FkkA ;fn ';ke vc muds lkFk tqM+
(a) 6 : 7 (b) 5 : 6
tkrk gS] rks mu pkjksa dh vk;q dk vkSlr 36 o"kZ gSA
di M

(c) 4 : 5 (d) 7 : 9
';ke dh orZeku vk;q gS%
11. The ratio of the present ages of a man and
SSC CHSL 14/10/2020 (Shift-01)
his son is 5 : 3. The average of their
present ages is 32 years. What will be the (a) 35 years (b) 32 years
ratio of their ages after six years? (c) 40 years (d) 30 years
,d O;fDr vkSj mlds iq=k dh orZeku vk;q dk vuqikr
16. The ratio of ages of A and B, 8 years ago,
5 : 3 gSA mudh orZeku vk;q dk vkSlr
32 o"kZ gSA Ng was 2:3. Four years ago, the ratio of their
o"kZ i'pkr~ mudh vk;q dk vuqikr fdruk gksxk\ ages was 5:7. What will be the ratio of their
ICAR Mains, 08/07/2023 (Shift-2) ages 8 years from now?
(a) 12 : 17 (b) 15 : 23 8 o"kZ iwoZ
A vkSjB dh vk;q dk vuqikr 2 % 3 FkkA
A

(c) 17 : 12 (d) 23 : 15 pkj o"kZ iwoZ] mudh vk;q dk vuqikr 5 % 7 FkkA vc

12. The ratio between Sumit and Prakash age ls 8 o"kZ ckn mudh vk;q dk vuqikr D;k gksxk\
at present is 2 : 3. Sumit is 6 years SSC CGL 5/03/2020 (Shift-01)
younger than Prakash. The ratio of Sumit’s
(a) 7:8 (b) 4:5
age to Prakash’s age after 6 years will be
orZeku esa lqfer vkSj çdk'k dh vk;q dk vuqikr 2%3 (c) 3:4 (d) 5:6
gSA lqfer] çdk'k ls 6 o"kZ NksVk gSA 6 o"kZ 17.ckn lqfer
Five year ago, the ratio of the ages of A and
dh vk;q dk çdk'k dh vk;q ls vuqikr gksxk B was 3 : 4. Five years from now, the ratio
(a) 2 : 3 (b) 1 : 2 of their ages will be 4:5. What is the ratio
(c) 4 : 3 (d) 3 : 4 of A and B, 10 years form now ?

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ikap o"kZ igys]

A vkSjB dh vk;q dk vuqikr 3%4 FkkA
21. 5 years ago, the ratio of the age of A to
vc ls ikap o"kZ ckn] mudh vk;q dk vuqikr 4%5 gksxkAthat of B was 4:5. Five years hence, the ra-
tio of the age of A to that of B will be 6:7.
vc 10 o"kZ ds :i esaA vkSjB dk vuqikr D;k gS\
If, at present, C is 10 years younger than
SSC MTS 22/08/2019 (Shift-02)
B, then what will be the ratio of the
(a) 9:11 (b) 6:7 present age of A to that of C ?
(c) 5:6 (d) 7:9 5 o"kZ igys]
A dh vk;q vkSjB dh vk;q dk vuqikr
18. Ramesh is three times older to Suresh. 4%5 FkkA ikap o"kZA ckn]
dh vk;q vkSjB dh vk;q
After two years Ramesh’s age will be twice dk vuqikr 6%7 gksxkA ;fn] orZeku C, esa]
B ls 10
the age of Suresh. What is the current age o"kZ NksVk gS]
A dhrks
orZeku vk;q vkSj
C dh orZeku
of Ramesh. vk;q dk vuqikr D;k gksxk\
jes'k] lqjs'k ls rhu xquk cM+k gSA nks o"kZ ckn jes'k dh SSC CGL Tier II 12/09/2019
vk;q lqjs'k dh vk;q dh nksxquh gksxhA jes'k dh orZeku
(a) 3:2 (b) 5:4
vk;q D;k gS\ (c) 4:3 (d) 5:3

r
SSC MTS 22/08/2019 (Shift-01) 22. The ratio of the ages of A and B, 8 years
ago, was 5 : 7. The ratio of their ages, 8

si
(a) 4 (b) 6
years from now, will be 9 : 11. If the present
(c) 3 (d) 2
age of C is 13 years less than that of B, and
19.
an by
One year ago, the ratio of the age (in years)
of A to that of B was 4:3. The ratio of their
the present age of D is 8 years less than
that of the age of A, then the sum of the

n
respective ages, 3 years from now, will be
present ages of C and D, in years, is:
6:5. What will be the ratio of respective
8 o"kZ iwoZ
A vkSj B dh vk;q dk vuqikr 5%7 FkkA

ja
ages of A and B, 9 years from now?
vc ls 8 o"kZ ckn mudh vk;q dk vuqikr 9%11 gksxkA
R s
,d o"kZ igys]A dh vk;q (o"kks± esa)Bdkdh vk;q
ls vuqikr 4%3 FkkA vc ls 3 o"kZ ckn mudh lacaf/r ;fn C dh orZeku vk;qB dh vk;q ls 13 o"kZ de
a th

vk;q dk vuqikr 6%5 gksxkA vc ls 9 o"kZ A ckn

vkSj gS] vkSjD dh orZeku vk;qA dh vk;q ls 8 o"kZ de
B dh lacaf/r vk;q dk vuqikr D;k gksxk\ gS] rks o"kks±
C vkSj
esaD dh orZeku vk;q dk ;ksx gS%
SSC CGL Tier II 11/09/2019 SSC PHASE IX 14/03/2022 (Shift-03)
ty a

(a) 7:6 (b) 10:9 (a) 47 (b) 55

(c) 9:8 (d) 8:7 (c) 43 (d) 53
di M

23. The sum of the present ages of father and

20. The present age of a husband and wife is in a son is 52 years. Four years hence, the
the ratio 5 : 4. After 6 years their ages will 1
be in the ratio 6 : 5. At the time of their son’s age will be that of the father.
marriage the ratio of their ages was 4 : 3. 4
What will be the ratio of the ages of the
How many years ago they were married? son and father,10 years from now?
ifr vkSj iRuh dh orZeku vk;q dk vuqikr 5 % 4 gSA 6 o"kZfirk vkSj iq=k dh orZeku vk;q dk ;ksx 52 o"kZ gSA
ckn mudh vk;q dk vuqikr 6 % 5 gks tk,xkA mudh 'kknh ds 1
pkj o"kZ ckn] iq=k dh vk;q firk dh vk;q dh
le; mudh vk;q dk vuqikr 4 % 3 FkkA mUgksaus fdrus o"kZ 4
igys 'kknh dh\ gksxhA 10 o"kZ ckn iq=k vkSj firk dh vk;q dk vuqikr
SSC PHASE XI 28/06/2023 (Shift-03) D;k gksxk\
(a) 8 yrs (b) 10 yrs (a) 2 : 7 (b) 2 : 5
A

(c) 6 yrs (d) 4 yrs (c) 3 : 8 (d) 1 : 3

ANSWER KEY

1. (b) 2.(a) 3. (b) 4. (d) 5. (b) 6. (d) 7. (c) 8. (b) 9. (c) 10. (d)

11.(d) 12.(d) 13.(d) 14.(c) 15.(d) 16.(b) 17.(a) 18.(b) 19.(c) 20.(c)

21.(c) 22.(c) 23.(d)

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Problems on Age/vk;q laca/h iz'u

( Practice Sheet With Solution)
1. Father is aged three times more than his son 6. Ayesha's father was 38 years of age when she
Ronit. After 8 years, he would be two and a was born while her mother was 36 years old
half times of Ronit's age. After further 8 years, when her brother four years younger to her
how many times would he be of Ronit's age? was born. What is the difference between the
firk dh vk;q mlds iq=k jksfur ls rhu xquk vf/d gSA 8 ages of her parents?
o"kZ ckn mldh vk;q jksfur dh vk;q dh <kbZ xquh gks tc vk;'kk dk tUe gqvk rc mlds firk dh mez 38 lky
tk,xhA vxys 8 o"kZ ckn] og jksfur dh vk;q dk fdruk Fkh] tcfd mlls pkj lky NksVs HkkbZ ds iSnk gksus
xquk gksxk\ mldh eka dh mez 36 lky FkhA mlds ekrk&firk dh vk;q

r
(a) 2 times (b) 3 times
(c) 4 times (d) 1 times ds chp dk varj fdruk gS\

si
2. Sum of ages of 5 children born at the intervals (a) 2 years (b) 4 years
of 3 years each is 50 years. What is the age of (c) 6 years (d) 8 years
an by
the youngest child? 7.
3 o"kZ ds varjky ij iSnk gq, 5 cPpksa dh vk;q dk ;ksx
The age of father 10 years ago was thrice the
age of his son. Ten years hence, father's age

n
50 o"kZ gSA lcls NksVs cPps dh vk;q D;k gS\ will be twice that of his son. The ratio of their
(a) 4 years (b) 8 years present ages is:
(c) 10 years ja (d) None of these 10 o"kZ iwoZ firk dh vk;q mlds iq=k dh vk;q dh rhu xqu
R s
3. A father said to his son, "I was as old as you
FkhA nl o"kZ ckn] firk dh vk;q mlds iq=k dh vk;q dh
a th

are at the present at the time of your birth".

If the father's age is 38 years now, the son's nksxquh gksxhA mudh orZeku vk;q dk vuqikr gS%
age five years back was: (a) 5 : 2 (b) 7 : 3
,d firk us vius iq=k ls dgk] rsjs tUe ds le; esjh mez (c) 9 : 2 (d) 13 : 4
ty a

mruh Fkh ftruh rqEgkjh vkt gSA ;fn firk dh vk;q vHkh 8. Q is as much younger than R as he is older
38 o"kZ gS] rks ik¡p o"kZ igys iq=k dh vk;q Fkh% than T. If the sum of the ages of R and T is 50
di M

(a) 14 years (b) 19 years years, what is definitely the difference between
(c) 33 years (d) 38 years R and Q's age?
4. Six years ago, the ratio of the ages of Kunal Q] R ls mruk gh NksVk gS ftrukTog ls cM+k gSA ;fn
and Sagar was 6 : 5. Four years hence, the
R vkSjT dh vk;q dk ;ksx 50 o"kZ gS] rks fuf'pr :i ls
ratio of their ages will be 11 : 10. What is
Sagar's age at present? R vkSjQ dh vk;q ds chp fdruk varj gS\
Ng o"kZ igys] dq.kky vkSj lkxj dh vk;q dk vuqikr 6 (a) 1 year (b) 2 years
% 5 FkkA pkj o"kZ ckn] mudh vk;q dk vuqikr 11 % 10(c) 25 years (d) Data inadequate
gksxkA orZeku esa lkxj dh vk;q fdruh gS\ 2
(a) 16 years (b) 18 years 9. A person's present age is of the age of his
5
(c) 20 years
mother. After 8 years, he will be one-half of
A

(d) Cannot be determined

5. The present ages of three persons in the age of his mother. How old is the mother
proportions 4 : 7 : 9. Eight years ago, the sum at present?
of their ages was 56. Find their present ages ,d O;fÙkQ dh orZeku vk;q mldh ekrk dh vk;q dk
(in years).
2
rhu O;fÙkQ;ksa dh orZeku vk;q dk vuqikr 4 % 7 % 9 gSA gSA 8 o"kZ ckn mldh vk;q viuh ekrk dh vk;q dh
5
vkB o"kZ iwoZ mudh vk;q dk ;ksx 56 FkkA mudh orZeku
vk;q (o"kks± esa) Kkr dhft,A vk/h gksxhA orZeku esa ek¡ dh mez fdruh gS\
(a) 8, 20, 28 (b) 16, 28, 36 (a) 32 years (b) 36 years
(c) 20, 35, 45 (d) None of these (c) 40 years (d) 48 years

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10. What is Sonia's present age? 13. I was married 10 years ago my wife is the 6th
lksfu;k dh orZeku vk;q D;k gS\ member of the family. Today my father died
I. Sonia's present age is five times Deepak's and a baby born to me.The average age of my
present age. family during my marriage was same as today.
What is the age of Father when he died ?
lksfu;k dh orZeku vk;q nhid dh orZeku vk;q dk
ikap xquk gSA esjh 'kknh 10 lky igys gqbZ Fkh esjh iRuh ifjokj dh NBh
II. Five years ago her age was twenty-five times lnL; gSA vkt esjs firk dh e`R;q gks xbZ vkSj esjs ,d cPps
Deepak's age at that time. dk tUe gqvkA esjh 'kknh ds nkSjku esjs ifjokj dh vkSlr
ik¡p o"kZ igys mldh vk;q ml le; nhid dh vk;q vk;q ftruh Fkh vkt Hkh mruh gh gSA firk dh e`R;q ds
dk iPphl xquk FkhA le; mudh vk;q D;k Fkh\
(a) II alone sufficient while I alone not (a) 50 yrs (b) 60 yrs
sufficient to answer
(c) 70 yrs (d) 65 yrs
II vdsys i;kZIr tcfd I vdsyk mÙkj nsus ds fy,
14. Raju got married 8years ago. His present age
i;kZIr ugha gwa
(b) Either I or II alone sufficient to answer 6
is times his age at the time of his marriage
;k rksI ;k II vdsys mÙkj nsus ds fy, i;kZIr gSa 5

r
(c) Both I and II are not sufficient to answer Raju's sister was 10 years younger to him at

si
I vkSjII nksuksa mÙkj nsus ds fy, i;kZIr ugha gSa the time of his marriage. The present age of
Raju's sister is ?
(d) Both I and II are necessary to answer

11.
an by
mÙkj nsus ds fy,I vkSjII nksuksa vko';d gSa
Divya is twice as old as Shruti. What is the
jktw dh 'kknh 8 lky igys gqbZ FkhA mldh orZeku vk;
6

n
difference in their ages? mlds fookg ds le; dh vk;q dk xquk gS jktw dh
5
fnO;k dh mez Jqfr ls nksxquh gSA mudh vk;q esa fdruk
cgu mldh 'kknh ds le; mlls 10 o"kZ NksVh FkhA jktw dh
varj gS\ ja
R s
cgu dh orZeku vk;q fdruh gS\
I. Five years hence, the ratio of their ages
a th

(a) 30 (b) 32
would be 9 : 5.
ikap o"kZ ckn] mudh vk;q dk vuqikr 9 % 5 gksxkA(c) 38 (d) None
II. Ten years back, the ratio of their ages was 15. Six years ago Anita was P times as old as Ben
3 : 1. was. If Anita is now 17 years old, how old is
ty a

nl o"kZ igys] mudh vk;q dk vuqikr 3 % 1 FkkA Ben now in terms of P ?

(a) II alone sufficient while I alone not N% o"kZ igys vuhrk dh vk;q csu dh vk;qP dh
xquh FkhA
di M

sufficient to answer ;fn vuhrk vHkh 17 o"kZ dh gS]Prks

ds lanHkZ esa csu dh
II vdsys i;kZIr tcfd I vdsyk mÙkj nsus ds fy, vk;q fdruh gS\
i;kZIr ugha gwa
(b) Either I or II alone sufficient to answer 11 P
(a) (b)
;k rksI ;k II vdsys mÙkj nsus ds fy, i;kZIr gSa P +6 11 + 6
(c) Both I and II are not sufficient to answer 17 – P 11 + 6P
I vkSjII nksuksa mÙkj nsus ds fy, i;kZIr ugha gSa (c)
6
(d)
11
(d) Both I and II are necessary to answer
16. The age of a person is thrice the total ages of
mÙkj nsus ds fy,I vkSjII nksuksa vko';d gSa
his 2 daughters. 0.5 decades hence, his age
12. If 6 years are subtracted from the present age will be twice of the total ages of his daughters.
of Arun and the remainder is divided by 18, then
A

Then what is the father's current age?

the present age of his grandson Gokul is obtained.
If Gokul is 2 years younger to Madan whose age ,d O;fÙkQ dh vk;q mldh 2 iqf=k;ksa dh dqy vk;q dh rhu
is 5 years, then what is the age of Arun ? xquh gSA 0-5 n'kd ckn] mldh vk;q mldh iqf=k;ksa dh dq
;fn v#.k dh orZeku vk;q esa ls 6 o"kZ ?kVkdj 'ks"k dksvk;q dh nksxquh gks tk,xhA rks firk dh orZeku vk;q D;k g
18 ls foHkkftr fd;k tk,] rks mlds iksrs xksdqy dh (a) 35 years (b) 40 years
orZeku vk;q çkIr gksrh gSA ;fn xksdqy enu ls 2 o"kZ NksVk
(c) 45 years (d) 47 years
gS ftldh vk;q 5 o"kZ gS] rks v#.k dh vk;q fdruh gS\
17. Ten years ago, Karan was thrice as old as Shiva
(a) 72 years (b) 54 years was but 10 years hence, he will be twice as
(c) 60 years (d) 47 years old. Find Shiva's present age ?

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nl o"kZ igys] dj.k dh vk;q f'ko dh vk;q dh rhu xquh (a) 39 yrs (b) 45 yrs
Fkh] ysfdu 10 o"kZ ckn] og nksxquh vk;q dk gksxkA f'ko (c) 42 yrs (d) 35 yrs
22. Five years ago Laurel was four years more than
dh orZeku vk;q Kkr dhft;s\
four times the age of his son. Three years
(a) 70 years (b) 30 years
hence Laurel`s age will be six years less than
(c) 60 years (d) 40 years
thrice the age of his son. After how many years
18. The average age of a couple is 24 years when
from now will their combined age be 50 years?
they were married five years ago but now the
average age of the husband, wife and child is ik¡p o"kZ igys ykWjsy dh vk;q mlds iq=k dh vk;q ds pk
20 years (the child was born during the interval). xqus ls pkj o"kZ vf/d FkhA rhu o"kZ ckn ykWjsy dh v
What is the present age of the child ? mlds iq=k dh vk;q ds rhu xqus ls Ng o"kZ de gksxhA v
ik¡p o"kZ iwoZ fookg ds le; ,d naifÙk dh vkSlr vk;q ls fdrus o"kZ ckn mudh la;qÙkQ vk;q 50 o"kZ gksxh\
24 o"kZ gS ysfdu vc ifr] iRuh vkSj cPps dh vkSlr vk;q CRPF HCM 23/02/2023 (Shift - 03)
20 o"kZ gS (varjky ds nkSjku cPps dk tUe gqvk)A cPps(a) 10 (b) 8
dh orZeku vk;q D;k gS\ (c) 6 (d) 3
(a) 2 yrs (b) 4 yrs 23. The persent age (in years) of Arun is one year

r
(c) 3 yrs (d) 5 yrs less then two times the present age (in years)
19. A woman says, "If you reverse my own age, of Varun. After 5 years from now, Varun's age

si
the figures represent my husband's age. He 2
is, of course, senior to me and the difference will be equal to of the present age of Arun.
an by
between our ages is one-eleventh of their sum."
The woman's husband age is ?
3
What is the sum of the ages (in years) of Arun

n
and Varun after 2 years from now?
,d efgyk dgrh gS] ;fn vki esjh mez dks mYVk djrs gSa] rks
v#.k dh orZeku vk;q (o"kks± esa) o#.k dh orZeku vk;q
vkadM+s esjs ifr dh mez dk çfrfuf/Ro djrs gSaA og fuf'pr
ja (o"kks± esa) ds nks xqus ls ,d o"kZ de gSA vc ls 5 o"
:i ls eq>ls ofj"B gSa vkSj gekjh mez ds chp dk varj
gekjs
R s
mez ds ;ksx dk X;kjgoka fgLlk gSA efgyk ds ifr dh mez gS\ ckn] o#.k dh vk;q v#.k dh orZeku vk;q ds2 ds
a th

(a) 45 (b) 24 3
(c) 42 (d) 54 cjkcj gksxhA vc ls 2 o"kZ ckn v#.k vkSj o#.k dh vk;q
20. A is two years older than B who is twice as (o"kks± esa) dk ;ksx fdruk gS\
ty a

old as C. If the total of the ages of A, B and C

CRPF HCM 24/02/2023 (Shift - 01)
be 27, then how old is B ?
(a) 54 (b) 50
A, B ls nks o"kZ cM+k gS] ftldhCvk;q
ls nksxquh gSAA;fn
]
di M

(c) 58 (d) 52
B vkSjC dh dqy vk;q 27 gS] rksB dh vk;q fdruh gS\ 24. The present ages of two cousins are in the
(a) 10 yrs (b) 11 yrs ratio of 4 : 7. After 5 years, their ages are in
(c) 12 yrs (d) 13 yrs the ratio of 37 : 61. The ratio of their ages
21. The sum of the ages of a mother, son and after 8 years is:
daughter is 70 yrs. If mother is thrice as old nks ppsjs Hkkb;ksa dh orZeku vk;q dk vuqikr 4 % 7 gS
as her son and the daughter is 5 yrs older than
her brother. How old is mother?
o"kZ ckn] mudh vk;q dk vuqikr 37 % 61 gSA 8 o"kZ d
ckn mudh vk;q dk vuqikr gS%
,d ek¡] iq=k vkSj iq=kh dh vk;q dk ;ksx 70 o"kZ gSA ;fn
ekrk dh vk;q mlds iq=k dh vk;q dh rhu xquh gS rFkk iq=kh CRPF HCM 28/02/2023 (Shift - 01)
vius HkkbZ ls 5 o"kZ cM+h gSA ek¡ fdrus lky dh gS\ (a) 8 : 5 (b) 5 : 9
(c) 5 : 8 (d) 5 : 7
A

CRPF HCM 23/02/2023 (Shift - 02)

ANSWER KEY
1.(a) 2.(a) 3.(a) 4.(a) 5.(b) 6.(c) 7.(b) 8.(d) 9.(c) 10.(d)

11.(*) 12.(c) 13.(b) 14.(c) 15.(d) 16.(c) 17.(b) 18.(a) 19.(d) 20.(a)

21.(*) 22.(*) 23.(a) 24.(c)

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PARTNERSHIP (lk>snkjh)
[CLASSROOM SHEET]
Basic Question 5. The ratio of investment by A to that by B
is a business is 14 : 15 and the ratio of
1. Two partners Deepa and Ziya start a their respective profits at the end of a year
business by investing ` 50,000 and is 2 : 5. If A invested the money for 3
` 40,000 respectively. What will be the months, then for how much time (in
ratio of their profits at the end of the year ? month) B invested his money?
nks lk>snkj nhik vkSj ft;k Øe'k% ` 50]000 vkSj ,d O;olk; esa A vkSj B ds }kjk fd;s x, fuos'k
` 40]000 dk fuos'k djds ,d O;olk; 'kq: djrs dk vuqikr 14%15 gS rFkk o"kZ ds var esa muds ykHkksa
gSaA o"kZ ds var esa muds ykHk dk vuqikr D;k gksxk\
dk vuqikr 2%5 gSA ;fnA us 3 ekg ds fy, jkf'k

r
(a) 5 : 4 (b) 3 : 6 fuos'k dh Fkh] rks
B }kjk fuos'k dh x;h jkf'k dh

si
(c) 4 : 5 (d) 6 : 3 vof/ (eghus esa) fdruh Fkh\
2. Raju and Sanju started a business by

an by
investing ` 36,000 and ` 63,000.Find the SSC CGL TIER II, 11/09/2019
share of each out of the annual profit of ` 5500. (a) 7 (b) 6

n
jktw vkSj latw `us36000 vkSj` 63000 dk fuos'k (c) 5 (d) 9
djds ,d O;olk; 'kq: fd;kA ` 5500 ds okf"kZd ykHk 6. Nikhil and Neha invested capital in the ratio

ja
esa ls çR;sd dk fgLlk Kkr dhft,A 5 : 4. The time Neha invested her money
R s for was one year' more than that invested
(a) 2000, 3500 (b) 2500,3500
a th
(c) 3500, 2500 (d) None of these by Nikhil. The ratio of their profits is in the
3. X, Y and Z invested Rs. 4,000, Rs. 6000 and ratio 6 : 5. Find the time Neha invested the
Rs. 8,000 respectively in a business. They money for.
invested the money for 3, 2 and 4 years fuf[ky vkSj usgk5us: 4. ds vuqikr esa iwath dk fuos'k
ty a

respectively. If the total profit is Rs. 5,6000, fd;kA usgk us fuf[ky dh rqyuk esa ,d o"kZ vf/d le; ds
then what is the share of Y in the profit?
fy, fuos'k fd;kA muds ykHk dk vuqikr 6 : 5 gSA Kkr
di M

X, Y vkSjZ us ,d O;olk; esa Øe'k% :- 4,000, :-

dhft, usgk us fdrus le; ds fy, /u dk fuos'k fd;k\
6000 vkSj:- 8,000 dk fuos'k fd;kA mUgksaus3,Øe'k%
2 vkSj4 o"kks± ds fy, /ujkf'k dk fuos'k fd;kA ;fn dqy SSC CHSL 21/03/2023 (SHIFT-01)
ykHk:- 5,6000 gS] rks ykHkY esadk fgLlk fdruk gS\ (a) 26 years (b) 23 years
SSC CHSL 15/03/2023 (SHIFT-02) (c) 24 years (d) 25 years
(a) ` 18,000 (b) ` 12,000 7. A, B and C invest ` 40000, ` 45,000 and
(c) ` 15,000 (d) ` 9,000 ` 60,000 respectively in a business. They
4. Three partners P, Q and R invested a total invest for 5, 4 and 3 months respectively.
of Rs 52,000 in a business. At the end of the How many percent of the total profit will
year. P got Rs. 1430, Q got Rs. 1870 and R be received by C?
got Rs 2420 as the share of profit. How A, B rFkk C futh O;kikj esa Øe'k% ` 40]000]
A

much amount did Q invest in the business? ` 45]000 rFkk` 60]000 fuos'k djrs gSaA ;s Øe'k%
rhu lk>snkjksa
P, Q vkSj R us ,d O;olk; esa dqy 5] 4 rFkk 3 eghus rd O;kikj esa jgsA dqy ykHk dk
52]000 #i;s dk fuos'k fd;kA lky ds var esa
P dks yxHkx fdruk izfr'kr Hkkx
C dks izkIr gksxk\
1430 #-] Q dks feys 1870 #- vkSjR dks ykHk ds (a) 32% (b) 36%
fgLls ds :i esa 2420 #i;s feysAQ us O;olk; esa (c) 40% (d) 27%
fdruh jkf'k fuos'k dh\
8. A, B and C invested capitals in the ratio
SSC MTS 13/06/2023 (SHIFT-03) 3 : 4 : 8. At the end of the business period,
(a) Rs. 17000 (b) Rs. 20400 they received profits in the ratio 2 : 3 : 5.
(c) Rs. 15300 (d) Rs. 18700 What is the ratio of their time invested?

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A, B vkSjC us 3 % 4 % 8 ds vuqikr esa iwath fuos'k pkj nwf/;ksa us ,d pkjkxkg fdjk, ij fy;kA
A&3
dhA O;kikj vof/ ds var esa] mUgsa 2 % 3 % 5 dseghus ds fy, 24 xk;ksa dks] B&5 eghus ds fy, 10
vuqikr esa ykHk izkIr gqvkA muds fuosf'kr le; dk xk;ksa dks]
C&4 eghus ds fy, 35 xk;ksa dks DvkSj
&3
vuqikr D;k gS\ eghus ds fy, 21 xk;ksa dk pjkrk gSA ;fn fdjk, esa
SSC CGL TIER- II 06/03/2023
A dk fgLlk ` 720 gS] rks {ks=k dk dqy fdjk;k Kkr
(a) 16 : 18 : 15 (b) 13 : 18 : 15
dhft,\
(c) 16 : 21 : 18 (d) 15 : 16 : 13
(a) ` 1,400 (b) ` 1,900
9. A, B and C invested capital in ratio 5 : 7 : 4,
then time of their investment being in the (c) ` 3,250 (d) ` 3,000
ratio x : y : z. If their profits are in the ratio 13. Ratio of the capital amount of A, B and C
45 : 42 : 28, then x : y : z = ? 4 2 5
respectively is : : and ratio of their
A, B vkSjC us 5 : 7 : 4 ds vuqikr esaiw¡th yxkbZA 5 3 8
time investment is respectively 10 : 9 : 4.
muds fuos'k dk le; x : y : z ds vuqikr esa gSA ;fn The profit amount of A is how much
mudk ykHk 45%42 %28 ds vuqikr esa gS]xrks :y:z percent more than C?

r
D;k gksxk\ A, B vkSj C ds }kjk yxk;h xbZ iw¡th dk vuqikr

si
CGL TIER II, 16/11/2020 4 2 5
(a) 9 : 6 : 7 (b) 6 : 7 : 9 Øe'k% : : gS vkSj buds }kjk yxk;s le;
5 3 8

an by
(c) 9 : 4 : 7 (d) 7 : 9 : 4 dk vuqikr 10 % 9 % 4 gS] rks A dk ykHkC ds
10. Three partners shared the profit in a ykHk ls fdruk izfr'kr T;knk gS\

n
business in the ratio 8 : 7 : 5. They invested
their capitals for 7 months, 8 months and (a) 160% (b) 220%

ja
14 months respectively. What was the ratio (c) 70% (d) 95%
R s
of their capitals? 14.
A, B anc C invest in a business. A invests
rhu Hkkxhnkjksa%7us%58 ds vuqikr esa ,d O;olk;
a th
1 1
of the total capital for th time. B
esa ykHk lk>k fd;k vkSj mUgksaus Øe'k% 7 eghus]4 8 4
1 1
eghus vkSj 14 eghus ds fy, viuk /u fuos'k fd;kA invests th of the total capital for th
muds /u dk vuqikr D;k Fkk Kkr djsA 5 5
ty a

time and the remaining capital is invested

SSC CPO 24/11/2020 (SHIFT-02) by C for the whole time. If the total profit
di M

(a) 49 : 64 : 20 (b) 20 : 64 : 49 is ` 7,830, then what will be the profit of

(c) 64 : 49 : 20 (d) 20 : 49 : 64 C?
11. A, B and C invested their capitals in the A, B vkSj C ,d O;kikj dh 'kq:vkr djrs gSa rFkk
ratio of 2 : 3 : 5. The ratio of months for 1 1
which A, B and C invested is 4 : 2 : 3. If C A O;kikj esa yxus okyh dqy iw¡th dkHkkx
gets a share of profit which is ` 1,47,000 4 4
1 1
more than that of A, then B’s share of le; ds fy,] B dqy iw¡th dk Hkkx le; ds
profit is: 5 5
fy, rFkk C 'ks"k iw¡th iwjs le; ds fy, yxkrk gSA
A, B vkS C us viuh iw¡th 2%3 %5 ds vuqikr esa
;fn dqy ykHk` 7]830 gks] rks mlesaC lsdk fgLlk
yxkbZAA, B vkSj C ds }kjk fuos'k dh xbZ jkf'k;ksa
D;k gksxk\
dh vof/ (eghus esa) dk vuqikr 4%2 %3 gSA ;fn
(a) ` 6,000 (b) ` 6,600
A

C dks ykHk dk ,d fgLlk izkIr gksrk gSAtksds

(c) ` 6,400 (d) ` 6,200
fgLls ls ` 1]47]000 vf/d gS] rks bl ykHk esa
B
15. A, B and C are partners in a business. A
dk fgLlk Kkr djsaA whose money has been used for 4 months
(a) ` 1,26,000 (b) ` 1,68,000 1
(c) ` 1,05,000 (d) ` 1,89,000 claims of profit, B whose money has
8
12. Four milkmen rented a pasture. A grazed 1
24 cows for 3 months, B-10 for 5 months, been used for 6 months, claims of the
3
C-35 cows for 4 months and D-21 cows for profit. C had invested ` 1560 for 8
3 months. If A’s share of rent is months. What is the difference between
` 720, find the total rent of the field ? investment of A and B.

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A, B vkSj C ,d O;olk; esa lk>snkj gSaA

A ftlds A, B vkSjC us ,d O;olk; dh 'kq:vkr dhA A ds
/u dk mi;ksx 4 eghus ds fy, fd;k tkrk gS]
1 fuos'k dk frxqukB ds fuos'k ds nksxqus rFkk
C ds
8 fuos'k ds pkj xquk ds cjkcj gSA ;fn dqy ykHk
C esa
ykHk dk nkok djrk gS]
B ftlds /u dk 6 eghus ds
1 dk fgLlk ` 4]863 gS] rks bl ykHk Aesa
dk fgLlk
fy, mi;ksx fd;k tkrk gS] ykHk dk nkok djrk Kkr djsaA
3
gSAC us 8 eghus ds fy, 1560 #i;s dk fuos'k fd;k SSC CGL TIER II 13/09/2019
FkkAA vkSjB ds fuos'k esa D;k varj gS\
(a) ` 7,272 (b) ` 6,484
(a) ` 720 (b) ` 560
(c) ` 9,726 (d) ` 8,105
(c) ` 420 (d) ` 500
20. Three partners A, B and C start a business.
16. A, B and C all together invest ` 48,000.
Ratio of their time investment is 99 : 77 : 84 Twice of A’s capital is equal to three times
and ratio of their profit amount is of B’s capital is equal to four times of C’s
respectively 3 : 2 : 4. Find the investment capital. Out of total profit of ` 19,500 at
amount of A? the end of the year, B’s share is ?
rhu lk>snkjA, B vkSjC ,d O;olk; 'kq: djrs gSaA

r
A, B vkSjC rhuksa feydj dqy` 48]000 ,d O;kikj
esa fuos'k djrs gSaA ;fn buds le; dk vuqikr Øe'k% A dh iwath dk nksxquk
B dh iw¡th ds rhu xquk ds

si
99 %77 %84 gks rFkk ykHk dk vuqikr Øe'k% %2 %
34 cjkcj gS vkSjC dh iw¡th ds pkj xquk ds cjkcj gSaA

an by
gks] rks
A ds }kjk fuos'k dh xbZ jkf'k crk,¡\ o"kZ ds var esa
` 19]500 dh dqy ykHk esaBlsdk
(a) ` 13,000 (b) ` 15,000 fgLlk Kkr djsaA

n
(c) ` 14,000 (d) ` 15,500 (a) ` 7,000 (b) ` 6,000
17. ` 15,000 was invested by A and B together (c) ` 9,000 (d) ` 9,700

ja
to start a small business. They got a profit
R s
of ` 2,000 at the end of the year. B took
21. A, B, C subscribe a sum of ` 75,500 for a
business. A subscribes ` 3,500 more than
a th
his profit share of ` 600. How much did A B, and B subscribes ` 4,500 more than C.
invest?
Out of a total profit of ` 45,300 how much
A vkSj B }kjk ,d lkFk fdlh NksVs O;olk; dh (in `) does A receive?
'kq:vkr djus ds fy, ` 15]000 fuos'k fd;s x,A o C ,d O;olk; ds fy, ` 75]500 dk fuos'k
ty a

A, B
mUgsa o"kZ ds var
` 2000
esa dk ykHk gqvkA
B us ykHk djrk gSAA, B ls ` 3]500 vfèkd fuos'k djrk gS]
esa ls viuk fgLlk` 600 fy;k] rks A dk fuos'k
di M

vkSjB, C ls ` 4]500 vfèkd fuos'k djrk gS] dqy

fdruk Fkk\ ykHk` 45]300 esa ls
A dks fdruk çkIr gksxkA
SSC CPO 16/03/2019 (SHIFT-03)
SSC CPO 25/11/2020 (SHIFT-02)
(a) ` 9,000 (b) ` 2,000
(a) ` 12,600 (b) ` 15,000
(c) ` 10,500 (d) ` 10,000
(c) ` 17,400 (d) ` 14,700
18. A, B and C entered into a partnership. A
invested ` 2560 and B ` 2000. At the end 22. A puts ` 375 more in a business than B,
of the year. they gained ` 1105, out of but B has invested his capital for 4 months
which A got ` 320. C’s capital was while A has invested his capital for 8
months. If the share of A is ` 75 more than
A, B vkSj C us ,d lk>snkjh esa izos'k fd;kA
A us
that of B out of the total profit of ` 125,
` 2560 vkSjB us ` 2000 #i;s dk fuos'k fd;kA o"kZ
A

find the capital contributed by B ?

ds var esa mUgksaus
` 1105 dk ykHk vftZr fd;k] ftlesa
A, B dh rqyuk esa fdlh O;olk; esa
` 375 vf/d
ls A dks ` 320 izkIr gq,A
C dh iw¡th fdruh Fkh\
yxkrk gS] ysfduB viuh iwath 4 eghus ds fy, fuos'k
(a) ` 4,280 (b) ` 2,840
(c) ` 4,820 (d) ` 4,028
djrk gS tcfd A us viuh iwath 8 eghus ds fy,
19. A, B and C started a business. Thrice the fuos'k dh gSA ;fn` 125 dh dqy ykHk esa Als dk
investment of A is equal to twice the fgLlk B ls ` 75 vf/d gSA rksB }kjk ;ksxnku dh
investment of B and also equal to four xbZ iwath dk irk yxk,a\
times the investment of C. If C’s share out
(a) ` 750 (b) ` 375
of the total profit is ` 4,863, then the share
(c) ` 735 (d) ` 573
of A in the profit is:

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jkgqy vkSj jeu us Øe'k% 16000 #i;s vkSj 12000 #i;s

When Someone dk fuos'k djds ,d O;olk; 'kq: fd;kA 4 eghus ds
Joined or Left ckn] jkgqy us O;olk; NksM+ fn;k vkSj eksgu 20000
23. Kapil starts some business with #i;s dk fuos'k djds O;olk; esa 'kkfey gks x;kA o"kZ ds
` 50000 . After 3 months Monu joins him var esa] 46000 #i;s dk ykHk gqvkA ykHk esa eksgu dk
with ` 70000 . At the end of the year. In fgLlk D;k gksxk\
what ratio should they share the profit ?
SSC MTS 20/06/2023 (SHIFT-02)
dfiy ` 50]000 ls dqN O;olk; 'kq: djrk gSA 3 (a) Rs.28700 (b) Rs.20000
eghus ds ckn eksuw
` 70]000 ds lkFk mlds lkFk tqM+ (c) Rs 36800 (d) Rs.23400
tkrk gSA lky ds var esa mUgsa fdl vuqikr esa ykHk
27. P invested ` 4000 for one year. Q joined
lk>k djuk pkfg,\ him with an investment of ` 6000 after a
few months. If at the end of one year the
(a) 1 : 3 (b) 1 : 5 profits of P and Q is 4 : 3, then Q joined
(c) 3 : 2 (d) 20 : 21 after how many months?
P us ,d o"kZ ds fy,` 4000 dk fuos'k fd;kA dqN eghuksa

r
24. A starts a business with Rs. 75,000 and B
joins the business 5 months later with an ds ckn Q ` 6000 ds fuos'k ds lkFk 'kkfey gks x;kA ;fn

si
investment of Rs. 80,000. After 1 year, they ,d o"kZ ds var esa
P vkSjQ ds ykHk dk vuqikr4 : 3 gS]
earn a profit of Rs. 4,08,800. Find the share rksQ fdrus eghuksa ds ckn 'kkfey gqvk\

an by
of A and B (in Rs.).
SSC CHSL 14/03/2023 (SHIFT-01)
A us #i;s 75]000 ds fuos'k ds lkFk ,d O;olk;

n
(a) 4 months (b) 3 months
'kq: fd;k vkSj 5 eghus ckn #i;s 80]000 ds fuos'k (c) 8 months (d) 6 months
28.
ds lkFkB Hkh bl O;olk; esa 'kkfey gks tkrk gSA 1 A started a business with a capital of `

ja
R s
o"kZ ds ckn mUgsa #i;s 4]08]800 dk ykHk çkIr gksrk
54000 and admitted B and C after 4
months and 6 months respectively. At the
gSAA vkSjB dk fgLlk (#i;s esa) Kkr dhft,A
a th
end of the year, the profit was divided in
the ratio 1 : 4 : 5. What is the difference
SSC CGL TIER- II 07/03/2023
between the capitals invested by B and C?
(a) 2,52,000 and 1,56,800
A us ` 54000 dh iwath ls ,d O;olk; dh 'kq:vkr
ty a

(b) 2,50,000 and 1,58,800 dh rFkk Øe'k% pkj vkSj N% eghusB ckn ,oa C dks
(c) 2,48,000 and 1,60,800 'kfey dj fy;kA o"kZ ds var esa ykHkksa dk forj.k
di M

(d) 2,49,500 and 1,59,300 1 %4 %5 ds vuqikr esas fd;k x;kA

B vkSjC ds }kjk
25. Ramesh started a business investing a sum yxkbZ xbZ iwath esa D;k varj gS\
of ` 40,000. Six moths later, Kevin Joined CGL TIER 11/09/2019
by investing ` 20,000. If they make a profit (a) ` 1,08,000 (b) ` 1,62,000
of ` 10,000 at the end of year, how much (c) ` 2,16,000 (d) ` 3,24,000
is the share of kevin?
29. X, Y and Z enter into a partnership. X invests
jes'k us` 40]000 dh jkf'k dk O;olk; 'kq: fd;kA some money at the beginning. Y Invests
Ng eghus ckn] dsfou` 20]000 fuos'k djds 'kkfey thrice the amount of X after 4 months and Z
gks x;kA ;fn os o"kZ ds var` 10]000
esa dk YkkHk invest double the amount of Y after 9 months
dekrs gSa] rks dsfou dk fgLlk fdruk gS\ from the beginning. If the annual gain be Rs
A

CGL TIER II 18/11/2020 450000, then what is the share of Y?

(a) ` 2,000 (b) ` 4,000 X, Y vkSjZ ,d lk>snkjh esa ços'k djrs gSaA
X 'kq#vkr
esa dqN iSlk fuos'k djrkYgSA
] 'kq#vkr ls 4 eghus ckn
(c) ` 3,000 (d) ` 2,500
X dh jkf'k dk rhu xquk fuos'k djrk gS vkSj
Y] 'kq#vkr
26. Rahul and Raman started a business by
ls 9 eghus cknY dh jkf'k dk nksxquk fuos'k djrk gSA
investing Rs 16000 and Rs 12000
respectively. After 4 months, Rahul left the ;fn okf"kZd ykHk # 450000 gS] Y dk
rksfgLlk D;k gS\
business and Mohan joined the business by SSC MTS 08/05/2023 (SHIFT-01)
investing Rs 20000. At the end of the year, (a) Rs. 200000 (b) Rs. 150000
there was a profit of Rs 46000. What will be
the share of Mohan in the profit? (c) Rs. 100000 (d) Rs. 300000

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30. Sumit started some business with A vkSjB, 5 : 6 ds vuqikr esa iw¡th ds lkFk lk>snkjh
` 26,000. After 3 months Amar joined him 1
with ` 16,000. After some more time Karan djrs gSaA 4 eghus ds ckn]
A viuh iw¡th esa ls fgLlk
joined them with ` 25,000. At the end of the 5
year, out of a total profit of ` 15,453 Karan 1
fudky ysrk gS] tcfd B viuh iw¡th esa33 %
get ` 3,825 as his share. How many months 3
after Amar, Karan joined the business? dh o`f¼ djrk gSA ` 6-3 yk[k ds okf"kZd ykHk
B esa
lqfer us ` 26]000 dh iw¡th fuos'k djds ,d O;kikj dk ( ` yk[k esa) fgLlk D;k gS\
'kq: fd;kA 3 ekg ds ckn vej ` 16]000 fuos'k dj CGL TIER II 16/11/2020
O;kikj esa 'kkfey gks x;k vkSj mlds dqN le; ckn (a) 2.34 (b) 2.61
dju Hkh` 25]000 fuos'k dj O;kikj esa 'kkfey gks x;kA (c) 3.69 (d) 3.96
;fn o"kZ ds var esa
` 15]453 ds dqy ykHk esa dju dk34. A, B and C start a business each investing
fgLlk ` 3]825 gS] rks Kkr djsa fd dju us vej ds ` 25,000. After 5 months A withdrew
'kkfey gksus ds fdrus ekg ckn O;kikj esa izos'k fd;k\ ` 6,000, B withdrew ` 7000, and C invested
(a) 3 months (b) 4 months ` 8000 more. At the end of the year, there

r
(c) 5 months (d) 2 months is a profit of ` 86,500. Find the difference
between the share of A and B.

si
Increase/Decrease In Capital A, B vkSj C çR;sd ` 25]000 ds fuos'k ds lkFk
31. Suresh, Dinesh and Ramesh became ,d O;olk; 'kq: djrs gSaA 5 eghus ckn
A us ` 6]000

an by
partners in a business by investing money fudky fy,] B us ` 7000 fudky fy,] vkSj C us
in the ratio of 3 : 6 : 8. If their investments ` 8000 dk vkSj fuos'k fd;kA o"kZ ds var esa

n
is increased by 5%, 15% and 20%,
` 86]500 dk ykHk gksrk AgSA vkSj B ds fgLls ds
respectively, then what will be the ratio of
chp dk varj Kkr dhft,A

ja
their profits for one year?
R s
lqjs'k] fnus'k vkSj jes'k 3 % 6 % 8 ds vuqikr esa (a) ` 900 (b) ` 12,500
/ujkf'k dk fuos'k djds ,d O;olk; esa lk>snkj curs
a th
(c) ` 700 (d) ` 8,600
gSaA ;fn muds fuos'k esa Øe'k% 5»] 15» vkSj 20» 35.dhA and B entered into a partnership (at the
o`f¼ dh tkrh gS] rks ,d o"kZ ds fy, muds ykHk dk beginning of the year) by investing their
vuqikr D;k gks tk,xk\
ty a

2 3
capitals in the ratio : . After 4 months,
SSC CGL TIER- II 03/03/2023 3 9
di M

(a) 7 : 46 : 64 (b) 19 : 46 : 64 A reduced his capital by 25% and B

(c) 21 : 46 : 64 (d) 35 : 46 : 64 increased his capital by 25%. What was
32. X and Y enter into a partnership with B's share (in ` lakhs) in the annual profit
capital in ratio 3 : 5. After 5 months X adds of ` 57.2 lakhs?
50% of his capital, while Y withdraws 60%
A vkSjB us (o"kZ dh 'kq:vkr esa) viuh iwath dks
of his capital. What is share (in ` Lakhs)
of X in the annual profit of ` 6.84 lakhs? 2 3
X vkSjY, 3 : 5 ds vuqikr esa iw¡th ds lkFk lk>snkjh
: ds vuqikr esa fuos'k djds ,d lk>snkjh dhA
4
3 9
djrs gSaA 5 eghus cknX viuh iw¡th dk 50» tksM+rk ekg ckn A us viuh iwath 25%
esa dh deh dh vkSjB
gS] tcfd Y viuh iw¡th dk 60» fudky ysrk gSA us viuh iwath esa
25% dh o`f¼ dhA` 57.2 yk[k ds
` 6-84 yk[k ds okf"kZd ykHk X esa
dk ( ` yk[k esa) okf"kZd ykHk B esa
dk fgLlk (` yk[k esa) fdruk gksxk\
fgLlk D;k gS\
A

ICAR MAINS, 07/07/2023 (SHIFT-2)

CGL TIER II 15/11/2020
(a) 3.72 (b) 4.2 (a) 21.2 (b) 29.4
(c) 3.6 (d) 3.12 (c) 25.2 (d) 27.4
33. A and B enter into a partnership with 36. Mohit and Ravi started a business with
capital in the ratio 5 : 6. After 4 months,
2 1
1 their capitals in the ratio : . Afther
A withdraws of his capital, while B 15 6
5 4 month, Mohit increased his capital by
1 25% and Ravi reduced his capital by one-
increases his capital by 33 % . What is
3 fifth. At the end of a year, if B's share in
the share (in ` Lakhs) of B in the annual the annual profit was ` 20.8 lakhs, then
profit of ` 6.3 Lakhs? what was the annual profit (in ` lakhs)?

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2 1
eksfgr vkSj jfo us : ds vuqikr esa viuh iwath Donation/Tax
15 6
yxkdj ,d O;olk; 'kq: fd;kA 4 eghus ckn] eksfgr 40. A and B invest in a business in the ratio
viuh iwath esa 25» dh o`f¼ dh vkSj jfo us viuh iwath 3: 2. If 5% of the total profit goes to charity
esa ,d&frgkbZ dh deh dhA ,d o"kZ ds var esa] ;fn and A's share is Rs 855, the total profit is:
okf"kZd ykHk B dk
esafgLlk ` 20-8 yk[k Fkk] rks okf"kZd A vkSjB ,d O;olk; esa 3%2 ds vuqikr esa fuos'k djrs
ykHk `( yk[k esa) fdruk Fkk\
gSaA ;fn dqy ykHk dk 5» nku esa tkrk gS
A dk
vkSj
ICAR MAINS, 07/07/2023 (SHIFT-3)
(a) 41.6 (b) 31.2 fgLlk 855 #i;s gS] rks dqy ykHk gS%
(c) 43.2 (d) 44.8 IARI ASISSTANT MAINS (21/06/2023)
37. A and B start a business and invest (a) 1500 (b) 1400
` 10,000 and ` 15,000 respectively. After (c) 1565 (d) 1475
3 months, A invests ` 2,000 more but B 41. A and B together start a business and
withdraw ` 5,000. After its 3 months, C invest in the ratio of 5 : 4 respectively.
joins the business with a capital ` 18,000. They deposit 10% of the total profit in a
If the total profit is ` 38,100, after one year trust and distribute the rest amount

r
then find C's profit? according their investment. If B's share is

si
` 1,200, then the total profit will be ?
A vkSjB Øe'k%` 10]000 rFkk` 15]000 yxkdj ,d
O;kikj 'kq: djrs gSaA rhu eghusA,ckn
` 2]000 vkSj fuos'k
A vkSj B feydj ,d O;kikj vkjaHk djrs gSa vkSj

an by
5 %4 ds vuqikr esa iw¡th fuos'k djrs gSaA O;kikj esa
dj nsrk gS rFkk B, ` 5]000 okil ys ysrk gSA mlds 3
gksus okyk ykHk dk 10» ,d VªLV esa tek djds 'ks"k
eghuss vkSj cknC, ` 18]000 yxkdj O;kikj esa 'kkfey gks

n
ykHk dks iw¡th ds vuqlkj ck¡Vk tkrk gSA B dk;fn
tkrk gSA ;fn ,d o"kZ ds ckn dqy ykHk` 38]100 gks] rks
fgLlk` 1]200 gks] rks dqy fdrus #i;s dk ykHk gqvk\
o"kZ ds var esa mlesaC dk
lsfgLlk D;k gksxk\

ja
(a) ` 9,800
R s (b) ` 10,800
(a) ` 4,200 (b) ` 3,600
(c) ` 3,200 (d) ` 3,000
a th
(c) ` 11,000 (d) ` 12,000
42. Atul Reader publication makes a profit of
38. Ajay and Vijay started a business and
investe ` 4,500 and ` 3,000 respectively. ` 9,00,000, 20% of which is paid as taxes.
After 9 months each of the decrease their If the rest is divided among the partners
capital to 30% and Satyam joins the 1
ty a

1 P, Q and R in the ratio of 1 : 1 : 2 then

2
business with ` 2,000. If after 1 years, the shares of P, Q and R are respectively :
2
di M

the total profit was ` 16,450, then the vrqy jhMj ifCyds'ku` 9]00]000 dk ykHk dekrh
share of Ajay and Vijay will be :
vt; vkSj fot; us ` 4]500 rFkk` 3]000 fuos'k dj gS ftlds 20» Hkkx dk Hkqxrku dj ds :i esa fd;k
,d O;kikj izkjaHk fd;kA 9 ekg ckn nksuksa us viuh&viuhtkrk gSA ;fn 'ks"k ykHk
P, Q rFkkR dks Øe'k%1 :
1
iw¡th 30» dj fn;k rFkk` 2]000 ds lkFk lR;e Hkh 1 ds vuqikr esa fn;k tkrk gS] rks Kkr djsa
: 2
1 2
muds lkFk 'kkfey gks x;kA ;fn1 o"kks± ds ckn izR;sd dk fgLlk D;k gS\
2
dqy ykHk` 16]450 gks] rks mlesa ls vt; vkSj fot; (a) ` 2,40,000, ` 3,20,000, ` 1,60,000
dks dqy fdrus ykHk izkIr gq,\ (b) ` 3,20,000, ` 2,40,000, ` 1,60,000
(a) ` 13,650 (b) ` 14,550 (c) ` 1,60,000, ` 3,20,000, ` 2,40,000
(c) ` 12,750 (d) ` 11,750 (d) ` 1,60,000, ` 2,40,000, ` 3,20,000
A

39. A, B and C invest in the ratio 5 : 7 : 6. After 43. The investments made by Ayan and Prince
1 year, they increase their investment are in the ratio 3 : 2. if 5% of total profit
respectively 26%, 20%, 15%. What will be is donated and Ayan get ` 8,550 as his
the ratio of their profit after 2 year? share of profit, then what is the amount
of total profit?
A, B vkSj C rhuksa 5 % 7 % 6 ds vuqikr esa fuos'k
v;ku rFkk ¯çl viuh iw¡th Øe'k% 3 % 2 ds vuqikr
djrs gSaA ,d o"kZ ckn ;s rhuksa vius fuos'kksa dks Øe'k%
esa fuos'k djrs gSaA ;fn dqy ykHk dk 5» nku ik=k esa
26»] 20» vkSj 15» ls c<+k nsrs gSaA 2 lky ckn tek fd;k x;k rFkk v;ku us ` 8]550 dk ykHk izkIr
buds ykHk dk vuqikr D;k gksxk\ fd;k ] rks dqy ykHk Kkr djsaA
(a) 7 : 6 : 9 (b) 71 : 53 : 63 (a) ` 14,000 (b) ` 15,000
(c) 112 : 117 : 105 (d) 113 : 154 : 129 (c) ` 11,050 (d) ` 12,020

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Distribution Management
44. A & B invest ` 30,000 & ` 20,000 and 80% 47. A and B entered into a partnership by
of total profit distribute equally among 1 5
them. Rest profit distribute according to investing their capitals in the ratio :
4 12
invest-ment ratio. The difference between A received 4% of the annual profit for
the share of A & B is 4000. Find the total providing services to the business and the
profit and find the share of A & B? remaining annual profit is divided between
A vkSjB Øe'k%` 30]000 vkSj` 20]000 fuos'k dj them in proportion to their investments. If
B's share in the annual profit is `30 lakhs.
lk>s esa ,d O;kikj dh 'kq:vkr djrs gSaA os yksx dqy then what is A's share (in ` lakhs)?
ykHk dk 80» vkil esa cjkcj ls ck¡V ysrs gSa rFkk
'ks"k ykHk dks vius }kjk fuosf'kr iw¡th ds vuqikr esa 1 5
A vkSjB us : vuqikr esa viuh iwath fuos'k djds
ck¡Vrs gSaA
A vkSj B ds fgLls esa` 4]000 dk varj gS] 4 12
dqy ykHk rFkk
A vkSjB dk fgLlk Kkr djsaA ,d lk>snkjh esa ços'k fd;k]A dks O;olk; esa lsok,a
çnku djus ds fy, okf"kZd ykHk4% dk çkIr gqvk vkSj

r
(a) ` 8000, ` 42000, ` 38000
(b) ` 100000, ` 52000, ` 48000 'ks"k okf"kZd ykHk muds chp muds fuos'k ds vuqikr esa

si
(c) ` 9000, ` 52000, ` 38000 foHkkftr fd;k x;kA ;fn okf"kZd ykHk B dk
esafgLlk
#i, 30 yk• gSA rks A dk fgLlk D;k gS (yk• esa)\

an by
(d) ` 12000, ` 62000, ` 58000
45. A & B start a business in partnership and ICAR MAINS, 07/07/2023 (SHIFT-1)
(a) 20

n
invest ` 40,000 & ` 60,000. 60% of total (b) 24
profit is distributed among them equally (c) 18 (d) 22
and the rest profit distributed between 48. A, B and C are three partners. A receives

ja
9
R s
them according to their investment ratio.
of the profit and B and C share the
The difference between their profit is ` 10
a th
6,000. find the total profit amount? remaining profit equally. A's income is
increased by ` 270 when the profit rises
A vkSj B lk>s esa ,d O;kikj dh 'kq:vkr djrs gSa from 12% to 15%. Find the capitals
rFkk Øe'k% ` 40]000 vkSj` 60]000 fuos'k djrs gSaA invested by B and C.
os yksx dqy ykHk dk 60» vkil esa cjkcj&cjkcj 9
ty a

A, B vkSj C rhu lk>snkj gSaAA dks ykHk dk

ck¡V ysrs gSa rFkk 'ks"k ykHk dks vius }kjk fuosf'kr 10
iw¡th ds vuqikr esa ck¡Vrs gSaA muds ykHk dk varj Hkkx izkIr gksrkBgSA
` 6]000 vkSj C 'ks"k ykHk dks vkil esa
di M

gks] rks dqy ykHk crk,¡A cjkcj&cjkcj ck¡V ysrs AgSaA

dh vk; esa ` 270 dh o`f¼
gks tkrh gS tc mldk ykHk 12» ls c<+dj 15» gks tkrk
(a) ` 52,000 gSA
B vkSjC }kjk fuos'k dh xbZ dqy jkf'k crk,¡A
(b) ` 60,000 (a) ` 5000 (b) ` 1000
(c) ` 62,000 (c) ` 500 (d) ` 1500
(d) ` 75,000 49. Ankit, Ashish and Ayan together started a
46. Two brother Yasir and Ankur invested business. Ankit invested ` 6,500 for 6
` 50,000, and ` 70,000 respectively in a months, Ashish invessted ` 8,400 for 5
business and agreed that 70% of the profit months and Ayan invested ` 10,000 for 3
should be divided equally between them months. Ankit is working member for which
and the remaining profit in the ratio of he gets 5% of total profit extra. If the total
A

investment. If Ankur gets ` 90 more Yasir. gain is ` 7,400, then Ayan's share is :
Find the total profit made in the business. vafdr] vk'kh"k rFkk v;ku us feydj ,d O;kikj 'kq:
nks HkkbZ ;kflj vkSj vadqj us ,d O;kikj dh 'kq:vkr esa fd;kA vafdr us 6 eghus ds fy,` 6]500 dk fuos'k
Øe'k%` 50]000] vkSj` 70]000 dh iw¡th fuos'k dhA fd;kA vk'kh"k us 5 eghus ds fy, ` 8400 dk fuos'k
lk>snkjh dh 'krZ ;g fd dqy ykHk dk 70» leku :i fd;k rFkk vk;ku us 3 eghus ds fy,` 10]000 dk
fuos'k fd;kA O;kikj laHkkyus ds fy, vafdr dks dqy
ls rFkk 'ks"k ykHk fuosf'kr iw¡th ds vuqikr esa ck¡Vk tk,xkA
;fn vadqj dks ;kflj ls ` 90 vfèkd feyrs gSa] rks Kkr ykHk dk 5» Hkh feyrk gSA ;fn dqy ykHk ` 7]400
djsa O;kikj esa dqy fdruk ykHk gqvk\ #i, gS] rks v;ku dk fgLlk Kkr dhft,A
(a) ` 1200 (b) ` 1400 (a) ` 1900 (b) ` 2100
(c) ` 1600 (d) ` 1800 (c) ` 3200 (d) Date incomplete

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50. Bhagat, Harish and Rohit started a business (a) ` 46000 (b) ` 45000
by investing ` 24,000, ` 32,000 and ` 18,000 (c) ` 48000 (d) ` 32000
respectively. Bhagat and Harish are active 53. A and B invest respectively ` 80,000 and
partners and get 7% and 19% of total profit ` 60,000 to start a business into
and remaining profit is to be distributed partnership. B got ` 250 per month for a
among them in the ratio of their investment. supervision. A and B both receive the
If Rohit got total ` 144000 as a profit, what premium at the rate of 10% p.a. and the
was the total amount of profit? rest profit distribute between them
Hkxr] gjh'k rFkk jksfgr ,d O;kikj esa Øe'k%
` 24000] according to their investment. If total profit
` 32000 rFkk` 18000 fuos'k djrs gSaA Hkxr rFkk gjh'k distributed between them is ` 20500, then
lfØ; lk>snkj gSa rFkk mudks dqy ykHk dk Øe'k% find the total profit amount received by B?
7» rFkk 19» izkIr gksrk gSA 'ks"k ykHk dks muds }kjkA vkSjB Øe'k%` 80]000 vkSj` 60]000 fuos'k dj
fuosf'kr iw¡th ds vuqikr esa ck¡V fn;k tkrk gSA ;fn lk>s esa ,d O;kikj dh 'kq:vkr djrs gSaA
B dks ns[kjs[k
jksfgr dks dqy` 144000 ykHk ds :i esa izkIr gqvk ds fy, ` 250 izfr eghuk vyx ls fn;k tkrk gSAA
gks] rks Kkr dhft, fd ykHk dk dqy jkf'k D;k Fkh\ vkSjB nksuksa dks vius fuos'k ij 10» okf"kZd ds nj

r
(a) ` 4,70,000 (b) ` 8,00,000 ls izhfe;e Hkh feyrk gS rFkk 'ks"k ykHk dks vius fuos'k

si
(c) ` 3,45,000 (d) ` 1,57,000 ds vuqikr esa vkil esa ck¡V ysrs gSaA ;fn dqy ykHk
51. A and B start a business investing ` 20000 ` 20]500 gS] rksB dks izkIr dqy ykHk crk,¡A

an by
and ` 8000 respectively. According to the
(a) ` 10,500 (b) ` 10,700
convenant, B gets ` 200 per month for
(c) ` 9900 (d) ` 9600

n
maintenance and both get interest at the
rate of 5% per annum on their capital. 54. X contributes ` 1500 and Y, ` 900 in a
Remaining profit will be distributed business. X is a sleeping partner and Y gets

ja
R s
according to their investment. If the 10% of the profit for management and the
annual profit is ` 8000, then find the share rest of the profit is divideding the
a th
of each person? proportion of their capital. If total profit
A vkSj B Øe'k%` 20000 rFkk` 8000 fuos'k djds is ` 800, what is the share of Y?
,d O;kikj vkjaHk djrs gSaA lk>snkjh dh 'krZ ;g gS X rFkkY ,d O;kikj esa Øe'k%` 1500 rFkk` 900
fd O;kikj dh ns[kHkky ds fy,B dks ` 200 izfr iw¡th fuos'k djrs gSaA
X ,d fuf"Ø; ikVZuj gS rFkk
ty a

Y
ekg fn, tk,axs rFkk 5» okf"kZd nj ls mudh iw¡th ij dqy ykHk dk 10» O;kikj laHkkyus ds fy, ysrk gS
mu nksuksa dks C;kt Hkh feysxkA 'ks"k ykHk dks oks nksuksa
rFkk 'ks"k ykHk buds chp yxkbZ xbZ iw¡th ds vuqikr esa
di M

fuosf'kr iw¡th ds vuqikr esa ck¡V ysaxsA ;fn okf"kZd ykHk

ck¡V nh tkrh gSA ;fn dqy ykHk
` 800 gS] rks blesa
Y
` 8000 gks] rks mlesa ls izR;sd dk fgLlk D;k gksxk\ dk fgLlk gS %
(a) ` 4000, ` 4000 (b) ` 4000, ` 3000 (a) ` 375 (b) ` 360
(c) ` 2000, ` 2500 (d) ` 2500, ` 2000
(c) ` 350 (d) ` 450
Miscllaneous 55. Anil is an active and Vimal is a sleeping
partner in a business. Anil invests ` 12000
52. A and B invest respectively ` 20000 and
30000 and start a business in partnership. and Vimal, invests ` 20000. Anil receives
A got ` 500 for a supervision. A and B both 10% profit for managing, the rest being
received premium on their investment divided in proportion to their capitals. Out
10% p.a. and the rest profit is distributed of the total profit of ` 9000, the money
A

among them according to their received by Anil is :

investment. If total profit is ` 71000, then vfuy ,d lfØ; vkSj foey ,d fuf"Ø; lk>snkj
find the profit of A.
gSaA vfuy` 12000 rFkk foey` 20000 fuos'k djrk
A vkSj B Øe'k%` 20000 vkSj` 30000 fuos'k dj
gSA vfuy O;olk; dh ns[kjs[k ds fy;s 10» dqy ykHk
lk>s esa ,d O;kikj dh 'kq:vkr djrs gSaA
A dks ns[kjs[k
dk vftZr djrk gS vkSj 'ks"k ykHk mudh jkf'k ds
ds fy, ` 500 izfr eghuk vyx ls fn;k tkrk gSA A
vkSjB nksuksa dks vius fuos'k ij 10» okf"kZd ds nj vuqikr esa ck¡Vrs gSaA
` 9000
dqy ds ykHk esa ls vfuy
ls izhfe;e Hkh fn;k tkrk gS rFkk 'ks"k ykHk dks viusdk fgLlk Kkr djsaA
fuos'k ds vuqikr esa vkil esa ck¡V ysrs gSaA ;fn dqy(a) ` 4500 (b) ` 4800
ykHk` 71000 gS] rksA dk ykHk crk,¡A (c) ` 4600 (d) ` 39375

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56. A, B, C invest in a business in the ratio A, B vkSjC us fdlh fctusl esa 4%5 %7 ds vuqikr
4 : 5 : 7. C is a sleeping partner, so his esa fuos'k fd;kA
C Lyh¯ix ikVZuj gSA vr% mldk fgLlk
share of profits will be half of what it would
ml fgLls dk vk/k gksxk vxj og o²dx ikVZuj gksrkA
have been if he were a working partner. If
they make ` 36,000 profit of which 25% ;fn mUgsa` 36]000 dk ykHk gksrk gSA ftlesa ls os
is reinvested in the business, how much 25» fctusl esa iqu% fuos'k dj nsrs gSa] B dks
rks
does B get (in `)? fdruk feysxk (` esa)
(a) 7560 (b) 10,800
(c) 8540 (d) 9200

ANSWER KEY
1. (a) 2.(a) 3. (b) 4. (a) 5. (a) 6. (d) 7. (a) 8. (a) 9. (a) 10. (c)

r
si
11.(a) 12.(c) 13.(b) 14.(b) 15.(b) 16.(c) 17.(c) 18.(a) 19.(b) 20.(b)

an by
21.(c) 22.(b) 23.(d) 24.(a) 25.(a) 26.(b) 27.(d) 28.(c) 29.(a) 30.(a)

n
31.(c) 32.(a) 33.(d) 34.(c) 35.(c) 36.(a) 37.(b) 38.(a) 39.(d) 40.(a)

ja
41. (d) 42.(d)
R s
43. (b) 44. (b) 45. (d) 46. (d) 47. (a) 48. (b) 49. (a) 50. (b)
a th
51.(a) 52.(d) 53.(a) 54.(c) 55.(d) 56.(b)
ty a
di M
A

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Partnership/lk>snkjh
( Practice Sheet With Solution)
1. A, B and C enter into a partnership and their A ,d O;olk; esa dk;Zjr gS vkSj
B Lyhfiax ikVZuj A
gSA
1 1 1
shares are in the ratio : : . After 2 months,
5000 #i;s Mkyrk gSA vkSj
B 6000 #i;s Mkyrk gSA
A dks
2 3 4 O;olk; ds çca/u ds fy, ykHk dk 12-5» çkIr gksrk gS
A withdraws half of his capital and after 10
months, a profit of Rs. 378 is divided among vkSj 'ks"k dks mudh iwath ds vuqikr esa foHkkftr fd;
them. What is B's share ? tkrk gSA 880 #i;s ds ykHk ls çR;sd dks D;k feyrk gS\
A] B vkSj C ,d lk>snkjh esa ços'k djrs gSa vkSj muds (a) 460, 420 (b) 480, 400
1 1 1 (c) 530, 350 (d) 550, 330
fgLls : : ds vuqikr esa gSaA 2 eghus dsAckn]

r
2 3 4 5. Radha began a business with Rs. 85,000. She
was joined afterwards by Shyam with Rs.
viuh iwath dk vk/k fudky ysrk gS vkSj 10 eghus ds

si
42,500. For how much period does Shyam join,
ckn 378 #i;s ds ykHk esa Blsdk fgLlk D;k gSA if the profits at the end of the year are divided
(a) 144
(c) 225
an by (b) 169
(d) 339
in the ratio of 3 : 1 ?
jk/k us 85]000 #i;s ds lkFk ,d O;olk; 'kq: fd;kA mlds

n
2. A, B, C started a business with their
investments in the ratio 1 : 3 : 5. After 4 ckn ';ke us 42]500 :i;s ds lkFk Tokbu fd;kA ;fn o"kZ ds
ja
months, A invested the same amount as before var esa ykHk dks 3 % 1 ds vuqikr esa foHkkftr fd;k tkrk gS
R s
and B as well as C withdrew half of their rks ';ke fdrus le; ds fy, 'kkfey gksrk gS\
investments. The ratio of their profits at the
a th

(a) 4 months (b) 5 months

end of the year is :
(c) 6 months (d) 8 months
A, B, C us 1 % 3 % 5 ds vuqikr esa vius fuos'k ds lkFk
6. A, B and C enter into a partnership with a
,d O;olk; 'kq: fd;kA 4 eghus ckn] A us igys dh rjg
ty a

capital in which A's contribution is Rs. 10,000.

gh fuos'k fd;k vkSjB vkSjC us vius fuos'k dk vk/k If out of a total profit of Rs. 1000, A gets Rs.
okil ys fy;kA o"kZ ds var esa muds ykHk dk vuqikr gS%
di M

500 and B gets Rs. 300, then C's capital is :

(a) 1 : 2 : 3 (b) 3 : 4 : 15 A, B vkSj C iwath ds lkFk lk>snkjh esa ços'k djrs gSa
(c) 3 : 5 : 10 (d) 5 : 6 : 10
3. A and B are partners in a business. A contributes
ftlesa A dk ;ksxnku 10]000 #i;s gSA ;fn 1000 #i;s ds
1 dqy ykHk esaAlsdk fgLlk 500 :i;s vkSj B dk fgLlk
of the capital for 15 months and B received 300 #i;s gSA rksC dh iwath gS%
4
2 (a) 4000 (b) 5000
of the profit. For how long B's money was
3 (c) 6000 (d) 7000
used ?
7. kiran and sushma began business with Rs.3000
A vkSjB ,d O;olk; esa Hkkxhnkj gSaAA us 15 eghus ds and Rs.4000 after 8 months, kiran withdraws
1 2 Rs.1000 and sushma advances Rs.1000 more.
fy, iwath dk Hkkx yxk;k vkSj B us ykHk dk çkIr At the end of the year, their profits amounted
A

4 3
fd;kAB dk iSlk fdrus le; rd bLrseky fd;k x;k\ to Rs.630 find the share of kiran ?
(a) 3 months (b) 6 months fdj.k vkSj lq"kek us 3000 #i;s vkSj 4000 #i;s ds lkFk
(c) 10 months (d) 12 months dkjksckj 'kq: fd;k 8 eghus ckn fdj.k 1000 #i;s
4. A is a working and B is sleeping partners in a fudkyrh gS vkSj lq"kek 1000 #i;s vkSj is'kxh nsrh gSA o
business. A puts in Rs. 5000 and B puts in
ds var esa] mudk ykHk 630 #i;s Fkk] fdj.k dk fgLlk
Rs.6000. A receives 12.5% of the profit for
managing the business and the rest is divided Kkr dhft;s\
in proportion to their capital. What does each (a) Rs. 240 (b) Rs. 75
get out of a profit of Rs. 880? (c) Rs. 125 (d) Rs. 354

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8. A and B start a business, with A investing the 7 4 6

total capital of Rs.50000, on the condition A, B vkSjC : : ds vuqikr esa ,d lk>snkjh esa
2 3 5
that B pays A interest @ 10% per annum on
his half of the capital. A is a working partner ços'k djrs gSaA 4 eghus ckn]
A vius fgLls esa 50» dh
and receives Rs.1500 per month from the total o`f¼ djrk gSA ;fn ,d o"kZ ds var esa dqy ykHk #-
profit and any profit remaining is equally shared 21600 gS] rks ykHkB esa
dk fgLlk gS%
by both of them. At the end of the year, it (a) Rs. 4000 (b) Rs. 6000
was found that the income of A is twice that (c) Rs. 9000 (d) Rs. 3000
of B. Find the total profit for the year?
12. Three friends, P, Q and R started a partnership
A vkSjB ,d O;olk; 'kq: djrs gSa] ftlesa A us 50000 business investing money in the ratio of 5 : 4 : 2
#i;s dh dqy iwath dk fuos'k fd;k gS] bl 'krZ ij fdB respectively for a period of 3 years. What is the
viuh iwath ds vk/s fgLls ij çfr o"kZ 10» C;kt dk amount received by P as his share in the total
profit ?
Hkqxrku djrk gSAA ,d dkedkth Hkkxhnkj gS vkSj dqy
rhu fe=kksa]
P, Q vkSj R us 3 o"kZ dh vof/ ds fy,
ykHk ls 1500 #i;s çfr ekg çkIr djrk gS vkSj 'ks"k ykHk
Øe'k% 5 % 4 % 2 ds vuqikr esa /u fuos'k djds ,d
nksuksa }kjk leku :i ls lk>k fd;k tkrk gSA o"kZ ds var
lk>snkjh O;olk; 'kq: fd;kA dqy ykHk esa mlds fgLls ds
esa] ;g ik;k x;k fd A dh vk; B ls nksxquh gSA o"kZ ds

r
:i esa P dks çkIr jkf'k fdruh gS\
fy, dqy ykHk Kkr dhft;s\

si
A. Total amount invested in the business in
(a) Rs. 39000 (b) Rs. 49000 Rs. 22,000.
(c) Rs. 59000 an by (d) Rs. 69000 O;olk; esa fuos'k dh xbZ dqy jkf'k #- 22]000A
9. Two partners investede Rs 1250 and Rs 850
3

n
respectively in a business. They distributed B. Profit earned at the end of 3 years is of
60% of the profit equally and decide to 8
the total investment.
distribute the remaining 40% as the ratio of
ja
R s
their capitals. If one partner received Rs 30 3
more than the other, find the total profit? 3 o"kZ ds var esa vftZr ykHk dqy fuos'k dk
gSA
8
a th

nks Hkkxhnkjksa us ,d O;olk; esa Øe'k% 1250 #i;s vkSj

C. The average amount of profit earned per
850 #i;s dk fuos'k fd;kA mUgksaus ykHk dk 60» leku year is Rs. 2750.
:i ls forfjr fd;k vkSj 'ks"k 40» dks viuh iwath ds çfr o"kZ vftZr ykHk dh vkSlr jkf'k 2750 #i;s gSA
ty a

vuqikr ds :i esa forfjr djus dk fu.kZ; fy;kA ;fn ,d (a) Only c is sufficient
Hkkxhnkj dks nwljs ls 30 #i;s vf/d çkIr gksrs gSa] rks dqy dsoy c i;kZIr gS
di M

ykHk Kkr dhft;s\ (b) Both a & b are sufficient

(a) 390.5 (b) 393.75 a vkSjb nksuksa i;kZIr gSa
(c) 395 (d) 396 (c) Both A & B not gives result
10. A starts business with Rs. 3500 and after 5 avkSjb nksuksa ifj.kke ugha nsrs gSa
months, B joins with A as his partner. After a (d) None/dksbZ ugha
year, the profit is divided in the ratio 2 : 3. 13.
A and B entered into a partnership investing
What is B's contribution in the capital? Rs 13,000 and Rs 12,000 respectively. After
A 3500 #i;s ds lkFk O;kikj 'kq: djrk gSA vkSj 5 eghus 3 months, A withdrew Rs 5000 while B invested
Rs 5000 more, After 3 more months, C joins
ds ckn] B] A ds lkFk vius lkFkh ds :i esa 'kkfey gks the business with a capital of Rs 21,000. The
tkrk gSA ,d o"kZ ds ckn] ykHk dks 2 % 3 ds vuqikr esashare of B exceeds that of A, out of a total
A

ckaVk tkrk gSA iwathB dkesa

;ksxnku fdruk gS\ profit of Rs 28,400 after one year by
(a) Rs. 7500 (b) Rs. 8000 A vkSjB us Øe'k% 13]000 :Ik;s vkSj 12]000 :Ik;s dk
(c) Rs. 8500 (d) Rs. 9000 fuos'k djds ,d lk>snkjh dhA 3 eghus ckn]A us 5000
11. A, B and C enter into a partnership in the #i;s okil ys fy, tcfd B us 5000 #i;s vkSj fuos'k
7 4 6 fd,] 3 vkSj eghuksa ds ckn]
C 21]000 #i;s dh iwath ds
ratio : : . After 4 months, A increases
2 3 5 lkFk O;kikj esa 'kkfey gks x;kA ,d o"kZ ds ckn 28]400
his share by 50%. If the total profit at the #i;s ds dqy ykHk esa Bls dk fgLlk A ls vf/d gSA
end of one year be Rs. 21600, then B's share (a) 5000 (b) 5200
in the profit is : (c) 3700 (d) 5400

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14. Three friends had dinner at a restaurant. When 18. A, B and C started a company where their initial
2 investments was in the ratio of 2:3:4. At the
the bill was received, Akshitha paid as much end of 6 months, A invested an amount such
3
that his total capital became equal to B's initial
1 capital investment. If the annual profit of B
as Veena paid and Veena paid as much as
2 is Rs. 3000 then what is the total profit of
Lasya paid. What fraction of the bill did Veena the company ?
pay ?
A] B vkSjC us ,d daiuh 'kq: dh ftlesa mudk çkjafHkd
rhu nksLrksa us ,d jsLVksjsaV esa fMuj fd;kA tc fcy çkIr
fuos'k 2 % 3 % 4 ds vuqikr esa FkkA 6 eghus dsAvar esa]
2
gqvk] rks vf{krk us ohuk ds HkqxrkuHkqxrku
dk fd;k us ,d jkf'k dk fuos'k bl çdkj fd;k fd mldh dqy
3
iwathB ds çkjafHkd iwath fuos'k ds cjkcj gks xbZA
B ;fn
1
vkSj ohuk us ykL; ds Hkqxrku Hkqxrku
dk fd;kA ohuk dk okf"kZd ykHk 3000 :i;s gS rks daiuh dk dqy ykHk
2
fdruk gS\
us fcy ds fdrus Hkkx dk Hkqxrku fd;k\
(a) Rs. 9500 (b) Rs. 10600
11 2 (c) Rs. 7500 (d) Rs. 8900
(a) (b)

r
3 13 19. K and L start a business jointly. K invests

si
3 13 Rs.16000 for 8 months and L remains in the
(c) (d) business for 4 months. Out of the total profit
11 4
15. an by
Three milkmen rented a pasture. A grazed 24
cows for 4 months; B 10 cows for 6 months; C L claims
2
7
th share. How much money is

n
56 cows for 5 months. If A's share of rent is
Rs. 960, find the total rent of the field? contributed by L?
rhu nwf/;ksa us ,d pkjkxkg fdjk, ij fy;kA
A 4 eghus K vkSjL la;qÙkQ :i ls ,d O;olk; 'kq: djrs gSaA
K8
ja eghus ds fy, 16000 #i;s dk fuos'k djrk gS vkSj
L4
R s
rd 24 xk;ksa dks pjkrk_
B 10 xk; 6 eghus rd_ C 56
xk; 5 eghus rd pjkrk gSA ;fnA dk fdjk, dk fgLlk
a th

2
960 :i;s gS rks •sr dk dqy fdjk;k Kkr djsa\ eghus ds fy, dkjksckj esa jgrk gSA dqy ykHk
L esa ls
7
(a) 4530 (b) 4440
(c) 4360 (d) 4280 fgLls dk nkok djrk gSA
L }kjk fdruk iSlk fn;k tkrk gS\
(a) Rs. 13,204 (b) Rs. 14,521
ty a

16. P, Q and R enter into a partnership in the

ratio 2 : 3 : 5. After 2 months, P increases his (c) Rs. 12,800 (d) Rs. 15,000
share 20% and Q by 10%. If the total profit at 20. A and B entered in a business by making
di M

the end of one year is Rs 1,90,500, what amount investment of Rs. 4000 & Rs. 5500 respectively.
will 'R' receive at the end of year as share in After six months A & B withdrew Rs. 1000
profit ?
and Rs. 1500 respectively and C joined them
P] Q vkSj R 2 % 3 % 5 ds vuqikr esa ,d lk>snkjh esa
with capital of Rs. 4x. If after one year and
ços'k djrs gSaA 2 eghus ds Pckn]
vius fgLls esa 20» vkSj three months C received Rs. 2250 as profit
Q esa 10» dh o`f¼ djrk gSA ;fn ,d o"kZ ds var esa dqy share out of total profit of Rs. 12250, then
ykHk 1]90]500 #i;s gS] rks ykHk esa fgLls dsR:i* esa ^ find investment of C?
dks o"kZ ds var esa fdruh jkf'k çkIr gksxh\ A vkSjB us 4000 :i;s vkSj 5500 #i;s dk fuos'k djds
(a) Rs. 90500 (b) Rs. 87500
,d O;olk; fd;kA A vkSj B us Ng eghus ds ckn
(c) Rs. 88900 (d) Rs. 90000
17. Arun, Kamal and Vinay invested Rs.8000, Øe'k% 1000 #i;s vkSj 1500 :i;s fudkys vkSj4x dh
iwath ds lkFk muds lkFk tqM+ x;kA ,d o"kZ rhu eghus
A

Rs.4000 and Rs. 8000 respectively in a

business. Arun left after six months. If after
ckn C dks 2250 #i;s dk ykHk gqvk ;fn dqy ykHk
eight months, there was a gain of Rs. 4005,
then what will be the share of Kamal? 12250 :i;s gS] rksC dk fuos'k Kkr dhft;s\
v#.k] dey vkSj fou; us #-8000] #-4000 vkSj #- (a) Rs. 3600 (b) Rs. 3200
8000 ,d O;olk; esa Øe'k% v#.k Ng eghus ckn pyk (c) Rs. 4400 (d) Rs. 3000
21. A, B & C started a business and invested in
x;kA ;fn vkB eghus ds ckn 4005 #i;s dk ykHk gksrk gSA
the ratio 7:6:5. Next Year, they increased their
gS] rks dey dk fgLlk D;k gksxk\ investment by 25%, 20% and 15%, respectively.
(a) 830 (b) 860 In what ratio should profit earned only during
(c) 890 (d) 900 2ndyear be distributed?

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A, B vkSjC us ,d O;olk; 'kq: fd;k vkSj 7 % 6 % 5 25. P and Q started a business by investing Rs
ds vuqikr esa fuos'k fd;kA vxys o"kZ] mUgksaus vius fuos'k
156000 and Rs 117000 respectively and their
time period of investment is same. If P's share
esa Øe'k% 25»] 20» vkSj 15» dh o`f¼ dhA dsoy nwljs
in the profit earned by them is Rs.12000, then
o"kZ esa vftZr ykHk dks fdl vuqikr esa ck¡Vuk pkfg,\ what is the total profit (in Rs) earned by both
(a) 155 : 144 : 175 (b) 155 : 124 : 95 of them together?
(c) 135 : 147 : 152 (d) 175 : 144 : 115 P vkSjQ us Øe'k% 156000 #i;s vkSj 117000 #i;s dk
22. A man who recently died left a sum of Rs.
3,90,000 to be divided among his wife, five
fuos'k djds ,d O;olk; 'kq: fd;k vkSj mudh fuos'k
sons and four daughters. He directed that each dh vof/ leku gSA ;fn muds }kjk vftZr ykHkPesadk
son should receive 3 times as much as each fgLlk # 12000 gS] rks mu nksuksa }kjk ,d lkFk vftZr dqy
daughter receives and that each daughter ykHk (#i;s esa) fdruk gS\
receives and that each daughter should receive (a) 25000 (b) 17000
twice as much as their mother receives. What (c) 21000 (d) 18000
was the wife's share? 26. Three partners, A, B and C, started a business
,d O;fÙkQ ftldh gky gh esa e`R;q gks xbZ] vius ihNs #-by investing Rs.48,000 each. After 5 months,
3]90]000 mldh iRuh] ikap csVksa vkSj pkj csfV;ksa ds chp A left the business; after 9 months, B left the

r
bl izdkj ckaVs tkus FksA fd çR;sd mrukiq=k dks
feys ftruk business; and after 12 months, C left the

si
çR;sd iq=kh dks çkIr gksrk gS mldk 3 xquk vkSj çR;sd iq=kh business. If the total earned profit is Rs.5,850,
then the share of C is what percentage more
dks çkIr gksrk gS vkSj çR;sd iq=kh dks mldh ek¡ dks çkIr gksus
an by than that of B?
okys dk nqxuk çkIr gksuk pkfg,A iRuh dk fgLlk D;k Fkk\rhu lk>snkjksa A] B vkSj C us çR;sd 48]000 #i;s dk

n
(a) Rs. 14,000 (b) Rs. 12,000
fuos'k djds ,d O;olk; 'kq: fd;kA 5 eghus ckn]A us
(c) Rs. 10,000 (d) Rs. 9,000
23. A sum of Rs 3170 is divided among X, Y and Z O;olk; NksM+ fn;k_ 9 eghus Bckn]us O;olk; NksM+ fn;k_
ja vkSj 12 eghuksa ds ckn]C us O;olk; NksM+ fn;kA ;fn
R s
such that if Rs 13, Rs 12 and Rs 18 will be
diminished from the shares of X, Y and Z dqy vftZr ykHk 5]850 #i;s gS] rks C dk fgLlk B ls
a th

respectively, then their shares will be in the fdrus çfr'kr vf/d gS\
ratio 20 : 18 : 21. What is the initial share (in
CRPF HCM 28/02/2023 (Shift - 01)
Rs) of Z?
(a) 43% (b) 37%
3170 #i;s dh jkf'k dksX] Y vkSjZ esa bl çdkj ckaVk
ty a

tkrk gS fd ;fn X] Y vkSjZ ds 'ks;jksa esa ls Øe'k% 13 (c) 33 1 % 1

(d) 39 %
#i;s] 12 #i;s vkSj 18 #i;s de dj fn, tk,a] rks muds 3 3
di M

fgLls 20 % 18 % 21- gks tk,xsaA

Z dk çkjafHkd fgLlk (# 27. A and B are partners in a business. A
esa) D;k gS\ 1
contributes th of the capital for 15 months
(a) 1131 (b) 1530 5
(c) 910 (d) 1350
24. A starts a cement trading business by investing 2
and B received of the profit. For how many
Rs 5 lakhs. After 2 months, B joins the business 3
by investing Rs 10 lakhs and then 4 months months was B's money invested in the
after B joined C too joins them by investing business?
Rs 20 lakhs. 1 year after A started the business A vkSjB ,d O;olk; esa Hkkxhnkj gSaA
A 15 eghus ds fy,
they make Rs 3,50,000 in profit. What is B's
share of the profit (in Rs)? 1 2
iwath dk oka ;ksxnku nsrk gS BvkSj
ykHk dk çkIr
A

A 5 yk• #i;s dk fuos'k djds ,d lhesaV O;kikj 5 3

O;olk; 'kq: djrk gSA 2 eghus ckn]
B 10 yk• #i;s dk djrk gSAB dk /u O;olk; esa fdrus eghuksa ds fy,
fuos'k djds O;olk; esa 'kkfey gks tkrk gS vkSjBfiQj fuosf'kr Fkk\
ds 'kkfey gksus ds 4 eghus ckn
C Hkh 20 yk• #i;s dk CRPF HCM 11/03/2023 (Shift - 02)
fuos'k djds O;kikj esa 'kkfey gks tkrkAgSA
ds O;olk;
1
'kq: djus ds 1 o"kZ ckn os 3]50]000 #i;s dk ykHk (a) 7 (b) 8
2
dekrs gSaA ykHkB dk
esafgLlk fdruk gS (#i;s esa)\
(a) 75000 (b) 1,25,000 1
(c) 7 (d) 6
(c) 1,50,000 (d) 1,00,000 2

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 MIXTURE (feJ.k)
(CLASSROOM SHEET)
4. If 49 litres of a milk solution has 63% milk
Questions Based on Addition in it, then how much milk should be added
to make the concentration of milk 70%
Subtraction of Some
in the solution?
Quantity ;fn 49 yhVj nw/ ds ,d ?kksy esa 63» nw/ gS] rks
1. A canister holds 36 litres of mixture of nw/ dh lkærk 70» djus ds fy, ?kksy esa fdruk
milk and water in the ratio 3 : 1. 15 litres nw/ vkSj feyk;k tkuk pkfg,\
of milk is added to the canister. The new

r
SSC CHSL 25/05/2022 (Shift- 02)
ratio of the mixture is :

si
,d duLrj esa 36 yhVj nw/ vkSj ikuh dk feJ.k 13 7
(a) 11 Litres (b) 14 Litres
3%1 ds vuqikr esa gSA duLrj esa 15 yhVj nw/ feyk;k 30 30
an by
tkrk gSA feJ.k dk u;k vuqikr gS%
11 1

n
(a) 12 : 5 (b) 14 : 3 (c) 12 Litres (d) 13 Litres
30 30
(c) 7 : 4
ja
(d) 9 : 4
5. An alloy contains copper, zinc and nickel
R s
2. In a mixture of 25 litres, the ratio of acid in the ratio of 5 : 3 : 2. The quantity of
a th

to water is 4 : 1. Another 3 litres of water nickel (in kg) that must be added to 100
is added to the mixture. The ratio of acid kg of this alloy to have the new ratio 5 : 3 : 3
to water in the new mixture is is :
ty a

25 yhVj ds feJ.k esa] vEy vkSj ikuh dk vuqikr ,d feJ /krq esa 5 %3 %2 ds vuqikr esa rkack]
4 %1 gSA feJ.k esa vkSj 3 yhVj ikuh feyk;k tkrk tLrk vkSj fudsy gSA u;k vuqikr%35%3 çkIr
di M

gSA u, feJ.k esa vEy vkSj ikuh dk vuqikr gS % djus ds fy, 100 fdyksxzke feJ /krq esa fudsy
(a) 5 : 2 (b) 2 : 5 dh ek=kk (fdyks esa) feykbZ tkuh pkfg,A
(c) 3 : 5 (d) 5 : 3 (a) 8 (b) 10

3. 200 litres of a mixture contains milk and (c) 12 (d) 15

water in the ratio 17 : 3. After the addition 6. The ratio of milk and water in a vessel is
of some more milk to it, the ratio of milk 2 : 3 by chemical process if we extract
to water in the resulting mixture becomes some water then ratio becomes 5 : 7 and
7 : 1. The quantity of milk added to it was quantity of mixture reduced to 36 ltr, then
find how much quantity of water was
200 yhVj feJ.k esa nw/ vkSj ikuh dk vuqikr%17
3 extracted?
A

gSA blesa dqN vkSj nw/ feykus ds ckn] ifj.kkeh

,d crZu esa nw/ vkSj ikuh dk vuqikr%32 gSA
feJ.k esa nw/ dk ikuh ls vuqikr % 71 gks tkrk
jklk;fud iz;ksx }kjk vxj ge feJ.k ls dqN yhVj
gSA blesa feyk;s x, nw/ dh ek=kk fdruh Fkh\
ikuh fudkyrs gSa rks vuqikr%7 5gks tkrk gS vkSj
(a) 20 litres feJ.k dh ek=kk 36 yhVj gks tkrh gSA rks irk yxk,¡
(b) 40 litres fd ikuh fdruh ek=kk esa fudkyk x;k Fkk\
(c) 60 litres (a) 11 ltr (b) 1.5 ltr
(d) 80 litres (c) 1.25 ltr (d) 1.15 ltr

[1]
7. A mixture is composed of 11 parts of pure 10. A beaker contains acid and water in the ratio
milk and 2 parts of water. If 35 litres of 1 : x. When 50 ml of water is mixed in 300
water were added to the mixture then the ml of the mixture the ratio of acid to water
new mixture will contain twice as much becomes 2 : 5. What is the value of x?
pure milk as water, then how many litres ,d chdj esa ,flM vkSj ikuh dk vuqikr 1%x gSA
of pure milk does the original mixture tc 300 feyh ds feJ.k esa 50 feyh ikuh dks feyk;k
contain? tkrk gS rks ,flM vkSj ikuh ds feJ.k dk vuqikr
,d feJ.k esa 11 Hkkx 'kq¼ nw/ vkSj 2 Hkkx ikuh 2 %5 gks tkrk gSA x dk eku D;k gksxk\
gSA ;fn bl feJ.k esa 35 yhVj ikuh Mkyk x;k rks SSC CGL TIER - II 18/02/2018
(a) 2 (b) 1
u, feJ.k esa ikuh dh rqyuk esa nks xquk 'kq¼ nw/(c) 3 (d) 4
gksxk] rks okLrfod feJ.k esa fdrus yhVj 'kq¼11.
nw/ A jar contains a blend of a fruit juice and
gks\ water in the ratio 5 : x. When 1 litre of
water is added to 4 litres of the blend the
SSC CGL TIER - II 18/02/2018 ratio of fruit juice to water becomes 1 :
(a) 110 (b) 55 1. What is the value of x?

r
(c) 220 (d) 70 ,d tkj esa iQy dk jl vkSj ikuh dk feJ.k j[kk gS
ftldk vuqikr 5 : x gSA tc 4 yhVj ds feJ.k esa 1

si
8. A mixture of acid and water contains 20
percent acid . When 10 litres of water is added yhVj ikuh feyk;k tkrk gS rks iQy ds jl vkSj ikuh

an by
to the mixture, then the percentage of acid
becomes 15 percent. What is the original
dk vuqikr 1%1 gks tkrk gSA x dk eku D;k gS\
SSC CGL TIER - II 21/02/2018

n
quantity of mixture? (a) 3 (b) 1
(c) 2 (d) 4
vEy vkSj ikuh ds fdlh ?kksy esa 20 izfr'kr vEy gSA
ja 12. The ratio of milk and water in a mixture
R s
tc ml feJ.k esa 10 yhVj ikuh feyk;k tkrk gS] rks is 1 : 3. We added x ltr of milk to the
vEy dk izfr'kr 15 izfr'kr gks tkrk gSA ?kksy dh izkjafHkdmixture then ratio becomes 7 : 15 and we
a th

added 50 ltr water to the mixture, then

ek=kk D;k gS\
ratio becomes 2 : 5. Find the value of x.
SSC CGL TIER - II 08/08/2022 ,d feJ.k esa nw/ vkSj ikuh dk vuqikr %
13 gSA
ty a

(a) 25 litres ;fn feJ.k esa x yhVj nw/ feyk;k tk;s rks feJ.k
(b) 40 litres esa nw/ vkSj ikuh dk vuqikr %157 gks tkrk gSA
di M

(c) 35 litres vc bl feJ.k esa 50 yhVj ikuh feykus ij vuqikr

(d) 30 litres
2 %5 gks tkrk gSAx dk eku Kkr djsaA
(a) 28 ltr (b) 32 ltr
9. A drink of chocolate and milk contains 8% (c) 40 ltr (d) 68 ltr
pure chocolate by volume. If 10 liters of 13. A vessel contains a 32 litre solution of acid
pure milk are added to 50 liters of this and water in which the ratio of acid and
drink, the percentage of chocolate in the water is 5 : 3. If 12litres of the solution
new drink is : 1
are taken out and 7 litres of water are
pkWdysV vkSj nw/ dk ,d is; esa 8» 'kq¼ pkWdysV 2
gksrk gSA ;fn bl is; ds 50 yhVj esa 10 yhVj 'kq¼ added to it, then what is the ratio of acid
and water in the resulting solution?
nw/ feyk;k tkrk gS] rks u, is; esa pkWdysV dk ,d crZu esa vEy vkSj ty dk 32 yhVj ?kksy gS]
A

izfr'kr gksrk gS % ftlesa vEy vkSj ty dk vuqikr 5 %3 gSA tc crZu

SSC CGL 2019 TIER - II 16/10/2020 esa ls 12 yhVj ?kksy fudky fy;k tkrk gS vkSj
1
1 1 crZu esa7 yhVj ty feyk fn;k tkrk gS] rks
(a) 5 (b) 6 2
3 3 izkIr ?kksy esa vEy vkSj ty dk vuqikr D;k gksxk\
SSC CGL TIER II 12/09/2019
2 2
(c) 6 (d) 5 (a) 4 : 7 (b) 8 : 11
3 3 (c) 4 : 9 (d) 5 : 6

[2]
 17. A vessel is full of 90 ltr milk, 18 ltr milk
Concept of Equal is taken out and replaced by water and
again this process is repeated 2 times, the
Replacement amount of milk left after the 3rd
14. A vessel full of pure acid contains 10 litres replacement is?
of it, of which 2 litres are withdrawn. The ,d crZu esa 90 yhVj nw/ gSA blesa ls 18 yhVj
vessel is then filled with water. Next 2 nw/ fudkydj mruh gh ek=kk esa ikuh feyk fn;k
litres of the mixture are withdrawn, and
x;kA bl izfØ;k dks nks ckj vkSj nksgjk;k x;kA rhljs
again the vessel is filled up with water.
izfrLFkkiu ds ckn nw/ dgh cph gqbZ ek=kk crkb;sA
The ratio of the acid left in the vessel with
(a) 11.52 ltr (b) 46.08 ltr
that of the original quantity is :
(c) 23.04 ltr (d) 69.12 ltr
'kq¼ vEy ls Hkjs ,d crZu esa bldk 10 yhVj gS]18. From a tank of petrol, which contains 200
ftlesa ls 2 yhVj fudky fy;k tkrk gSA fiQj crZu ltr of petrol, the seller replaces each time
esa ikuh Hkj fn;k tkrk gSA vxys 2 yhVj feJ.k with kerosene when he sells 40 ltr of petrol
(or its mixture). Every time he sells out
dks fudky fy;k tkrk gS] vkSj fiQj ls crZu esa
only 40ltr of petrol (pure or impure).After

r
ikuh Hkj fn;k tkrk gSA crZu esa cps vEy dk ewy replacing petrol with kerosene 4th time, a
ek=kk ls vuqikr gS %

si
total amount of kerosene in the mixture is?
(a) 1 : 5 (b) 4 : 5 isVªksy ds ,d VSad esa 200 yhVj isVªksy Hkjk gqvk

15.
(c) 4 : 25
an by (d) 16 : 25
A vessel contains 20 litres of acid. 5 litres
gSA O;kikjh izR;sd ckj 40 yhVj isVªksy csprk gS
vkSj VSad esa 40 yhVj dsjksflu Hkj nsrk gSA ;fn og

n
of acid is taken out of the vessel and
;gh izfØ;k 4 ckj nksgjkrk gS rks pkSFks izfrLFkkiu
replaced by the same quantity of water.
ds ckn feJ.k esa dsjksflu dh ek=kk Kkr dhft,A
ja
Next 5 litres of the mixture are withdrawn,
R s
and again the vessel is filled with the same (a) 81.92L (b) 96L
(c) 118.08L (d) None
a th

quantity of water. The ratio of acid left

19. A vessel full of 1600ltr milk. A person draw
in the vessel with the quantity of acid
out 25% of milk form the vessel and
initially in the vessel is :
replaced with water. He has repeated the
,d crZu esa 20 yhVj vEy gSA crZu ls 5 yhVj
ty a

same process 2 times more. Find the final

vEy fudky fy;k tkrk gS vkSj mlds LFkku ij amount of milk in the vessel?
mruh gh ek=kk esa ikuh Mky fn;k tkrk gSA vxys 5,d crZu esa 1600 yhVj nw/ Hkjk gqvk gSA ,d O;fDr
di M

yhVj feJ.k dks fudky fy;k tkrk gS] vkSj fiQj crZu esa ls 25» nw/ fudkydj mlesa mruk gh ikuh
Hkj nsrk gSA ;fn og ;gh izfØ;k nks ckj vkSj nksgjkrk
ls crZu esa mruh gh ek=kk esa ikuh Hkj fn;k tkrk gSA
crZu esa cps vEy dk ewy ek=kk ls vuqikr gS % gS rks vafre feJ.k esa nw/ dh ek=kk Kkr dhft,A
(a) 4 : 5 (b) 4 : 25 (a) 675 L (b) 750 L
(c) 16 : 25 (d) 9 : 16 (c) 800 L (d) 1200 L
20. A vessel contains some milk. 6 litre of the
16. The ratio of milk to water in a 100 litres
milk was taken out of the vessel and
mixture is 2 : 3. 10 litres of this mixture
replaced with 6 litre of water and again
is withdrawn and replaced with milk. This
6 litre of mixture was taken out and was
process is repeated 2 more times. What
replaced with water. Now the ratio of milk
is the percentage of milk in final mixture?
A

to water become 100 : 69. Find the initial

100 yhVj ds ,d feJ.k esa nw/ vkSj ikuh dk quantity of milk in the vessel.
vuqikr 2 % 3 gSA bl feJ.k eas ls 10 yhVj fudky ,d cjru esa dqN nw/ gS ml cjru ls 6 yhVj nw/
fy;k tkrk gSA rFkk mruk gh nwèk Mky fn;k tkrk fudkydj 6 yhVj ikuh feyk fn;k tkrk gS vkSj
gSA ;g izfØ;k 2 ckj vkSj nksgjkbZ tkrh gSA vafrenksckjk 6 yhVj feJ.k fudkydj mlesa ikuh feyk
feJ.k esa nw/ dk izfr'kr D;k gS\ fn;k tkrk gS ftlesa nw/ vkSj ikuh dk vuqikr %
100
69
SSC CGL TIER - II 08/08/2022 gks tkrk gS] rks cjru esa nw/ dh vkjafHkd ek=kk crkb,\
(a) 56.26 percent (b) 58.21 percent (a) 28 litre (b) 26 litre
(c) 51.24 percent (d) 54.27 percent (c) 36 litre (d) 46 litre

[3]
 24. A jar contained a mixture of two liquids
Type-02 (Replacement ) A and B in the ratio 4 : 1. When 10 litres
21. The ratio of milk and water in a mixture of the mixture was taken out and 10 litres
is 7 : 5. How much part of the mixture of liquid B was poured into the jar, this
should be replaced by water so hat ratio ratio became 2 : 3. The quantity of liquid
of milk and water is 2 : 3? A contained in the jar initially was
,d feJ.k esa nw/ vkSj ikuh dk vuqikr 7 % 5 gSA ,d tkj esa nks rjy inkFkZA vkSj B dk feJ.k
feJ.k dk feruk Hkkx ikuh ls izfrLFkkfir fd;k 4%1 ds vuqikr esa gSA tc 10 yhVj feJ.k fudkyk
tk, rkfd feJ.k esa nw/ vkSj ikuh dk vuqikr 2 %
tkrk gS vkSj 10 yhVj rjyB tkj esa Mkyk tkrk
3 jg tk,\
gS] rks ;g vuqikr % 2 3 gks tkrk gSA rjy dh ek=kk
11 11 'kq: esa tkj esa fufgr Fkk %
(a) (b)
35 25 (a) 4 litres (b) 8 litres

13 13 (c) 16 litres (d) 40 litres

r
(c) (d)
24 36 25. A container contains a mixture of two liquids,

si
22. A beaker is filled with a liquid, 3 parts of A and B, in the proportion 7 : 5. If 9 liters of
which are water and 7 parts some the mixture is replaced by 9 liters of Liquid B,

an by
medicine. What part of the mixture should
be replaced with water so that that the
then the ratio of the two liquids becomes 7 :
9. How much of liquid A was there in the

n
resultant mixture has water and medicine container initially?
in a ratio1:1? ,d daVsuj esa nks rjy inkFkZ
A vkSjB dk feJ.k
ja
R s
,d chdj esa nzo Hkjk gqvk gS] ftldk 3 Hkkx ikuh gS] tks 7 % 5 ds vuqikr esa gSaA ;fn blds 9 yhVj
vkSj 7 Hkkx vkS"kf/ gSA bl feJ.k dk fdruk Hkkx ikuh feJ.k dks 9 yhVj rjy inkFkZB ls cny fn;k
a th

ls cnyus ij ifj.kkeh feJ.k ls ikuh vkSj vkS"kf/ dk tk,] rks nksuksa rjg inkFkksZa dk vuqikr 7 % 9 gks
vuqikr 1 % 1 gks tk,xk\ tkrk gSA vkjaHk esa bl feJ.k esaArjy
dh ek=kk
ty a

SSC CHSL 02/06/2022 (Shift- 01) fdruh Fkh\

2 1 SSC MTS 05/07/2022 (Shift- 03)
di M

(a) (b)
7 7
(a) 21 liters
2 1 (b) 35 liters
(c) (d)
5 5
(c) 40 liters
23. A vessel contained a solution of acid and
(d) 19 liters
water, in which water was 64%. Four litres
of the solution was taken out of the vessel 26. The ratio of milk and water in a vessel is
and the same quantity of water was added. 13:11. If 48ltr of mixture is taken out and
If the resulting solution contains 30% acid, 81 ltr water is added then ratio of milk
the quantity (in litres) of the water in the and water becomes 7:8. Find quantity of
solution, at the beginning in the vessel, was: milk in initial mixture.
A

,d crZu esa ,flM vkSj ikuh dk ?kksy Fkk] ftlesa ,d crZu esa nw/ vkSj ikuh dk vuqikr 13%11 gSA
ikuh 64» FkkA crZu esa ls pkj yhVj ?kksy fudky
;fn feJ.k esa ls 48 yhVj nzO; fudkydj blesa
fy;k x;k vkSj mruh gh ek=kk esa ikuh feyk fn;k
81 yhVj ikuh feyk;k tkrk gS rks nw/ vkSj ikuh
x;kA ;fn ifj.kkeh ?kksy esa 30» vEy gS] rks crZu esa
dk vuqikr 7%8 gks tkrk gSA izkjafHkd feJ.k esa nw/
'kq#vkr esa ?kksy esa ikuh dh ek=kk (yhVj esa) Fkh%
dh ek=kk Kkr djsaA
SSC CGL TIER - II 03/02/2022
(a) 11.36 (b) 15.36 (a) 301 ltr (b) 325 ltr
(c) 8.64 (d) 12.64 (c) 295 ltr (d) 299 ltr

[4]
27. A vessel contains 64 liter of mixture of 30. An alloy contains a mixture of two metals
milk and water in the ratio 7 : 3 X and Y in the ratio of 2 : 3. The second
respectively. 8L of mixture is replaced by alloy contains a mixture of the same
12 liter milk. What is the ratio of milk and metals, X and Y, in the ratio 7 : 3. In what
water in the resulting mixture? ratio should the first and the second alloys
be mixed so as to make a new alloy
,d crZu esa 64 yhVj feJ.k gS ftlesa nw/ vkSj containing 50% of metal X?
ikuh dk vuqikr 7%3 gSA 8 yhVj feJ.k fudkydj ,d feJ/krq esa nks /krqvksa
X vkSjY dk vuqikr 2 %
blesa 12 yhVj nw/ feyk;k tkrk gSA vc u, feJ.k 3 gSA ,d vU; feJ/krq esa leku /krqvksa
X vkSjY dk
esa nw/ vkSj ikuh dk vuqikr Kkr dhft,\ vuqikr 7 % 3 gSA nksuksa feJ/krqvksa dks fdl vuqikr
(a) 64 : 21 (b) 35 : 22 esa feyk;k tkuk pkfg, ftlls u;s cus feJ.k esa /krq
(c) 64 : 23 (d) 65 : 21 X dk izfr'kr 50» gks\
SSC MTS 12/07/2022 (Shift- 02)
Concept of Mixing Different (a) 3 : 4 (b) 3 : 1

r
Mixture to form a Single (c) 5 : 6 (d) 2 : 1

si
Mixture 31. A and B are two alloys of gold and copper
prepared by mixing metals in ratios 7 : 2
28. an by
Alloys A and B contain copper and zinc
and 7 : 11 respectively. If equal quantities
of the alloys are melted to form a third

n
in the ratio 7 : 8 and 4 : 1, respectively.
alloy C, the ratio of gold and copper in C
In what ratio should A and B be mixed
will be;

ja
to obtain a new alloy C containing copper
R s
and zinc in the ratio 2 : 1 ? vkSjB lksus vkSj rkacs dh nks feJ/krq,¡ gSa tks /
A
krqvksa dks Øe'k% %2 vkSj
7 7%11 ds vuqikr esa
a th

feJ /krq A vkSj B esa rkack vkSj tLrk Øe'k% 7%8

feykdj rS;kj dh tkrh gSaA ;fn feJ/krqvksa dh leku
vkSj 4%1 ds vuqikr esa gSaA 2 % 1 ds vuqikr esa
ek=kk dks fi?kykdj ,d rhljk feJ/krqC cuk;k
rkack vkSj tLrk ;qÙkQ ,d u;k feJ /krqC çkIr
tk,] rks C esa lksus vkSj rkacs dk vuqikr gksxk %
ty a

djus ds fy, A vkSjB dks fdl vuqikr esa feyk;k

(a) 7 : 5 (b) 5 : 9
tkuk pkfg,\
di M

(c) 9 : 5 (d) 5 : 7
SSC Phase IX 2022 32. One cup has juice and water in the ratio
(a) 2 : 3 (b) 5 : 6 5 : 2, while another cup of the same
capacity has them in the ratio 7: 4,
(c) 4 : 5 (d) 3 : 4
respectively. If contents of both the cups
29. Two containers have mixtures of milk and (when full) are poured in a vessel, then
water, respectively, in the ratios 3 : 2 and what will be the final ratio of water to juice
6 : 5. In what ratio should the contents in the vessel?
be mixed so that the ratio of milk to water ,d di esa jl vkSj ikuh dk vuqikr 5 % 2 gS]
in the final mixture is 4 : 3? tcfd mlh /kfjrk ds nwljs di esa mudk vuqikr
A

nks ik=kksa esa nw/ vkSj ikuh ds feJ.k Øe'k% 3 %Øe'k%

2 7% 4 gSA ;fn nksuksa diksa dh lkexzh (tc
vkSj 6 % 5 ds vuqikr eas Hkjs gSaA bu feJ.kksa didksiw.kZr% Hkjh gksa) ,d crZu esa Mky nh tkrh gS]
fdl vuqikr esa feyk;k tkuk pkfg, rkfd vafre rks crZu esa ikuh dk jl ls vafre vuqikr D;k gksxk\
SSC CGL TIER - II 29/01/2022
feJ.k esa nw/ vkSj ikuh dk vuqikr 4 % 3 gks tk,\
(a) 52 : 25
SSC MTS 05/10/2021 (Shift- 01)
(b) 25 : 26
(a) 10 : 11 (b) 6 : 13 (c) 26 : 25
(c) 5 : 8 (d) 9 : 14 (d) 25 : 52

[5]
33. In two types of brass, the ratios of Copper 36. Alloy A contains metals x and y only in
to Zinc are 8:3 and 15:7 respectively. If the ratio 5 : 2, while alloy B contains them
the two types of brass be melted and mixed in the ratio 3 : 4 Alloy C is prepared by
in the ratio 5:2 a new type of brass is mixing alloys A and B in the ratio 4 : 5.
obtained. The ratio of Copper to Zinc in The percentage of x in alloy C is:
this new type of brass is feJ /krq A eas] /krq,ax vkSjy dsoy 5 % 2 ds
nks çdkj ds ihry esa] dkWij ls ftad dk vuqikr vuqikr esa gS] tcfd feJ /krqB esa] mudk vuqikr
Øe'k% 8%3 vkSj 15%7 gSA ;fn nksuksa çdkj ds 3 % 4 gSA feJ /krqA vkSjB dks 4 % 5 ds vuqikr
ihry dks fi?kykdj 5 %2 ds vuqikr esa feyk;k esa feykdj feJ /krq C rS;kj dh tkrh gSA feJèkkrq
tk, rks ,d u, çdkj dk ihry çkIr gksrk gSA bl C esax dk izfr'kr Kkr djsaA
u, çdkj ds ihry esa dkWij ls ftad dk vuqikr gS % SSC CGL TIER - II 29/01/2022
(a) 3:2 (b) 2:3
2 1
(c) 3:4 (d) 5:2 (a) 55 (b) 55
9 9
34. The ratios of copper to zinc in alloys A

r
and B are 3 : 4 and 5 : 9, respectively. A 4 5
(c) 55 (d) 55
and B are taken in the ratio 2 : 3 and 9 9

si
melted to form a new alloy C. What is the 37. Mixture A contains chocolate and milk in
ratio of copper to zinc in C? the ratio 4:3 and mixture B contains
an by
feJ/krq A vkSj B esa rkacs vkSj tLrk ds vuqikr chocolate and milk in the ratio 5 : 2. A
and B are taken in the ratio 5:6 and mixed

n
Øe'k% 3 % 4 vkSj 5 % 9 gSA
A vkSj B dks 2 % 3
to form a new mixture. The percentage of
ds vuqikr esa fy;k tkrk gS vkSj ,d u, feJ/krq chocolate in the new mixture is closest

ja
C dks cukus ds fy, fi?kyk;k tkrk gSA
C esa rkacs
R s
to:
vkSj tLrk dk vuqikr D;k gS\ feJ.k A esa pkWdysV vkSj nw/ 4%3 ds vuqikr esa gS
a th

SSC CGL TIER - II 11/09/2019 vkSj feJ.k B esa pkWdysV vkSj nw/ 5%2 ds vuqikr
(a) 27 : 43 (b) 8 : 13 esa gSA
A vkSj B dks 5 % 6 ds vuqikr esa fy;k
(c) 3 : 5 (d) 9 : 11 tkrk gS vkSj ,d u;k feJ.k cukus ds fy, feyk;k
ty a

35. In vessels X and Y, the ratios of acid and tkrk gSA u, feJ.k esa pkWdysV dk çfr'kr fudVre gS%
water are 3 : 7 and 1 : 3, respectively. The
di M

SSC CGL TIER - II 03/02/2022

contents of X and Y are mixed in the ratio (a) 35% (b) 69%
of 1 : 2 to get a solution in which acid (c) 31% (d) 65%
and water are in the ratio a : b. What is 38. Alloy A contain metals x and y in the ratio
b a 5 : 2 and alloy B contains these metals
the value of ? in the ratio 3 : 4. Alloy C is prepared by
b –a
mixing A and B in the ratio 4 : 5.The
orZuX vkSjY esa vEy vkSj ikuh dk vuqikr Øe'k% percentage of y in alloy C is:
3 % 7 vkSj 1 % 3 gSA X vkSjY dh lkexzh dks 1 % feJ /krq A esa] /krq
x vkSjy dk vuqikr 5 % 2 gS
2 ds vuqikr esa feyk;k tkrk gS rkfd ,d ?kksy vkSj feJ /krqB esa] /krq
x vkSjy dk vuqikr 3 %
izkIr fd;k tk lds ftlesa vEy vkSj ikuh dk vuqikr 4 gSA A vkSjB dks 4 % 5 vuqikr esa feykdj feJ
A

b a /krq C rS;kj dh tkrh gSA feJ /krqC esay dk

a:b gksA
b –a izfr'kr Kkr djsaA
SSC Phase IX 2022 SSC CGL 18/08/2021(Shift 02)

15 11 4 4
(a) (b) (a) 44 % (b) 33 %
7 7 9 9

13 12 4 5
(c) (d) (c) 66 % (d) 55 %
7 7 9 9

[6]
39. The proportion of acid and water in three 42. Three containers whose volumes are in the
samples is 2 : 1, 3 : 2 and 5 : 3. A mixture ratio of 2 : 3 : 4 are full of mixture of spirit
containing equal quantities of all three and water. In the 1st container, the ratio
samples is made. The ratio of water and of spirit and water is 4 : 1, in the 2nd
container the ratio is 11 : 4 and in the
acid in the mixture is:
3rd container ratio is 7 : 3. All the three
rhu uewuksa esa vEy vkSj ikuh dk vuqikr %1] 2 mixtures are mixed in a big container. The
3 %2 vkSj 5%3 gSA rhuksa uewuksa dh leku ek=kk ratio of spirit and water in the resultant
okyk
mixture is:
feJ.k cuk;k tkrk gSA feJ.k esa ikuh vkSj vEy dk
rhu daVsuj ftuds vk;ru 2%3 %4 ds vuqikr esa
vuqikr gS%
gSa] fLçV vkSj ikuh ds feJ.k ls Hkjs gq, gSaA igys
(a) 120 : 133 (b) 227 : 133 daVsuj esa] fLçV vkSj ikuh dk vuqikr %1 gS]
4
(c) 227 : 120 (d) 133 : 227 nwljs daVsuj esa vuqikr
%411gS vkSj rhljs daVsuj
40. Three utensils contain equal quantity of esa vuqikr %
73 gSA rhuksa feJ.kksa dks ,d cM+s daVsuj
mixtures of milk and water in the ratio 6 esa feyk;k tkrk gSA ifj.kkeh feJ.k esa fLçV vkSj

r
: 1, 5 : 2 and 3 : 1 respectively. If all the ikuh dk vuqikr gS%

si
solutions are mixed together, the ratio of (a) 4 : 9 (b) 11 : 4
milk and water in the final mixture is :

an by
rhu crZuksa esa nw/ vkSj ikuh ds feJ.k dh leku
(c) 5 : 10

Miscellaneous
(d) 9 : 5

n
ek=kk Øe'k%%16 5 %2 vkSj 3%1 ds vuqikr
esa gSA ;fn lHkh foy;uksa dks ,d lkFk feyk
ja 43. 60 kg of an alloy A is mixed with 100 kg
R s
fn;k tkrk gS] rks vafre feJ.k esa nw/ vkSj ikuh of alloy B. If alloy A has lead and tin in
dk vuqikr gS %
a th

the ratio 3 : 2 and alloy B has tin and

copper in the ratio 1 : 4, the amount of
(a) 65 : 28 (b) 65 : 19
tin in the new alloy is
(c) 19 : 65 (d) 19 : 28 feJ /krq A ds 60 fdxzk dks 100 fdxzk feJ /krq
ty a

41. Three containers have their volumes in the B ds lkFk feyk;k tkrk gSA ;fn feJ /krqA esa
lhlk vkSj fVu dk vuqikr 3 % 2 gS vkSj feJ /krq
di M

ratio 3 : 4 : 5. They are full of mixtures

of milk and water. The mixtures contain B esa 1%4 ds vuqikr esa fVu vkSj rkack gS] rks u,
milk and water in the ratio of (4 : 1), (3:1)
feJ /krq esa fVu dh ek=kk gS %
and (5 : 2) respectively. The contents of
(a) 53 kg (b) 44 kg
all these three containers are poured into
a fourth container. The ratio of milk and (c) 80 kg (d) 24 kg
water in the fourth container is : 44. In two alloys A and B, the ratio of zinc
to tin is 5 : 2 and 3 : 4 respectively. Seven
rhu daVsujksa dk vk;ru%43 %5 ds vuqikr esa gSA kg of the alloy A and 21 kg of the alloy B
os nw/ vkSj ikuh ds feJ.k ls Hkjs gq, gSaA feJ.k esaare mixed together to form a new alloy.
nw/ vkSj ikuh dk vuqikr Øe'k%% (4
1)] (3 %1) What will be the ratio of zinc and tin in
A

the new alloy?

vkSj (5%2) gSA bu rhuksa daVsujksa dh lkexzh dks
nks feJ/krqA vkSj B esa ftad ls fVu dk vuqikr
pkSFks daVsuj esa Mkyk tkrk gSA pkSFks daVsuj esa nw/
Øe'k% 5%2 vkSj 3%4 gSA feJ/krq
A ds lkr fdyksxzke
vkSj ikuh dk vuqikr gS %
vkSj feJ/krqB ds 21 fdyksxzke dks ,d lkFk feykdj
(a) 4 : 1 ,d ubZ feJ /krq cukbZ tkrh gSA u, feJ/krq esa
(b) 151 : 48 ftad vkSj fVu dk vuqikr D;k gksxk\
(c) 157 : 53 (a) 2 : 1 (b) 1 : 2
(d) 5 : 2 (c) 2 : 3 (d) 1 : 1

[7]
45. There are three bottles of mixture of syrup 48.
Two vessels A and B, each with the capacity
and water of ratios 2 : 3, 3 : 4 and 7 : 5. of 8 litres, are full of solutions of acid and
10 litres of the first and 21 litres of the water. The ratio of acid and water in Vessel
A is 3 : 1 and that in case of Vessel Bis 5
second bottles are taken. How much
: 3. Two litres of solution are taken out from
quantity from third bottle is to be taken B and added to A. After mixing thoroughly,
so that final mixture from three bottles will 2 litres of solution are taken out from A
be of ratios 1 : 1. and added to B. What is the ratio of acid
2 %3 ] 3 %4 vkSj 7%5 ds vuqikr esa flji vkSj and water in the final solution in B?
ikuh ds feJ.k dh rhu cksrysa gSaA igyh cksry ds izR;sd 8 yhVj dh {kerk okys nks crZu A vkSjB
gSa] tks vEy vkSj ty ds foy;u ls Hkjs gq, AgSaA
10 yhVj vkSj nwljh cksry ds 21 yhVj fy, tkrs
esa vEy vkSj ty dk vuqikr 3 % 1 gS vkSj B esa
gSaA rhljh cksry ls fdruh ek=kk ysuh gS fd rhu ;g 5 % 3 gSA B ls nks yhVj foy;u fudkyk tkrk
cksryksa dk vafre feJ.k 1%1 ds vuqikr esa gksA gS vkSj A esa feyk;k tkrk gSA bls vPNh rjg feykus
SSC CGL TIER - II 12/01/2017 ds ckn] A esa ls 2 yhVj foy;u fudkyk tkrk
(a) 25 litres (b) 20 litres vkSjB esa feyk;k tkrk gSA B esa vafre foy;u esa
vEy vkSj ty dk vuqikr D;k gS\

r
(c) 35 litres (d) 30 litres
46. In a mixture of three varieties of tea, the ICAR Assistant 29/07/2022 (Shift- 01)

si
ratio of their weights is 4 : 5 : 8. If 5 kg (a) 11 : 8 (b) 13 : 7
tea of the first variety, 10 kg tea of the (c) 7 : 3 (d) 9 : 4
an by
second variety and some quantity of tea
of the third variety are added to the
49. The
A and
ratios
B
of
are 3
alcohol
: 5 and
to water in solutions
9 : 7, respectively.

n
A and B are mixed in the ratio 5 : 8. In
mixture, the ratio of the weights of three
520 ml of the resulting solution, how much
varieties of tea becomes as 5 : 7 : 9. In

ja water (in ml) should be mixed so as to

R s
the final mixture, the quantity (in kg) of obtaina solution in which the ratio of
the third variety of tea was alcohol to water is 3 : 4?
a th

pk; dh rhu fdLeksa ds feJ.k esa] muds Hkkj dk foy;u A vkSjB esa ,sYdksgkWy vkSj ty dk vuqikr
vuqikr 4%5 %8 gSA ;fn igyh fdLe dh 5 fdxzk Øe'k%3 : 5vkSj9 : 7 gSA A vkSjB dks 5 : 8 ds
pk;] nwljh fdLe dh 10 fdxzk pk; vkSj rhljh vuqikr esa feyk;k tkrk gSA ifj.kkeh foy;u520 ds
ty a

ml esa fdruk ty (ml esa ) feyk;k tkuk pkfg,

fdLe dh pk; dh dqN ek=kk feyk nh tkrh gSA
rkfd ,d ,slk foy;u izkIr gks lds ftlesa ,sYdksgkWy
feJ.k] pk; dh rhu fdLeksa ds Hkkj dk vuqikr
di M

vkSj ty dk vuqikr 3 : 4 gks\

5 %7 %9 gks tkrk gSA vafre feJ.k esa] rhljh fdLe ICAR Assistant 29/07/2022 (Shift- 02)
dh pk; dh ek=kk (fdyks esa) Fkh (a) 85 (b) 75
(a) 42 (b) 45 (c) 80 (d) 90
(c) 48 (d) 40 50. The ratio of acid and water in solution A is
47. A solution of 45% alcohol is mixed with 5 : 4 and 7 : 11 in solution B. 10 litres of
A is mixed with 8 litres of B. In 324 ml
a solution of 60% alcohol in the ratio of
of the resulting solution, how much water
2 : 3. In what ratio should the resultant (in ml) should be added to get a solution
solution be mixed with a 72% alcohol
1
solution to get a 66% alcohol solution? containing 33 % acid?
3
45» ,sYdksgkWy okys ,d foy;u vkSj 60» ,sYdksgkWy,d foy;u A esa vEy vkSj ikuh dk vuqikr 5 %
A

okys ,d vU; foy;u dks 2 % 3 ds vuqikr esa 4 gS vkSj foy;uB esa ;g vuqikr 7 % 11 gSA A
feyk;k tkrk gSA bl izdkj cus foy;u dks] 72» ds nl yhVj dks B ds vkB yhVj esa feyk;k tkrk
,sYdksgkWy okys foy;u esa fdl vuqikr esa feyk;k 1
gSA ifj.kkeh foy;u ds
324 mL esa]33 % vEy
tkuk pkfg, ftlls izkIr foy;u esa 66» ,sYdksgkWy 3
;qDr ?kksy izkIr djus ds fy, fdruk ikuh
(mL esa
)
gks\
feyk;k tkuk pkfg,\
SSC MTS 07/07/2022 (Shift- 01) ICAR Assistant 29/07/2022 (Shift- 03)
(a) 4 : 7 (b) 1 : 3 (a) 400 (b) 250
(c) 1 : 2 (d) 2 : 3 (c) 300 (d) 350

[8]
 Answer Key
1. (b) 2.(a) 3. (b) 4. (a) 5. (b) 6. (b) 7. (a) 8. (d) 9. (c) 10. (a)

11.(a) 12.(c) 13.(d) 14.(d) 15.(d) 16.(a) 17.(b) 18.(c) 19.(a) 20.(b)

21.(a) 22.(a) 23.(b) 24.(c) 25.(b) 26.(d) 27.(a) 28.(c) 29.(a) 30.(b)

31.(a) 32.(d) 33.(d) 34.(a) 35.(a) 36.(d) 37.(d) 38.(d) 39.(d) 40.(b)

41. (c) 42.(b) 43. (b) 44. (d) 45. (d) 46. (b) 47. (a) 48. (b) 49. (b) 50. (c)

r
si
an by
n
ja
R s
a th
ty a
di M
A

[9]
Join Telegram- Maths by Aditya Ranjan Mixture

Mixture/feJ.k
( Practice Sheet With Solution)
1. 8 liters are drawn from a cask full of wine 150 yhVj 'kjkc vkSj ikuh ds feJ.k esa 20» ikuh gSA
and is then filled with water. This operation
fdruk ikuh vkSj feyk;k tk, fd ikuh u, feJ.k dk
is performed three more times. The ratio of
the quantity of wine now left in cask to that
25» gks tk,\
of the water is 16 : 65. How much wine the (a) 10 liters (b) 20 liters
cask hold originally? (c) 30 liters (d) 40 liters
6. A vessel contains 20 liters of a mixture of milk
'kjkc ls Hkjs ,d ihis ls 8 yhVj fudkyk tkrk gS vkSj
and water in the ratio 3:2. 10 liters of the
fiQj ikuh ls Hkj fn;k tkrk gSA ;g vkWijs'ku rhu ckj vkSj mixture are removed and replaced with an
fd;k tkrk gSA ihis esa vc 'kjkc dh ek=kk dk ikuh ls

r
equal quantity of pure milk. If the process
vuqikr 16 % 65 gSA ewy :i ls ihis esa fdruh 'kjkc gS\ is repeated once more, find the ratio of milk

si
(a) 18 liters (b) 24 liters and water in the final mixture obtained ?
(c) 32 liters (d) 42 liters ,d crZu esa 20 yhVj nw/ vkSj ikuh dk feJ.k 3%2 ds
2.
an by
Tea worth of Rs 135/kg & Rs 126/kg are
mixed with a third variety in the ratio 1: 1 :
vuqikr esa gSA 10 yhVj feJ.k dks gVk fn;k tkrk gS
vkSj mlds LFkku ij mruh gh ek=kk esa 'kq¼ nw/ fe

n
2. If the mixture is worth Rs 153 per kg, the fn;k tkrk gSA ;fn çfØ;k dks ,d ckj vkSj nksgjk;k
price of the third variety per kg will be____?
ja tkrk gS] rks çkIr vafre feJ.k esa nw/ vkSj ikuh dk
135 #i;s@fdxzk vkSj 126 #i;s@fdxzk ewY; okyh pk; vuqikr Kkr dhft;s\
R s
dks rhljh fdLe ds lkFk 1%1%2 ds vuqikr esa feyk;k (a) 5 : 3 (b) 1 : 4
a th

tkrk gSA ;fn feJ.k dk ewY; 153 #i;s çfr fdyksxzke (c) 9 : 1 (d) 6 : 1
gS] rks rhljh fdLe dh çfr fdyksxzke dher ----- gksxh\
7. The ratio of petrol and kerosene in the
(a) Rs. 169.50 (b) Rs.1700 container is 3:2 when 10 liters of the mixture
ty a

(c) Rs. 175.50 (d) Rs. 180 is taken out and is replaced by the kerosene,
3. A can contains a mixture of two liquids a and the ratio become 2:3. Then total quantity of
the mixture in the container is:
di M

b in the ratio 7 : 5. When 9 liters of mixture

are drawn off and the can is filled with b, the ,d ik=k esa isVªksy vkSj feêðh ds rsy dk vuqikr 3%2 g
ratio of a and b becomes 7 : 9. How many liters tc 10 yhVj feJ.k dks fudkydj feêðh ds rsy ls
of liquid a was contained by the can initially? cny fn;k tkrk gS] rks vuqikr 2%3 gks tkrk gSA rks
A esa nks rjy inkFkZ
a vkSjb dk feJ.k 7%5 ds vuqikr daVsuj esa feJ.k dh dqy ek=kk gS%
esa gSA tc 9 yhVj feJ.k fudkyk tkrk gS vkSj dSu dks (a) 25 (b) 30
b ls Hkj fn;k tkrk gS] rks
a vkSj b dk vuqikr 7%9 (c) 45
gks tkrk gSA izkjEHk
A esa
eas
fdrus yhVj rjya FkkA (d) Cannot be determined
8. The diluted wine contains only 8 liters of wine
(a) 10 (b) 20
and the rest is water. A new mixture whose
(c) 21 (d) 25
concentration is 30%, is to be formed by
4. In what proportion water must be added to replacing wine. How many liters of mixture
A

spirit to gain 20% by selling it at the cost shall be replaced with pure wine if there was
price ? initially 32 liters of water in the mixture ?
ykxr ewY; ij cspus ij 20» ykHk çkIr djus ds fy, ruqÑr 'kjkc esa dsoy 8 yhVj 'kjkc gksrh gS vkSj 'ks"k
fLifjV esa ikuh fdl vuqikr esa feyk;k tkuk pkfg,\ ikuh gksrk gSA okbu ds LFkku ij ,d u;k feJ.k ftldh
(a) 1 : 4 (b) 1 : 5 lkUærk 30» gS] cukuk gSA ;fn feJ.k esa çkjaHk esa
(c) 2 : 3 (d) 3 : 5
yhVj ikuh Fkk] rks fdrus yhVj feJ.k dks 'kq¼ okbu
5. A mixture of 150 liters of wine and water
contains 20% water. How much more water
ls cnyk tk,xk\
should be added so that water becomes 25% (a) 4 (b) 5
of the new mixture? (c) 8 (d) None of these

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9. One type of liquid contains 24% of milk, and nks vyx&vyx daVsujksa esa ikuh vkSj vYdksgy dk vuqi
the other contains 38% of milk. A can is filled 2%3 vkSj 4%5 gSA gesa fdl vuqikr esa nks daVsuj
with 8 parts of the first liquid and 4 parts of
the second liquid. Find the percentage of milk feJ.k dks feykuk gS rkfd u;k feJ.k çkIr gks ftlesa
in the new mixture? vYdksgy vkSj ikuh dk vuqikr 7%5 gks\
,d çdkj ds rjy esa 24» nw/ gksrk gS] vkSj nwljs esa 38» (a) 7:3 (b) 5:3
(c) 8:5 (d) 2:7
nw/ gksrk gSA ,d dSu esa igys æo ds 8 Hkkx vkSj nwljs æo
14. A vessel is filled with liquid, 3 parts of which
ds 4 Hkkx Hkjs x, gSaA u, feJ.k esa nw/ dk çfr'kr Kkr are water and 5 parts of syrup. How much of
dhft,\ the mixture must be drawn off and replaced
CRPF HCM 01/03/2023 (Shift - 02) with water so that the mixture may be half
water and half syrup?
5 2
(a) 29 % (b) 28 % ,d ik=k esa æo Hkjk gS] ftlds 3 Hkkx ikuh vkSj 5
7 3
Hkkx pk'kuh gSaA feJ.k dk fdruk Hkkx fudkyk tkuk
(c) 27
5
%
3
(d) 37 % pkfg, vkSj ikuh ls çfrLFkkfir fd;k tkuk pkfg, rkfd
8 8 feJ.k vk/k ikuh vkSj vk/k flji cu lds\

r
10. From a container, 6 liters milk was drawn out
and was replaced by water. Again 6 liters of 1 1

si
(a) (b)
mixture was drawn out and was replaced by 3 4
the water. Thus the quantity of milk and water
an by
in the container after these two operations
is 9:16. The quantity of mixture is:
(c)
1
5
(d)
1
7

n
,d ik=k ls 6 yhVj nw/ fudkyk x;k vkSj mls ikuh ls15. In a pot, there is a mixture of milk and water
cny fn;k x;kA fiQj ls 6 yhVj feJ.k fudkyk x;k in the ratio 4 : 5. If it is filled with an
ja
vkSj mls ikuh ls cny fn;k x;kA bl çdkj bu nks additional 8 liters of milk, the pot would be
R s
full and ratio of milk and water would become
lafØ;kvksa ds ckn ik=k esa nw/ vkSj ikuh dh ek=kk 9%16
a th

6 : 5. Find the capacity of the pot ?

gSA feJ.k dh ek=kk gS%
(a) 15 (b) 16 ,d crZu esa nw/ vkSj ikuh dk feJ.k 4 % 5 ds vuqikr
(c) 25 (d) 31 esa gSA ;fn bls vfrfjÙkQ 8 yhVj nw/ ls Hkj fn;k tk,]
11. A milk man sells the milk at the cost price rks crZu Hkj tk,xk vkSj nw/ vkSj ikuh dk vuqikr 6 %
ty a

but he mixes the water in it and thus he gains

5 gks tk,xkA crZu dh {kerk Kkr dhft;s\
9.09%. The quantity of water in the mixture
di M

of 1 liter is : (a) 11 lit (b) 35 lit

,d nw/okyk nw/ dks ykxr ewY; ij csprk gS ysfdu og (c) 22 lit (d) 44 lit
mlesa ikuh feyk nsrk gS vkSj bl çdkj mls 9-09» dk 16. Equal quantities of three mixtures of milk and
water are mixed in the ratio 1:2, 2:3 and 3:4.
ykHk gksrk gSA 1 yhVj ds feJ.k esa ikuh dh ek=kk gS%
The ratio of water and milk in the mixture is?
(a) 83.33 ml (b) 90.90 ml
(c) 99.09 ml (d) Can't be determined nw/ vkSj ikuh ds rhu feJ.kksa dh leku ek=kk dks 1%2
12. In a mixture of milk and water the proportion 2%3 vkSj 3%4 ds vuqikr esa feyk;k tkrk gSA feJ.k es
of water by weight was 75%. If in 60 gm of ikuh vkSj nw/ dk vuqikr gS\
mixture 15 gm water was added, what would
(a) 193 : 122 (b) 97 : 102
be the percentage of water ? (Weight in gm)
(c) 115 : 201 (d) 147 : 185
nw/ vkSj ikuh ds feJ.k esa otu ds fglkc ls ikuh dk
17. A container contains 40 liters of milk. From
A

vuqikr 75» FkkA ;fn 60 xzke feJ.k esa 15 xzke ikuh

this container 4 liters of milk was taken out
feyk fn;k tk,] rks ikuh dk çfr'kr D;k gksxk\ (otu and replaced by water. This process was
xzke esa) repeated further two times. How much milk
(a) 80% (b) 70% is now contained by the container.
(c) 75% (d) 62%
,d ik=k esa 40 yhVj nw/ gSA bl daVsuj ls 4 yhVj nw/
13. The ratio of water and alcohol in two different
containers is 2:3 and 4:5. In what ratio we fudkyk x;k vkSj ikuh ls cny fn;k x;kA ;g çfØ;k
are required to mix the mixtures of two vkxs nks ckj nksgjkbZ xbZA daVsuj esa vc fdruk nw/
containers in order to get the new mixture (a) 26.34 liters (b) 27.36 liters
in which the ratio of alcohol and water be 7:5? (c) 28 liters (d) 29.16 liters

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18. From a tank of petrol , which contains 200 liters 22. From a container of wine, a thief has stolen
of petrol, the seller replaces each time with 15 liters of wine and replaced it with same
kerosene when he sells 40 liters of petrol(or quantity of water. He again repeated the same
mixture). Every time he sells out only 40 liters process. Thus, in three attempts the ratio of
of petrol (pure or impure). After replacing the wine and water became 343 : 169. The initial
petrol with kerosene 4th time, the total amount of wine in the container was:
Quantity of kerosene in the mixture is 'kjkc ds ,d daVsuj ls] ,d pksj us 15 yhVj 'kjkc
isVªksy ds ,d VSad ls] ftlesa 200 yhVj isVªksy gS] tc pqjk yh vkSj bls ikuh dh leku ek=kk ls cny fn;kA
foØsrk 40 yhVj isVªksy (;k feJ.k) csprk gS rks gj mlus fiQj ogh çfØ;k nksgjkbZA bl çdkj] rhu ç;klksa es
ckj feêðh ds rsy ls cny nsrk gSA gj ckj og dsoy 'kjkc vkSj ikuh dk vuqikr 343 % 169 gks x;kA daVsuj
40 yhVj isVªksy ('kq¼ ;k v'kq¼) csprk gSA pkSFkh ckj esa 'kjkc dh çkjafHkd ek=kk Fkh%
isVªksy dks feêðh ds rsy ls cnyus ds ckn] feJ.k esa (a) 75 liters (b) 100 liters
feêðh ds rsy dh dqy ek=kk fdruh gS\ (c) 150 liters (d) 120 liters
(a) 81.92L (b) 96L 23. The concentration of glucose in three different
(c) 118.08L (d) None of these 1 3
mixtures (glucose and alcohol) is , and

r
1 2 5
19. 4 kg of a metal contains copper and rest
5

si
4
respectively. If 2 liters, 3 liters and 1 liters
1 5
an by
in Zinc. Another 5 kg of metal contains

copper and rest in Zinc. The ratio of Copper

6 are taken from these three different vessels
and mixed. What is the ratio of glucose and

n
and Zinc into the mixture of these two metals: alcohol in the new mixture?
rhu vyx&vyx feJ.kksa (Xywdkst vkSj vYdksgy) esa
1
ja
,d 4 fdxzk /krq esa rk¡ck rFkk 'ks"k ftad gSA vU; 5
R s
5 1 3 4
Xywdkst dh lkaærk Øe'k%
, vkSj gSA ;fn bu
2 5 5
a th

1
fdxzk /krq esa
rkack vkSj 'ks"k ftad gSA bu nks /krqvksa
rhu vyx&vyx crZuksa ls 2 yhVj] 3 yhVj vkSj 1
6
yhVj fy;k tkrk gS vkSj feyk;k tkrk gSA u, feJ.k esa
ds feJ.k esa dkWij vkSj ftad dk vuqikr%
Xywdkst vkSj vYdksgy dk vuqikr D;k gS\
ty a

(a) 49 : 221 (b) 39 : 231

(a) 3 : 2 (b) 4 : 3
(c) 94 : 181 (d) None of these
(c) 2 : 3 (d) 3 : 4
20. The amount of water (in ml) that should be added
di M

to reduce 9 ml lotion, containing 50% alcohol, 24. Three boxes of capacity 24 kg, 36 kg and 84
to a lotion containing 30% alcohol is ? kg are completely filled with three varieties
of wheat A, B and C respectively. All the three
30» vYdksgy okys yks'ku esa 50» vYdksgy okys 9 boxes were emptied and the three types of
feyh yks'ku dks de djus ds fy, ikuh dh ek=kk (feyhyhVj wheat were thoroughly mixed and the mixture
esa) feykbZ tkuh pkfg,\ was put back in the three boxes. How many
(a) 6 ml (b) 11 ml kg of type A wheat would be there in the third
(c) 15 ml (d) 9 ml box (in kg)?
21. There are two mixtures of honey and water 24 fdxzk] 36 fdxzk vkSj 84 fdxzk dh {kerk okys rhu
in which the ratio of honey and water are as cDlksa dks Øe'k% rhu çdkj ds xsgw¡
A] B vkSj C ls
1:3 and 3:1 respectively. Two liters are drawn Hkjk x;k gSA lHkh rhu cDlksa dks •kyh dj fn;k x;k
from first mixture and 3 liters from second vkSj rhuksa çdkj ds xsgwa dks vPNh rjg ls feyk;k x;k
A

mixture, are mixed to form another mixture.

What is the ratio of honey and water in it ? vkSj feJ.k dks okil rhuksa cDlksa esa Mky fn;k x;kA
'kgn vkSj ikuh ds nks feJ.k gSa ftuesa 'kgn vkSj ikuh rhljs fMCcs esa (fdxzk esa) A
çdkj
dk fdruk fdyks
dk vuqikr Øe'k% 1%3 vkSj 3%1 gSA igys feJ.k ls nksxsgw¡ gksxk\
(a) 10 (b) 12
yhVj fudkyk tkrk gS vkSj nwljs feJ.k ls 3 yhVj
(c) 14 (d) 16
fudkyk tkrk gS] ,d vkSj feJ.k cukus ds fy, feyk;k
25. In a colored picture of blue and yellow color,
tkrk gSA blesa 'kgn vkSj ikuh dk vuqikr D;k gS\ is used in the ratio of 4:3 respectively. If in
(a) 111:108 (b) 11:9 upper half, Blue : yellow is 2:3, then in the
(c) 103:72 (d) None lower half blue : yellow is

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uhys vkSj ihys jax ds ,d jaxhu fp=k esa uhys vkSj ihys240 yhVj jl vkSj ikuh ds feJ.k esa 15» ikuh gSA
jax dk ç;ksx Øe'k% 4%3 ds vuqikr esa fd;k x;k gSA blesa vkSj fdruk ikuh (yhVj esa) feyk;k tk, fd u,
;fn Åijh vk/s Hkkx esa uhyk % ihyk 2%3 gS] rks fupysfeJ.k esa ikuh dh rkdr 25» gks tk,\
vk/s Hkkx esa uhyk % ihyk gS (a) 28 (b) 32
(a) 1 : 1 (b) 2 : 1 (c) 26 (d) 34
(c) 26 : 9 (d) 9 : 26 30. A dishonest milkman professes to sell his milk
26. There are three bottles of mixture of syrup at cost price but he mixes it with water and
and water of ratios 2:3, 3:4 and 7:5. 10 liters there by gains 25%. The percentage of water
of first and 21 Liters of second bottles are in the mixture is:
taken. How much quantity from third bottle ,d csbZeku nw/okyk vius nw/ dks ykxr ewY; ij cspus
is to be taken so that final mixture from three
bottles will be of ratios 1:1. dk nkok djrk gS ysfdu og bls ikuh esa feykdj 25»
2%3] 3%4 vkSj 7%5 ds vuqikr esa flji vkSj ikuh ds dk ykHk çkIr djrk gSA feJ.k esa ikuh dk çfr'kr gS%
feJ.k dh rhu cksrysa gSaA 10 yhVj igyh vkSj 21 yhVj (a) 4% (b) 25/4%
nwljh cksry yh tkrh gSA rhljh cksry ls fdruh ek=kk (c) 20% (d) 25%

r
31. A man buys juice at Rs 10/liter and dilutes
fudkyh tk, fd rhu cksryksa ls vafre feJ.k dk vuqikr
it with water. He sells the mixtures at the
1%1 gksA

si
cost price and thus gains 11.11%. Find the
(a) 25 liters (b) 20 liters quantity of water mixed by him in every liter

27.
(c) 35 liters an by (d) 30 liters
In a mixture, unbroken and broken rice grains
of juice.
,d vkneh 10 #i;s çfr yhVj dh nj ls twl •jhnrk

n
are in the ratio 3 : 2. How much fraction of
the mixture must be drawn off and substituted
gS vkSj mlesa ikuh feyk nsrk gSA og feJ.k dks Ø;
ja
with broken grains, so that the ratio of ewY; ij csprk gS vkSj bl çdkj mls 11-11» dk ykHk
R s
unbroken and broken grains becomes 1 : 1? gksrk gSA çR;sd yhVj jl esa mlds }kjk fefJr ikuh dh
,d feJ.k esa fcuk VwVs vkSj VwVs gq, pkoy ds nkus 3 ek=kk
% Kkr dhft,A
a th

2 ds vuqikr esa gSaA feJ.k dk fdruk va'k fudkydj (a) 0.1 L (b) 0.909 L
VwVs gq, nkuksa ls çfrLFkkfir fd;k tkuk pkfg,] rkfd (c) 0.125 L (d) 0.111 L
fcuk VwVs vkSj VwVs gq, nkuksa dk vuqikr 1 %32.1 gksIntk,\
a bucket, paint and oil are in the ratio 7:
ty a

5. 24 liters of mixture is drawn off and 24

1 1 liters of oil is added. If the ratio of paint and
di M

(a) (b)
3 6 oil becomes 1: 1, then how many liters of paint
was contained in the bucket initially?
1 2
(c)
4
(d)
5 ,d ckYVh esa] isaV vkSj rsy 7%5 ds vuqikr esa gSaA
28. Wheat costing Rs 30/kg, Rs 35/kg and a third yhVj feJ.k fudkyk tkrk gS vkSj 24 yhVj rsy Mkyk
variety of wheat are mixed in the ratio of 3 tkrk gSA ;fn isaV vkSj rsy dk vuqikr 1%1 gks tkrk gS
: 4 : 2. If the mixture is costs Rs 34/kg, then rks 'kq: esa ckYVh esa fdrus yhVj isaV Fkk\
what will be the cost (in Rs/kg) of the third (a) 49 (b) 63
variety of wheat?
(c) 84 (d) 98
xsgw¡ dh dher 30 #i;s@fdxzk] 35 #i;s@fdxzk vkSj ,d
33. A vessel is full of a mixture of methanol and
rhljh fdLe ds xsgw¡ dks 3%4%2 ds vuqikr esa feyk;k ethanol in which there is 20% ethanol. 10
tkrk gSA ;fn feJ.k dh dher 34 #i;s@fdyks gS] rks
A

liters of mixture are drawn off and filled with

ykxr (#i;s esa) D;k gksxh\ @ fdxzk) xsgw¡ dh rhljh methanol. If the ethanol is now 15%, what
fdLe gS\ is the capacity of the vessel?
(a) 46 (b) 42 ,d crZu esFksukWy vkSj bFksukWy ds feJ.k ls Hkj
(c) 32 (d) 38 ftlesa 20» bFksukWy gSA 10 yhVj feJ.k dks fudky
29. A mixture of 240 liters of juice and water tkrk gS vkSj esFkukWy ls Hkj fn;k tkrk gSA ;fn bFks
contains 15% water. How much more water
(in liters) should be added to this so that the
vc 15» gS] rks crZu dh {kerk D;k gS\
strength of water will become 25% in the new (a) 40 L (b) 30 L
mixture? (c) 50 L (d) 36 L

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34. What would be the ratio of milk and water ,d nw/okyk vius nw/ dks ykxr ewY; ij cspus dk
in a final mixture formed by mixing milk and nkok djrk gSA ;fn og 4 % 1 ds vuqikr esa nw/ rFkk
water that are present in three vessels of
capacity 1l, 2l, and 3l respectively and in the
ikuh feykrk gSA rks mldk ykHk » Kkr djsaA
ratios 5:1, 3:2 and 4:3 respectively? (a) 20% (b) 25%
nw/ vkSj ikuh dks feykdj cuus okys vafre feJ.k esa (c) 30% (d) 50/3%
nw/ vkSj ikuh dk vuqikr D;k gksxk tks Øe'k% 38. 1yh] In a parking there are some two wheelers &
rest are four wheelers. If wheels are counted,
2yh vkSj 3yh {kerk ds rhu crZuksa esa ekStwn gSa there vkSj are total 520 wheels but the Incharge
Øe'k% 5%1] 3%2 vkSj 4%3 ds vuqikr esa gSa\ of the parking told that there are only 175
(a) 747:443 (b) 787:1260 vehicles. Find the number of two wheelers?
(c) 787:473 (d) 747:473 ,d ikfdZax esa dqN nks ifg;k vkSj ckdh pkj ifg;k
35. Two blends of a commodity costing Rs 35 and okgu gSaA ;fn ifg;ksa dh fxurh dh tkrh gS] rks dqy
Rs. 40 per kg respectively are mixed in the
ratio 2:3 by weight. If one-fifth of the mixture
520 ifg, gSa] ysfdu ikfdZax ds çHkkjh us crk;k fd
is sold at Rs 46 per kg and the remaining at dsoy 175 okgu gSaA nks ifg;k okguksa dh la[;k Kk

r
the rate Rs 55 per kg, the profit percent is. dhft;s\
,d oLrq ds nks feJ.kksa dks ftudk ewY; Øe'k% 35 (a) 108 (b) 95

si
:i;s vkSj 40 :i;s izfr fdyksxzke gS] dks 2 % 3 ds (c) 72 (d) 90
an by 1
vuqikr esa fefJr fd;k tkrk gSA ;fn feJ.k dks ]
5
39. In a zoo there are some pigeons and some
rabbits. If their heads are counted these are

n
300 and if their legs are counted these are
46 :i;s izfr fdyksxzke vkSj 'ks"k dks 55 :i;s izfr 750. Find the number of pigeons in the zoo.
fdyksxzke dh nj ls cspk tkrk gS] rks ykHk izfr'kr Kkr ,d fpfM+;k?kj esa dqN dcwrj vkSj dqN •jxks'k gSaA ;f
ja
R s
djsaA muds flj fxus tkrs gSa rks mudh la[;k 300 gksrh gS
a th

(a) 50 (b) 20 vkSj ;fn muds iSj fxus tkrs gSa rks ;s 750 gSaA fpfM+
(c) 40 (d) 30 esa dcwrjksa dh la[;k Kkr dhft,A
36. Three vessels whose capacities are in the ratio
(a) 210 (b) 225
of 3:2:1 are completely filled with milk mixed
ty a

(c) 195 (d)190

with water. The ratio of milk and water in the
mixture of vessels are 5:2, 4:1 and 4:1 40. In two alloys, copper and zinc are related in
di M

the ratios of 4:1 and 1:3. 10 kg of first alloy,

1 1 16 kg of second alloy and some of pure copper
respectively. Taking of first, of second
3 2 are melted together. An alloy was obtained
in which the ratio of copper to zinc was 3:2.
1
and of third mixtures, a new mixture kept Find the weight of the new alloy?
7
nks feJ /krqvksa esa] rkack vkSj tLrk 4%1 vkSj 1% 3
in a new vessel in prepared. The percentage
of water in the new mixture is.
vuqikr esa gSaA igys feJ/krq ds 10 fdyks] nwljs feJ /
rhu ik=k ftudh {kerk 3%2%1 ds vuqikr esa gS] os iwjh rjgkrq ds 16 fdyks vkSj dqN 'kq¼ rkacs dks ,d lkFk fi?kyk;k
tkrk
ls ikuh feys gq, nw/ ls Hkjs gSaA ik=kksa ds feJ.k esa nw/ vkSjgSA ,d feJ /krq çkIr dh xbZ ftlesa rkack ls
ikuh dk vuqikr Øe'k% 5 % 2] 4 % 1 vkSj 4 % 1 gSA tLrk dk vuqikr 3% 2 FkkA ubZ feJ /krq dk otu Kkr
dhft,\
A

1 1 1
igys dk nwljs dk vkSj rhljs feJ.k dk ysdj] (a) 34 kg (b) 35 kg
3 2 7
(c) 36 kg (d) 30 kg
,d u, crZu esa u;k feJ.k rS;kj fd;k x;kA u, feJ.k 41. A vessel is filled with 36 liters of milk. If 9
rS;kj fd;k x;kA u, feJ.k esa ikuh dk izfr'kr gSA liters of milk is taken out and replaced with
(a) 32 (b) 28 the same quantity of water and then 4 liters
(c) 30 (d) 24 of the mixture is taken out and replaced with
37. A milkman promise to sell his milk at cost the same quantity of water then find the
price. If he mixes milk & water in the ratio amount of water in the mixture at the end
4:1. Find his profit %. of the second process.

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,d crZu 36 yhVj nw/ ls Hkjk gSA ;fn 9 yhVj nw/ 45. The diluted wine contains only 8 liters of wine
fudky fy;k tkrk gS vkSj leku ek=kk esa ikuh ls cnyk and the rest is water. A new Mixture whose
tkrk gS vkSj fiQj 4 yhVj feJ.k fudkyk tkrk gS vkSj concentration is 30%, is to be formed by
leku ek=kk esa ikuh ls cnyk tkrk gS rks nwljh çfØ;k replacing wine. How many liters of mixture
shall be replaced with pure wine if there was
ds var esa feJ.k esa ikuh dh ek=kk Kkr dhft,A
initially 32 liters of water in the mixture?
(a) 6 (b) 8
ruqÑr okbu esa dsoy 8 yhVj okbu gksrh gS vkSj 'ks"
(c) 10 (d) 12
42. From a container of beer, a thief has stolen
ikuh gksrk gSA okbu ds LFkku ij ,d u;k feJ.k ftldh
15 liters of beer and replaced it with same lkUærk 30» gS] cuk;k tkuk gSA ;fn feJ.k esa 'kq: esa
quantity of water. He again repeated the same 32 yhVj ikuh Fkk] rks fdrus yhVj feJ.k dks 'kq¼
process. If this process is done three times the 'kjkc ls cny fn;k tk,xk\
ratio of beer and water became 343:512. The
(a) 4 (b) 5
initial amount of beer in the container was?
(c) 8 (d) None of these
ch;j ds ,d daVsuj ls] ,d pksj us 15 yhVj ch;j 46. A can contains 50 litres of a solution of spirit
pqjk yh vkSj mlh ek=kk esa mls ikuh ls cny fn;kA mlusand water with 40% spirit in it. 5 litres of the

r
fiQj ls ogh çfØ;k nksgjkbZA ;fn ;g çfØ;k rhu ckj solution is removed and 5 litres of spirit is

si
dh tkrh gS rks ch;j vkSj ikuh dk vuqikr 343%312 gks added. The same process is done two more
tkrk gSA daVsuj esa ch;j dh 'kq#vkrh ek=kk Fkh\
an by times. Find the percentage of water in the
(a) 90 (b) 105 solution at the end (rounded off to the nearest
integer).

n
(c) 120 (d) 135
43. In an alloy 80% is copper, and the remaining ,d dSu esa 50 yhVj fLifjV vkSj ikuh dk ?kksy gS ftlesa
is tin, in another alloy, copper is 85% and 40» fLifjV gSA 5 yhVj ?kksy fudky fn;k tkrk gS vkSj 5
ja
R s
tin is 12%. In what ratio should the two alloys yhVj fLçV feyk;k tkrk gSA ;gh çfØ;k nks ckj vkSj dh
be mixed so that the new mixture must have
tkrh gSA var esa lek/ku esa ikuh dk çfr'kr Kkr djsa
a th

15% tin, and also find the percentage the

copper in the new mixture? (fudVre iw.kkZad rd xksy)A
,d feJ /krq esa 80» rkack gS] vkSj 'ks"k fVu gS] ,d CRPF HCM 11/03/2023 (Shift - 02)

vU; feJ /krq esa] rkack 85» gS vkSj fVu 12» gSA nks(a) 40% (b) 44%
ty a

(c) 54% (d) 48%

feJ /krqvksa dks fdl vuqikr esa feyk;k tkuk pkfg,
47. A person buys tea of three different qualities
di M

rkfd u, feJ.k esa 15» fVu gks vkSj u, feJ.k esa at Rs 800, Rs 500, and Rs 300 per kg,
rkacs ds çfr'kr dk Hkh irk yxk,a\ respectively, and the amounts bought are in
(a) 3:5, 83.125% the proportion 2 : 3 : 5. She mixes all the
(b) 5:3, 81.75% tea and sells one-sixth of the mixture at ?
(c) 3:4, 83.25% 700 per kg. The price, in per kg, at which she
(d) 3:7, 80% should sell the remaining tea, to make an
44. A container contains x liters of wine. 10 liters overall profit of 50%, is.
are drawn from this container and is then ,d O;fÙkQ rhu vyx&vyx xq.kksa dh pk; Øe'k% 800
filled with water. This Operation is performed
#i;s] 500 #i;s vkSj 300 #i;s çfr fdyks •jhnrk gS]
2 more times. The ratio of quantity of the
wine now left in container to that of capacity vkSj •jhnh xbZ ek=kk 2 % 3 % 5 ds vuqikr esa gSA og lH
A

of container is 27:64. How much wine did the pk; dks feykrk gS vkSj pk; dk NBk fgLlk 700 #i;s
container hold originally. izfr fdxzk esa csprk gSA 50» dk lexz ykHk çkIr djus ds
,d daVsuj esax yhVj 'kjkc gSA bl daVsuj ls 10 yhVj fy, mls 'ks"k pk; fdrus #i;s izfr fdxzk cspuh pkfg,A
fudkyk tkrk gS vkSj fiQj mls ikuh ls Hkj fn;k tkrk (a) 692 (b) 688
gSA ;g fØ;k 2 ckj vkSj dh tkrh gSA daVsuj esa NksM+h (c) 653 (d) 675
xbZ 'kjkc dh ek=kk ls daVsuj dh {kerk dk vuqikr 27%64
48. What is the ratio in which water should be
gSA daVsuj esa ewy :i ls fdruh 'kjkc FkhA mixed with a coke concentrate costing Rs 15/
(a) 22 liters (b) 40 liters liter to make a profit of 30% by selling the
(c) 24 liters (d) 28 liters resultant drink at Rs 18/liter?

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foy;u A vkSjB esa vYdksgy vkSj ikuh dk vuqikr Øe'k%

15 #i;s çfr yhVj dh ykxr okys dksd dkWUlsaVªsV esa
ikuh dks fdl vuqikr esa feyk;k tkuk pkfg, rkfd 5 % 4 vkSj 7 % 11 gSA ikap yhVjA dks 6 yhVj B ds
ifj.kkeh is; dks 18 #i;s çfr yhVj dh nj ls cspdj lkFk feyk;k tkrk gSA blds vykok] ifj.kkeh feJ.k esa 1
30» dk ykHk dek;k tk lds\ yhVj vYdksgy vkSj 3 yhVj ikuh Hkh feyk;k tkrk gSA
(a) 12 : 1 (b) 11 : 1 vafre feJ.k esa vYdksgy vkSj ikuh dk vuqikr D;k gS\
(c) 1 : 10 (d) 1 : 12 CRPF HCM 26/02/2023 (Shift - 01)
49. 450 litres of a mixture of milk and water contain
(a) 46 : 53 (b) 11 : 16
the milk and water in the ratio 9 : 1. How much
(c) 27 : 32 (d) 55 : 53
water should be added to get a new mixture
53. A container contains 40 litres of concentrated
containing milk and water in the ratio 3 : 1?
syrup. 4 litres of it was taken out and replaced
nw/ vkSj ikuh ds 450 yhVj feJ.k esa nw/ vkSj ikuh dk with water and the same process was repeated
vuqikr 9 % 1 gSA nw/ vkSj ikuh ds feJ.k dk vuqikr 3 % 1 thrice. In the end, what percentage of the
gks] blds fy, blesa fdruk ikuh feyk;k tkuk pkfg,\ solution will be syrup in the container?
(a) 54 (b) 90 ,d daVsuj esa 40 yhVj dalUVªsVsM flji gksrk gSA blesa
(c) 45 (d) 63 yhVj fudky fy;k x;k vkSj ikuh ls cny fn;k x;k vkSj
;gh çfØ;k rhu ckj nksgjkbZ xbZA var esa ik=k esa fd

r
50. The ratio of acid to water in solution A and B
is 4:11 and 3:7, respectively. Three litres of A çfr'kr ?kksy esa pk'kuh gksxh\

si
is mixed with five litres of B and then one litre
CRPF HCM 27/02/2023 (Shift - 02)
of water is added to the resuling mixture. What

?kksy
an by
is the percentage of acid in the final mixture?
A vkSj b esa ,flM dk ikuh ls vuqikr Øe'k% 4%11
(a) 67.23%
(c) 63.72%
(b) 65.61%
(d) 64.15%

n
vkSj 3%7 gSA rhu yhVjA dks ik¡p yhVjB ds lkFk feyk;k 54. A solution of 60 litres is made of dye and water
in the ratio 2 : 3. Water is added to the solution
tkrk gS vkSj fiQj ,d yhVj ikuh dks ifj.kkeh feJ.k esa so as to make the ratio of dye to water as 3 :
ja
feyk;k tkrk gSA vafre feJ.k esa vEy dk çfr'kr D;k gS\
R s
5. One fourth of the solution is to be removed,
CRPF HCM 22/02/2023 (Shift - 02) and dye is to be added to make dye and water
a th

in the ratio 2 : 3 in the final solution. Find how

3 5 many litres of dye is to be added.
(a) 28 % (b) 25 %
4 9 MkbZ vkSj ikuh dk 2%3 ds vuqikr esa 60 yhVj dk ?kk
1 2 cuk;k tkrk gSA ikuh ls MkbZ dk vuqikr 3%5 djus ds fy,
(c) 27 % (d) 26 %
ty a

2 3 ikuh dks ?kksy esa feyk;k tkrk gSA ?kksy dk ,d pkSF

1 1
Hkkx fudkyuk gksrk gS] vkSj vafre ?kksy esa 2%3 ds vu
di M

51. Two tins of equal dimensions have and

5 6 esa MkbZ vkSj ikuh cukus ds fy, MkbZ feykbZ tkrh gS
portions filled with acid. If the remaining
portions of the tins are filled with water and dhft, fd fdrus yhVj MkbZ feykuh gSA
the resultant contents are mixed in a tumbler,
then how many units of acid should be added CRPF HCM 27/02/2023 (Shift - 03)
to the number so that the ratio of acid and (a) 2 (b) 6
water becomes 1 : 1 in the resulting solutions? (c) 8 (d) 4
1 1 55. The ratios of alcohol and water in solutions A
leku vk;keksa ds nks fVuksavkSj
esa Hkkx ,flM ls Hkjs and B are 7 : 8 and 3 : 2, respectively. If 9
5 6
gq, gSaA ;fn fVu ds 'ks"k Hkkxksa dks ikuh ls Hkj fn;k tkrk gS of A is mixed with 6 litres of B and then
litres
vkSj ifj.kkeh lkexzh dks ,d fxykl esa feyk;k tkrk gS] rks 1 litre of alcohol and 2 litres of water are
vEy dh fdruh bdkbZ la[;k esa tksM+h tkuh pkfg, rkfd added to the resulting mixture, what is the
ifj.kkeh ?kksy esa vEy vkSj ikuh dk vuqikr 1%1 gks tk,\ percentage of alcohol in the final mixture so
A

CRPF HCM 24/02/2023 (Shift - 02) obtained (correct to one decimal place)?
(a) 32 (b) 38 foy;u A vkSjB esa vYdksgy vkSj ikuh dk vuqikr Øe'k%
(c) 35 (d) 30 7%8 vkSj 3%2 gSA ;fn 9 yhVjA dks 6 yhVj B ds lkFk
52. The ratios of alcohol and water in solutions A feyk;k tkrk gS vkSj fiQj ifj.kkeh feJ.k esa 1 yhVj vYdksgy
and B are 5 : 4 and 7 : 11, respectively. Five vkSj 2 yhVj ikuh feyk;k tkrk gS] rks çkIr vafre feJ.k esa
litres of A is mixed with 6 litres of B. vYdksgy dk çfr'kr D;k gS (,d n'keyo LFkku rd lgh)\
Furthermore, 1 litre of alcohol and 3 litres of
CRPF HCM 28/02/2023 (Shift - 03)
water are also added in the resulting mixture.
What is the ratio of alcohol and water in the (a) 46.7% (b) 47.8%
final mixture? (c) 47.4% (d) 48.9%

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ANSWER KEY
1.(b) 2.(c) 3.(c) 4.(b) 5.(a) 6.(c) 7.(b) 8.(b) 9.(b) 10.(a)

11.(a) 12.(a) 13.(b) 14.(c) 15.(c) 16.(a) 17.(d) 18.(c) 19.(a) 20.(a)

21.(b) 22.(d) 23.(a) 24.(c) 25.(c) 26.(d) 27.(b) 28.(d) 29.(b) 30.(c)

31.(d) 32.(d) 33.(a) 34.(c) 35.(c) 36.(d) 37.(b) 38.(d) 39.(b) 40.(b)

41.(d) 42.(c) 43.(a) 44.(b) 45.(b) 46.(b) 47.(b) 48.(a) 49.(b) 50.(b)

51.(b) 52.(b) 53.(b) 54.(a) 55.(d)

r
SOLUTION

si
1. (b)
an by 4. (b)

n
4
 8 1  Water
x
1 –  20% =
 x 16 5  Spirit

x ja
16  65
R s
4 4
1:5
 8 16  2 
a th

1 – 
  = =
   5. (a)
 x 81  3 
8 2 150
1– 
x 3
ty a

8 1

x 3
di M

x = 24 litres Wine Water

2. (c) 120 30
135  1  126  1  x  2 +x
= 153 :
4 3 1
261+ 2x = 612
3 unit = 120
351
x= = 175.5 1 unit = 40
2
3. (c) Add water = 40 – 30 = 10
a : b 6. (c)
7 : 5
2
A

2  10 
water left =  20 
1 – 

–9 5  20 

7 :5 2
+9
 1
8
= 1 – 

7 9 = 16  2
4 unit = 9
1
16 unit = 36 = 8 =2
4
36
a=  7 = 21 litre m : w = 18 : 2  9 : 1
12

Aditya Ranjan (Excise Inspector) Selected gSSelection fnyk,axs

8
 ALLIGATION (,yhxs'ku)
(CLASSROOM SHEET)
dks fdl vuqikr esa feyk;k tkuk pkfg, rkfd u,
MIXTURE BASED QUESTIONS feJ.k esa nkftZfyax vkSj vle pk; dk vuqikr%
613
1. Two vessels are full of milk with milk- gks tk,A gS
water ratios 1 : 4 and 3 : 8, respectively. (SSC CGL Tier-II Exam, 2014 12.04.2015
If both are mixed in the ratio 3 : 2, what (a) 22 : 35 (b) 26 : 35
is the ratio of milk and water in the new (c) 35 : 78 (d) 13 : 22
mixture? 5. Acid and water are mixed in a vessel A
nks crZu nw/ vkSj ikuh ls Øe'k% 1 %4 vkSj in the ratio of 5 : 2 and in the vessel B
3 %8ds vuqikr esa Hkjs gq, gSaA ;fn nksuksa
%2ds dks3 in the ratio 8 : 5. In what proportion

r
vuqikr esa feyk;k tkrk gS]rks u, feJ.k esa nw/ should quantities be taken out from the
vkSj ikuh dk vuqikr D;k gksxk\ two vessels so as to form a mixture in

si
which the acid and water will be in the
(a) 4 : 15 (b) 3 : 7
ratio of 9 : 4?

2.
(c) 63 : 212
an by (d) N.O.T
Two mixtures contain milk and water in ,d crZu A esa 5%2 ds vuqikr esa ,flM vkSj ikuh
feyk;k tkrk gS vkSj crZu
B esa 8 %5 ds vuqikr esa

n
the ratios 3 : 2 and 4 : 5. How many litres
of the second mixture must be mixed feyk;k tkrk gSA nksuksa crZuksa ls fdl vuqikr esa ek=k
with 3 litres of the first mixture so that fudkyuh pkfg, rkfd ,d feJ.k cu tk, ftlesa
ja
R s
the new mixture thus formed contain
equal quantities of milk and water?
,flM gks vkSj ikuh%94 ds vuqikr esa gksxk\
a th

SSC CHSL, DEO & LDC Exam (04.12.2011)

nks feJ.kksa esa nw/ vkSj ikuh dk vuqikr
%2 vkSj
3
(a) 7 : 2 (b) 2 : 7
4 %5 gSA nwljs feJ.k dh fdrus yhVj ek=kk dks igys
(c) 7 : 4 (d) 2 : 3
feJ.k dh 3 yhVj ek=kk ls feyk;k tk, rkfd çkIr
6. Solution A contains 10% acid and
u, feJ.k esa nw/ vkSj ikuh dh ek=kk leku gks\
ty a

solution B contains 30% acid. In what

(a) 5 ltr (b) 5.4 ltr ratio should solution A be mixed with
di M

(c) 5.5 ltr (d) 6 ltr Solution B to obtain a mixture with 25%
3. The milk and water in two vessels A and acid?
B are in the ratio 4 : 3 and 2 : 3
feJ.k A esa 10» ,flM gS rFkk feJ.k B esa 30»
respectively. In what ratio, the liquids in
both the vessels be mixed to obtain a new ,flM gSA feJ.kA dks feJ.k B ds lkFk fdl vuqikr
mixture in vessel C containing half milk esa feyk;k tk, fd feJ.k esa 25» ,flM izkIr gks tk,\
and half water? CGL Mains 2018
nks crZuA vkSj B esa nw/ vkSj ikuh dk vuqikr (a) 1 : 2 (b) 3 : 1
Øe’k% 4%3 vkSj 2%3 gSA vk/k nw/ vkSj vk/k (c) 1 : 3 (d) 2 : 1
ikuh okys crZuB esa ,d u;k feJ.k çkIr djus ds 7. Two alloys are both made up of copper
fy, nksuksa crZuksa esa rjy inkFkZ dks fdl vuqikr esa
and tin. The ratio of copper and tin in the
feyk;k tkrk gS\ first alloy is 1 : 3 and in the second alloy
A

is 2 : 5. In what ratio should the two

(a) 7 : 5 (b) 5 : 2
alloys be mixed to obtain a new alloy in
(c) 3 : 11 (d) 1 : 2
which the ratio of tin and copper be 8 : 3?
4. In two blends of mixed tea, the ratios of
Darjeeling and Assam tea are 4 : 7 and nks feJ/krq,a nksuksa rkacs vkSj fVu ls cuh gSaA igy
2 : 5. The ratio in which these two blends feJ/krq esa rkacs vkSj fVu dk vuqikr%3 gS
1 vkSj
should be mixed to get the ratio of nwljh feJ /krq esa %25 gSA ,d ubZ feJ/krq çkIr
Darjeeling and Assam tea in the new djus ds fy, nksuksa feJ/krqvksa dks fdl vuqikr esa
mixture as 6 : 13 is
feyk;k tkuk pkfg, ftlesa fVu vkSj rkacs dk vuqikr
fefJr pk; ds nks feJ.kksa esa nkftZfyax vkSj vle
8 %3 gks\
pk; dk vuqikr 4 %7 vkSj 2%5 gSA bu nksuksa feJ.kksa
[1]
 (SSC CHSL DEO & LDC Exam. (27.10.2013) 11. 40 litres of a mixture of milk and water
(a) 3 : 5 (b) 4 : 7 contains 10% of water, the amount of
(c) 3 : 8 (d) 5 : 11 water to be added, to make the water
content 20% in the new mixture is :
8. The ratio of two liquids in a mixture is
3 : 5 and that in another mixture is 6 : 1. 40 yhVj okys nw/ vkSj ikuh ds feJ.k esa 10»
The ratio in which these two mixtures ikuh gSA fdl ek=kk esa ikuh feyk;s ftlls u;s feJ.k
should be mixed so as to make the ratio esa 20» ikuh gks\
of the liquids 7 : 3 is (a) 6 litre (b) 6.5 litre
,d feJ.k esa nks æoksa dk vuqikr%53 gS vkSj (c) 5.5 litre (d) 5 litre
nwljs feJ.k esa %
61 gSA bu nksuksa feJ.kksa dks12.fdl 300 gram of sugar solution has 40% of
vuqikr esa feyk;k tkuk pkfg, rkfd æoksa dk vuqikr sugar in it. How much sugar should be
added to make it 50% in the solution?
7 %3 gks tk,
300 xzke phuh ds ?kksy esa 40 izfr'kr phuh gSA blesa
(CGL Tier-II Exam, 2014 12.04.2015
fdruh phuh vkSj feykbZ tkuh pkfg, ftlls og bl
(a) 44 : 71
?kksy dk 50 izfr'kr gks tk,\
(b) 44 : 81
(a) 60 gms (b) 80 gms

r
(c) 44 : 91
(c) 10 gms (d) 40 gms
(d) 44 : 61
13. An alloy contains copper and tin the ratio

si
9. In an alloy 80% is copper and remaining 3 : 2. If 250 gm of copper is added to this
is tin. In another alloy, copper is 85% and alloy then the copper in it becomes
an by
tin is 12%. In what ratio should the two
alloy be mixed so that the new mixture
double the quantity of tin in it. What is
the amount (in gms) of tin in the alloy?

n
must have 15% tin. Also find the ,d feJ/krq esa rkacs vkSj fVu dk vuqikr
3%2
percentage of copper in the new mixture?
gSA ;fn bl feJ/krq esa 250 xzke rkack feyk fn;k
ja
,d feJ/krq esa 80» dkWij vkSj 'ks"k fVu gSA nwljh tkrk gS rks blesa mifLFkr rkack blesa mifLFkr fVu
R s
feJ/krq esa 85» dkWij vkSj 12» fVu gSA bu nksuksa dh ek=kk dk nksxquk gks tkrk gSA bl feJ/krq esa fVu
a th

feJ/krqvksa dk vuqikr D;k gksuk pkfg, fd u;s feJ.k fdruh ek=kk (xzke esa) gS\
esa 15» fVu gks rFkk ;g Hkh irk djsa fd u;s feJ.k CGL Mains 2018
esa dkWij fdrus izfr'kr gSa\ (a) 250 (b) 750
ty a

(a) 3 : 5 (c) 1000 (d) 500

(b) 5 : 3 14. A jar full of 60 litres syrup contains 40%
di M

(c) 2 : 3 honey. A part of this syrup is replaced by

(d) 3 : 4 another containing 19% of honey and now
10. If a dairy mixes cow’s milk which ratio of honey and other would be 13 : 37.
Find the quantity syrup is replaced.
contains 10% fat with buffalo’s milk
which contains 20% fat, then the 60 yhVj flji ls Hkjs tkj esa 40» 'kgn gSA bl
120 flji dk ,d fgLlk nwljs fgLls ls cny fn;k tkrk
% of fat.
resulting mixture has fat
7 gS ftlesa 19» 'kgn gS vkSj vc 'kgn vkSj vU; dk
What ratio was the cow’s milk mixed with vuqikr 13%37 gksxkA flji dh cnyh ek=kk Kkr djsaA
buffalo’s milk? (a) 40 (b) 45
dksbZ Ms;jh xk; dk nw/ ftlesa olk (iQSV) dk izfr'kr (c) 35 (d) 80
10» gS] rks HkSal ds nw/ ds lkFk feykrh gSa15. ftlesaA jar full of 70 litres syrup contains 50%
20» olk gS rks ifj.kkeh feJ.k eas olk] olk dk honey. A part of this syrup is replaced by
A

another containing 29% of honey and now

120
% gksrk gSA xk; dk nw/ fdl vuqikr esa ratio of honey and other would be 8 : 25.
7 Find the quantity syrup is replaced.
HkSal ds nw/ ds lkFk feyk;k x;k\ 70 yhVj flji ls Hkjs tkj esa 50» 'kgn gSA bl
CGL Mains 2018 flji dk ,d fgLlk nwljs fgLls ls cny fn;k tkrk
(a) 2 : 5 gS ftlesa 29» 'kgn gS vkSj vc 'kgn vkSj vU; dk
(b) 1 : 5 vuqikr 8% 25 gksxkA flji dh cnyh ek=kk Kkr djsaA
(c) 2 : 3 (a) 10 (b) 50
(d) 2 : 1 (c) 60 (d) 80

[2]
 20. A shopkeeper bought one type of rice at
PROFIT AND LOSS ` 12 per kg and other type at ` 16.25 per
kg. After mixing both types of rice he
BASED QUESTIONS. fixed the cost of mixture as ` 14.75 per
16. In what ratio should coffee powder kg. if the total quantity of the rice be 85
kg, find the quantity of first type of rice.
costing ` 2500/kg be mixed with coffee
powder costing ` 1500/kg so that the cost ,d O;kikjh ,d çdkj ds pkoy tks fd ` 12 çfr
of the mixture is ` 2250/kg? fdxzk gS vkSj nwljs çdkj ds pkoy tks` fd16-25
dkWiQh ikmMj ftldh dher ` 2500 izfr fdxzk gSa] çfr fdxzk •jhnrk gSA mlds ckn og mu nksuksa dks
dks fdl vuqikr esa` 1500 izfr fdxzk dher okys feykdj mudk ewY;` 14-75 çfr fdxzk fuf'pr djrk
dkWiQh ikmMj ds lkFk feyk;k tk, fd feJ.k dh gSA ;fn pkoy dh dqy ek=kk 85 fdxzk gks] rks igys
dher ` 2250 izfr fdxzk gks tk,\ çdkj ds pkoy dh ek=kk Kkr djsa\
(a) 1 : 4 (b) 4 : 1 (a) 55 kg (b) 30 kg
(c) 3 : 1 (d) 1 : 3 (c) 35 kg (d) 40kg
17. In what ratio, sugar costing ` 60 per kg 21. A shopkeeper have 65 kg daal , he sell one
be mixed with sugar costing ` 42 per kg part at 8% profit and sell other part to

r
such that by selling the mixture at ` 56 18% profit. In overall business he gain
14%, than find the quantity of rice that

si
per kg there is a gain of 12%?
is sell on 8% profit .
` 60 çfr fdxzk- okyh phuh dks
` 42 çfr fdxzk-
,d nqdkunkj ds ikl 65 fdxzk- nky gS mles ls
an by
okyh phuh esa fdl vuqikr esa fefJr fd;k tk,
ftlls fd fefJr phuh dks ` 56 çfr fdxzk- ds ewY;
dqN fgLls dks og 8» ykHk ij rFkk ‘ks”k dks og
18» ykHk ij csprk gSA iwjs O;kikj esa mls 14» ykHk

n
esa cspus ij 12» dk ykHk çkIr gks lds\
çkIr~ gksrk gSA 8» ykHk ij csph xbZ nky dh ek=kk
(a) 5 : 7 (b) 8 : 9
ja Kkr djsa A
R s
(c) 5 : 6 (d) 4 : 5
(a) 39 kg (b) 26 kg
18. How many kg of salt costing ` 28 per kg
a th

(c) 18 kg (d) 32 kg
must be mixed with 39.6 kg of salt
costing ` 16 per kg, so that selling the
mixture at ` 29.90, there is a gain of DISCOUNT BASED QUESTIONS
15%?
ty a

22. A seller sells 2 watches at 8% and 15%

` 16 çfr fdxzk ewY; ds 39-6 fdxzk ued `esa28 discount each. Total marked price of both
çfr fdxzk ewY; dk fdrus fdxzk ued feyk;k tk,
di M

the items are ` 2100 . Find the difference

ftlls fd feJ.k dks ` 29-90 dh nj ij cspus ij between marked price of both items, if
15» dk ykHk gks\ total discount is of 12%.
CGL Tier-II (2019) ,d foØsrk 2 ?kfM+;k¡ 8» vkSj 15» NwV ij csprk
(a) 198 (b) 133 gSA nksuksa oLrqvksa dk dqy vafdr
` 2100
ewY;
gSA
(c) 132 (d) 135 ;fn dqy NwV 12» gS] rks nksuksa oLrqvksa ds vafdr
19. A student bought 10 pencils and 8 pens ewY; ds chp dk varj Kkr dhft,A
at ` 150 . He sells pencil at 4% profit and CGL Tier II (2019)
pen at 7% profit. Overall he gains ` 9. (a) 360 (b) 300
Find the cost price of each pencil and (c) 500 (d) 200
pen.
,d Nk=k us ` 150 esa 10 isafly vkSj 8 isu •jhnsA SIMPLE INTEREST BASED
A

og isafly dks 4» ykHk ij vkSj isu dks 7» ykHk

ij csprk gSA dqy feykdj mls` 9 dk ykHk gksrk
QUESTIONS
gSA çR;sd isafly vkSj isu dk Ø; ewY; Kkr dhft,A 23. Harish is having ` 40,000 . He deposited
CGL Tier-II (2019) it in 2 banks. Interest given by 1st bank
(a) 3, 6 is 9.5% per annum and that of 2nd bank
(b) 5, 10.5 is 5.5% per annum. If at t he end of a
year Harish got ` 3200. Then find the
(c) 5, 12.5
difference of the balance amount
(d) 3, 6 deposited in both banks?

[3]
 gjh'k ds ikl ` 40]000 gSaA mlus bls 2 cSadksa
27. esa
A sum of ` 15,600 is invested partly at
tek dj fn;kA igys cSad }kjk fn;k x;k C;kt 7% per annum and the remaining at 9%
9-5» çfr o"kZ gS vkSj nwljs cSad dk 5-5» çfr o"kZ per annum simple interest. If the total
interest at the end of 3 years is ` 3738,
gSA ;fn ,d o"kZ ds var esa gjh'k`dks
3200 feyrs how much money was invested at 7% per
gSaA rks nksuksa cSadksa esa tek 'ks"k jkf'k dk varj Kkr
annum?
dhft,\ ` 15]600 dh jkf'k vkaf'kd :i ls 7» izfr o"kZ
(a) ` 36000 (b) ` 30000 vkSj 'ks"k 9» izfr o"kZ lk/kj.k C;kt ij fuos'k dh
(c) ` 10000 (d) ` 20000
tkrh gSA ;fn 3 o"kks± ds var esa dqy` C;kt
3738
24. A sum of ` 12,800 is invested partly at
15% per annum and the remaining at
gS] rks izfr o"kZ 7» ij fdruk /u fuos'k fd;k x;k
12% per annum simple interest. If the Fkk\
total interest at the end of 3 years is (a) ` 7800 (b) ` 7900
` 5085. Then how much money was (c) ` 7600 (d) ` 7700
invested at 15% per annum. 28. A sum of ` 10,200 is invested partly at 8%
` 12]800 dh ,d jkf'k va'kr% 15» izfr o"kZ rFkk per annum and remaining at 6% per
va'kr% 12» izfr o"kZ lk/kj.k C;kt ij fuos'k dh annum for 3 years at simple interest. If

r
tkrh gSA ;fn 3 o"kZ ds var esa dqy `C;kt5]085 the total interest is ` 2,124, how much

si
money was invested at 6% per annum?
gS] rks 15» izfr o"kZ ij fdruh jkf'k fuos'k dh x;h
Fkh\ ` 10]200 dh ,d jkf'k 3 o"kks± ds fy, va'kr% 8»
an by
SSC CPO 12 March 2019 izfro"kZ vkSj 'ks"k 6» izfr o"kZ lk/kj.k C;kt dh nj
ls fuos'k dh tkrh gSA ;fn dqy C;kt ` 2124 gS]

n
(a) ` 5200 (b) ` 7500
(c) ` 5800 (d) ` 5300 rks 6» izfro"kZ ij fdruh jkf'k fuos'k dh xbZ Fkh\
SSC CPO 13 March 2019 (Evening)
25.
ja
A person lends some amount of ` 8400 to
R s
the rate of 12% and at some at rate of (a) ` 4900 (b) ` 5200
21%. If the interest earned in the last (c) ` 4800 (d) ` 5400
a th

three year is ` 3906, then how much

29. A man has ` 10,000. He lent a part of it
money did they get at the rate of 21%?
at 15% simple interest and the remaining
,d O;fDr ` 8400 dh jkf'k esa ls dqN jkf'k 12» at 10% simple interest. The total interest
dh nj ij vkSj dqN jkf'k 21» dh nj ij m/kj
ty a

he received after 5 years amounted to

nsrk gSA ;fn dqy rhu o"kZ esa` C;kt
3960 feyk ` 6,500. The difference between the parts
gks] rks 21» dh nj ls mUgsa fdruk /u C;kt ds :Ik
di M

of the amounts he lent is :

esa feyk\ ,d O;fDr ds ikl ` 10]000 gSaA mlus blds ,d
(a) 2712 (b) 1848 fgLls dks 15» lk/kj.k C;kt rFkk 'ks"k fgLls dks
(c) 936 (d) 2058 10» lk/kj.k C;kt ij m/kj ns fn;kA 5 o"kks± ckn
26. A sum of ` 15,000 is invested partly at mls dqy` 6]500 lk/kj.k C;kt izkIr gqvkA mlds
12% per annum and the remaining at }kjk m/kj nh xbZ jkf'k;ksa dk varj gS %
10% per annum simple interest. If the
SSC CHSL 18/03/2020 (Morning)
total interest at the end of 2 years is
` 3,344, how much money was invested (a) ` 2,000 (b) ` 2,500
at 10% per annum? (c) ` 1,500 (d) ` 1,750
` 15]000 dh ,d jkf'k dk dqN Hkkx 12» izfr o"kZ
rFkk 'ks"k Hkkx 10» izfr o"kZ lkèkkj.k C;kt ij fuos'kTIME,SPEED AND DISTANCE
A

fd;k tkrk gSA ;fn 2 o"kks± ds var esa dqy C;kt BASED QUESTIONS
` 3]344 gS] rks 10» izfr o"kZ dh nj ls fdruh
jkf'k fuos'k dh xbZ Fkh\ 30. A person went to Delhi to Agra. He
SSC CPO 12 March 2019 (Morning) covered some distance by bus and
remaining distance by train. He covered
(a) ` 6,200 complete distance which is 360 km in 6
(b) ` 6,600 hours. Average speed of bus is 48 km/h
(c) ` 6,400 and average speed of train is 120 km/h.
(d) ` 6,500 Find distance covered by train.

[4]
 ,d O;fÙkQ fnYyh ls vkxjk x;kA mlus dqN nwjh cl ,d vkneh 61 fdeh dh nwjh 9 ?k.Vs esa r; djrk
ls vkSj 'ks"k nwjh Vªsu ls r; dhA mlus iwjh nwjh r; gS] ftles dqN lkbfdy rFkk dqN iSnyA ;fn lkbfdy
dh tks fd 6 ?kaVs esa 360 fdeh gSA cl dh vkSlr dh xfr 9 fdeh@?kaVk vkSj iSny dh xfr 4 fdeh@?kaVk
xfr 48 fdeh@?kaVk vkSj Vªsu dh vkSlr xfr 120 gS] rks mlds }kjk lkbfdy vkSj iSny pyus esa fy,
fdeh@?kaVk gSA Vªsu }kjk r; dh xbZ nwjh Kkr dhft,A x, le; dk vuqikr crkb, A
(a) 120 (b) 240 (a) 4 : 5 (b) 5 : 4
(c) 360 (d) 180 (c) 2 : 7 (d) 7 : 2
31. A car travel 20 km/h for 30 min and at x 35. A man covered a distance of 220km in 11
km/h for 45 min. If the average speed of hour partly by bus at 14 km\h and partly
the car for entire journey is 14 km/h find by car at 25 km\h. Find what percent of
the value of x distance he covered by bus.
,d dkj 20 fdeh@?kaVk ls 30 feuV pyrh gS rFkk ,d vkneh 220 fdeh dh nwjh 11 ?kaVs esa r; djrk
x fdeh-@?kaVk dh pky ls 45 feuV pyrh gSA ;fn gSA dqN fgLlk cl ls 14 fde@?kaVk dh pky ls
iwjh ;k=kk ds fy, dkj dh vkSlr pky 14 fdeh@?kaVk rFkk dqN dkj ls 25 fdeh@?kaVk dh pky ls r;
gS] rks
x dk eku crkb,A djrk gSA crkb, mlus fdruh izfr'kr dh nwjh cl

r
(a) 10 km/h ls r; dh\
(b) 15 km/h (a) 31.82% (b) 68.18%

si
(c) 12 km/h (c) 41.7% (d) 58.33%

32.
(d) 20 km/h
an by
A man covered a distance of 60 km in 5 PERCENTAGE

n
hour partly by train at 15 km/h and
partly by foot at 10km/h. The distance (POPULATION BASED QUESTIONS)
covered by train is.

ja
,d vkneh 60 fdeh dh nwjh 5 ?kaVs esa r; djrk36. Population of a town is 1,20,000 . If
R s
number of male increases by 7% and
gSA bldk ,d fgLlk Vªsu esa 15 fdeh@?kaVk dh pky females increases by 10%, then the
a th

ls rFkk nwljk fgLlk iSny 10 fdeh@?kaVk dh pky population of town would increase by
ls r; djrk gS] rks Vªsu ls r; dh xbZ nwjh crkb,A 9.5%. Find the difference between male
(a) 45 km to female population living in that town?
ty a

(b) 30 km ,d dLcs dh tula[;k 1]20]000 gSA ;fn iq#"kksa dh

(c) 20 km la[;k esa 7» vkSj efgykvksa dh la[;k esa 10» dh
di M

(d) 40 km o`f¼ gksrh gS] rks 'kgj dh tula[;k esa 9-5» dh

33. A person travels 255 km in 7 hours in two o`f¼ gksxhA ml 'kgj esa jgus okys iq#"k ls efgyk
stages. In the first part of journey, he vkcknh ds chp varj Kkr dhft,\
travels by bus at the speed of 30km\h.
In the second part of journey, he travels (a) 25000
by train at the speed of 45km\h. How (b) 80000
much distance he travel by bus? (c) 24000
,d vkneh 255 fdeh 7 ?kaVs esa nks pj.k esa ;k=kk (d) 10800
djrk gSA çFke pj.k esa og cl ls 30 fdeh@?kaVk 37. Population of town is 15,000. If number
of male decreases by 10% and number of
dh pky ls rFkk nwljs pj.k esa Vªsu ls 45 fdeh@?kaVkfemale increases by 5% then the
dh pky ls ;k=kk djrk gSA crkb, mlus cl ls fdruh population of town would increase by 600.
A

nwjh r; dh \ Find the number of male in the town.

(a) 135 km ' kgj dh vkcknh 15]000 gSA ;fn iq#"kksa dh la[;k
(b) 145 km esa 10» dh deh gksrh gS vkSj efgykvksa dh la[;k esa
(c) 120 km 5» dh o`f¼ gksrh gS] rks 'kgj dh tula[;k esa 600
(d) 125 km dh o`f¼ gksxhA 'kgj esa iq#"kksa dh la[;k Kkr dhft,A
34. A person travelled 61 km in 9 hours (a) 1500
partly by cycle and partly on foot. Speed
(b) 1000
of cycle is 9 km\h and speed of foot is 4
km\h. find the ratio of time travelled by (c) 1400
cycle and foot. (d) 1080

[5]
 42. There are 125 middle level employee in
PERCENTAGE Due North Inc. The average monthly
salary of the middle level employees is
(INCOME EXPENDITURE ` 5500 and that of the senior level
employees is ` 14000. If the average
BASED QUESTIONS) monthly salary of all these employees
` 8687.5, find the total number of
38. If the income of a family decreases by 6% employees in the company, if middle and
and expenditure decreases by 8% , and its senior level employees of Due North Inc.
saving increases by 4%. Find the ratio of form 80% of their total employees?
income and expenditure of that family.
Due north daiuh esa eè; Js.kh ds 125 deZpkjh
;fn ,d ifjokj dh vk; esa 6» dh deh gks tkrh
gSaA eè; Js.kh ds deZpkfj;ksa dk vkSlr osru
gS vkSj O;; esa 8» dh deh gks tkrh gS] vkSj mldh
` 5500 gS] tcfd mPp Js.kh ds deZpkfj;ksa dk
cpr esa 4» dh o`f¼ gksrh gSA ml ifjokj dh vk; vkSlr osru ` 14000 gSA ;fn dqy deZpkfj;ksa dh
vkSj O;; dk vuqikr Kkr dhft, A vkSlr ekfld osru ` 8687-5 gSA daiuh esa deZpkfj;ksa
(a) 6 : 5 (b) 2 : 1
dh lka[; Kkr dhft;s ;fn eè; vkSj mPp Js.kh ds
(c) 5 : 6 (d) 3 : 1
deZpkfj;ksa dh la[;k daiuh ds dqy deZpkfj;ksa dh

r
39. Raghav spends 80% of his income. If his
la[;k dk 80» gSA

si
income increase by 12% and the savings
decrease by 10%, then what will be the (a) 175 (b) 200
(c) 220 (d) 250
an by
percentage increase in his expenditure?
jk?ko viuh vk; dk 80» [kpZ djrk gSA ;fn mldh 43.
vk; 12» ls c<+ tkrh gS vkSj cpr 10» de gks
A company has undergraduate and
graduate employee. The average salary of

n
each graduate employee is ` 16550 and
tkrh gS] rks mlds O;; esa izfr'kr o`f¼ Kkr djsaA undergraduate employee is ` 11950,

ja
CGL Mains 11 September 2019 average salary of workers in company is
R s
(a) 20.5% (b) 16% ` 14750 if there are total 575 worker in
company then find out total number of
a th

(c) 17.5% (d) 22%

graduate employee in company?

PERCENTAGE ,d daiuh esa vaMj xzstq,V vkSj xzstq,V deZpkjh gSaA

izR;sd xzstq,V deZpkjh dh vkSlr ‘vk;
16550 gS]
ty a

MISCELLANEOUS QUESTIONS tcfd vaMj xzstq,V deZpkjh dh vkSlr vk;

` 11950
gSA tcfd deZpkfj;ksa dh vkSlr vk;` 14750 gSA
di M

40. There are 2 types coins in a box 25p and

50p. The total money in box is ‘ 42 and ;fn daiuh esa dqy deZpkfj;ksa dh la[;k 575 gS rks
the total number of coins is 120. Find the daiuh esa xzstq,V deZpkfj;ksa dh la[;k Kkr djsaA
number of 25p coins. (a) 280
fdlh ckWDl esa 25 iSls vkSj 50 iSls ds nks izdkj ds (b) 350
flDds gSaA ckWDl esa dqy ` 42/ugS vkSj flDdksa (c) 301
dh dqy la[;k 120 gSA 25 iSls ds flDds dh la[;k (d) 322
crkb,A 44. The income of A is 50% more than that
of B. If the income of A is increased by
(a) 72 (b) 48
40% and the income of B is increased by
(c) 52 (d) 60
90%, then the percentage increase in
41. There are 2 types coins in a box 25p and their combined income will be :
50p the total money in box is ` 36 and
A

A dh vk; B dh vk; ls 50» vf/d gSA ;fn A

the total number of coin is 90. If the
number of coins are interchanged then dh vk; 40» ls c<+k nh tk, vkSjB dh vk; 90»
find the total money. ls c<+k nh tk, rks mudh la;qDr vk; esa fdrus izfr'kr
fdlh ckWDl esa 25 iSls vkSj 50 iSls ds nks izdkj ds dh o`f¼ gksxh\
flDds gSaA ckWDl esa dqy ` 36 /u
gS vkSj flDdksa dh SSC CGL 6 June 2019 (Morning)
dqy la[;k 90 gSA ;fn flDdksa dh la[;k dks vkil (a) 64
esa cny fn;k tk, rks vc dqy /u fdruk gksxk\ (b) 55
(a) ` 30 (b) ` 35 (c) 60
(c) ` 31.5 (d) ` 40 (d) 70

[6]
45. Raghav spends 80% of his income. If his nks d{kkvksa
M rFkk N ds vkSlr vad Øe'k% 25
income increases by 12% and the savings rFkk 40 gS vkSj izkIr lexz vkSlr 30 gSAMd{kk
decrease by 10%, then what will be the
rFkkN ds Nk=kksa dk vuqikr gS %
percentage increase in his expenditure?
SSC MTS 9 August 2019 (Evening)
jk?ko viuh vk; dk 80» [kpZ djrk gSA ;fn mldh
(a) 2 : 1 (b) 5 : 6
vk; 12» ls c<+ tkrh gS vkSj cpr 10» ls de gks (c) 1 : 2 (d) 5 : 3
tkrh gS] rks mlds O;; esa izfr’kr o`f¼ Kkr djsaA
50. In a company with 600 employees, the
SSC CGL Tier II (11 September 2019) average age of male employees is 42 years
(a) 20.5 (b) 16 and that of female employees is 41 years.
(c) 17.5 (d) 22 If the average age of all the employees in
46. A spends 65% of his income. His income the company is 41 years and 9 months,
has increased by 20.1% and his then the number of female employees is :
expenditure has increased by 25%. His 600 deZpkfj;ksa okyh daiuh esa iq#"k deZpkfj;ksa dh
savings : vkSlr vk;q 42 o"kZ gS vkSj efgyk deZpkfj;ksa dh
A viuh vk; dk 65» [kpZ djrk gSA mldh vk; vkSlr vk;q 41 o"kZ gSA ;fn daiuh esa lHkh deZpkfj;ksa
20-1» ls c<+ tkrh gS vkSj O;; esa 25» dh o`f¼ dh vkSlr vk;q 41 o"kZ vkSj 9 eghus gS] rks efgyk

r
gks tkrh gSA mldh cpr gS % deZpkfj;ksa dh la[;k gS %

si
SSC CGL Tier II (12 September 2019) SSC CHSL 16/10/2020 (Morning)
(a) increase by 11% (b) increase by 5% (a) 150 (b) 250

47.
an by
(c) Decrease by 5% (d) Decrease by 11%
Monika spends 72% of her income. If her 51.
(c) 450 (d) 350
The average of 21 data is 36 out of which

n
income increase by 20% and savings the first 12 data are having an average of
increase by 15%, then her expenditure 15. The average of the rest 9 data is :

ja
increase by (correct to 1 decimal place) 21 vkadM+ksa dk vkSlr 36 gS ftlesa ls igys 12
R s
eksfudk viuh vk; dk 72» [kpZ djrh gSA ;fn vkadM+ksa dk vkSlr 15 gSA 'ks"k 9 vkadM+ksa dk vkSlr g
mldh vk; 20» c<+ tk, vkSj mldh cpr 15»
a th

SSC MTS 14 August 2019 (Evening)

c<+ tk, rks mlds O;; esa fdrus dh o`f¼ gksxh\ (a) 87 (b) 65
(,d n'keyo LFkku rd lgh) (c) 64 (d) 50
52. The average weight of 16 boys in a class
ty a

(a) 20.8% (b) 20.2%

(c) 21.9% (d) 19.8% is 60.25 kg and that of the remaining 10
boys is 45.75 kg. The average weight of
di M

2
48. A student answered rd of total all boys in the class is :
3
questions. 60% right. How much percent fdlh d{kk esa 16 yM+dksa dk vkSlr otu 60-25
he should answer rest questions right so fdxzk gS rFkk 'ks"k 10 yM+dksa dk vkSlr otu 45-75
that he may get 70% marks in fdxzk- gSA bl d{kk esa lHkh yM+dksa dk vkSlr otu
examination. D;k gksxk\
2 SSC CPO 16 March 2019 (Evening)
,d Nk=k us dqy ç'uksa esa dk
ls mÙkj fn;kA 60»
3 (a) 56.27 (b) 55.37
lghA mls 'ks"k ç'uksa dk fdrus çfr'kr lgh mÙkj (c) 54.67 (d) 53.76
nsuk pkfg, rkfd og ijh{kk esa 70» vad çkIr dj53. In a class of 50 students, 46% are girls
ldsA and the remaining are boys. The average
(a) 25% (b) 60% of the boys marks is 58 and that of the
A

(c) 80% (d) 90% girls is 62. What are average marks of the
whole class?
WEIGHTED AVERAGE BASED 50 Nk=kksa dh ,d d{kk esa 46» yM+fd;k¡ gSa rFkk 'ks"
yM+ds gSaA yM+dksa ds vadksa dk vkSlr 58 gS rF
QUESTIONS yM+fd;ksa ds vadksa dk vkSlr 62 gSA iwjh d{kk dk
49. The average marks of two classes M and vkSlr vad Kkr djsaA
N are 25 and 40 respectively and the SSC CGL 11 June 2019 (Evening)
overall average is 30. The ratio of the (a) 59.84 (b) 60.65
students of classes M and N is : (c) 60.38 (d) 60.12

[7]
54. The number of students in classes A and 58. The average age of 120 students in a
B are 60 and 70, respectively. The group is 13.56 years, 35% of the number
average score in mathematics of students of students are girls and the rest are boys.
in B is 57 and that of all students in A If the ratio of the average age of boys and
and B is 63. What is the average score of girls is 6.5, then what is the average age
students in A? (in years) of the girls?
d{kkA vkSj B esa Nk=kksa dh la[;k Øe'k% 60 vkSj ,d lewg ds 120 Nk=kksa dh vkSlr mez 13-56 o"kZ
70 gSAB esa xf.kr esa Nk=kksa dk vkSlr vad 57 rFkk
gSA Nk=kksa esa 35» yM+fd;k¡ gSa rFkk 'ks"k yM+ds
A vkSj B ds lHkh Nk=kksa dk xf.kr esa vkSlr vad
yM+dksa vkSj yM+fd;ksa dh vkSlr mez 6dk%5vuqikr
63 gSA
A ds Nk=kksa dk vkSlr vad Kkr djsaA
SSC MTS 22 August 2019 (Afternoon)
gS] rks yM+fd;ksa dh vkSlr mez (o"kZ esa) fdruh gS\
CGL Tier II (13 September 2019)
(a) 69 (b) 70
(c) 68 (d) 71 (a) 12 (b) 11.6
55. In a class of 60 students, 40% are girls. (c) 10 (d) 14.4
The average weight of the whole class is 59. In a class of 80 students, the ratio of the
59.2 kg and the average weight of the urban to the rural is 5 : 3. In a test, the
girls is 55 kg. What is the average weight average score of the rural students is 40%

r
of the boys? more than that of the urban students. If
60 Nk=kksa dh ,d d{kk esa 40» yM+fd;k¡ gSaA iwjh

si
the average score of all the students is
d{kk dk vkSlr otu 59-2 fdxzk gS vkSj yM+fd;ksa 69, then what is the average score of the

Kkr djsaA an by
dk vkSlr otu 55 fdxzk gSA yM+dksa dk vkSlr otu rural students?
80 Nk=kksa dh ,d d{kk esa] 'kgjh vkSj xzkeh.k dk

n
SSC CGL 12 June 2019 (Afternoon) vuqikr 5%3 gSA fdlh ijh{kk esa] xzkeh.k Nk=kksa ds
(a) 63 kg (b) 60 kg vkSlr vad 'kgjh Nk=kksa ds vkSlr vad ls 40» vfèkd
(c) 61 kg
ja (d) 62 kg FksA ;fn lHkh Nk=kksa ds vkSlr vad 69 gSa] rks xzke
R s
56. The average weight of 8 gold cons is 20 Nk=kksa ds vkSlr vad Kkr djsaA
a th

gram per coin. The average weight of 12

SSC CHSL 3 July 2019 (Evening)
coins of silver is 35 gram per coin. What
is the average weight per coin for 2 (a) 80 (b) 76
coins? (c) 92 (d) 84
ty a

8 lksus ds flDdksa dk vkSlr 20 xzke izfr flDdk

60. The number of students in section A and
gSA pk¡nh ds 12 flDdksa dk vkSlr Hkkj 35 xzke izfr section B of the class are 40 and 52
di M

flDdk gSA 2 flDds ds fy, izfr flDdk vkSlr Hkkj respectively. The average score in
fdruk gS\ mathematics of all the students is 75. If
SSC MTS 2 August 2019 (Afternoon) the average score of the students in A is
20%, more than that of students in B,
(a) 25 g (b) 29 g
then what is the average score of students
(c) 21 g (d) 31 g in B?
57. In a class of 80 students, 60% participate
in games and the rest do not. The average d{kkA vkSj d{kkB ds Nk=kksa dh la[;k Øe'k% 40
weight of the former group is 5% more vkSj 52 gSA lHkh Nk=kksa ds xf.kr esa vkSlr Ldksj 7
than that of the latter. If the average gSA ;fnA esa Nk=kksa dk vkSlrB vad esa Nk=kksa dh
1
weight of all the students is 51 kg, then rqyuk esa 20» gS] rks
B esa Nk=kksa dk vkSlr Ldksj
2 D;k gS\
what is the average weight (in kg) of the
A

former group? SSC CGL 2019 Tier II (16/11/2020)

80 Nk=kksa dh ,d d{kk esa 60» [ksyksa esa Hkkx ysrs
(a)gSa
65 (b) 63
rFkk 'ks"k [ksyksa esa Hkkx ugha ysrs gSaA igys lewg dk
(c) 71 (d) 69
vkSlr otu nwljs lewg ds vkSlr otu ls 5» vfèkd 61. The average score in Mathematics of 90
1 students of section A and B of class IX
gSA ;fn lHkh Nk=kksa dk vkSlr 51otu fdxzk gS] was 63. The number of students in A were
2
rks igys lewg dk vkSlr otu Kkr djsaA 10 more than those in B. The average
(a) 57.6 (b) 54.5 score of students in A was 30% more than
that of students in B. The average score
(c) 60 (d) 52.5
of students in B is :

[8]
 d{kk IX ds lsD'ku A vkSj B ds 90 Nk=kksa dk students is 63, then what is the average
xf.kr esa vkSlr Ldksj 63 gSA
A esa Nk=kksa dh la[;k score of the girls in mathematics?
B ls 10 vf/d FkhA A esa Nk=kksa dk vkSlrB vad ,d d{kk esa 96 Nk=k gSa] ftuesa ls yM+fd;ksa dh
ds Nk=kksa dh rqyuk esa 30» vf/dB FkkA
esa Nk=kksa la[;k yM+dksa dh la[;k ls 40» vf/d gSA yM+dksa
dk vkSlr vad gS % dk xf.kr esa vkSlr izkIrkad yM+fd;ksa ds vkSlr izkIrkad
SSC CGL 2019 Tier II (15/11/2020) ls 40» vf/d gSA ;fn xf.kr esa lHkh Nk=kksa dk
(a) 60 (b) 54 vkSlr izkIrkad 63 gS] rks xf.kr esa yM+fd;ksa dk vkSlr
(c) 50 (d) 56 izkIrkad Kkr djsaA
62. The total number of students in section SSC MTS 22 August 2019 (Evening)
A and B of a class is 110. The number of
(a) 51 (b) 54
students in section A is 10 more than
that of section B. The average score of the (c) 55 (d) 57
students in B, in a test is 20% more than 65. In a class, the number of girls is 60%
that of students in A. If the average score more than that of boys. the average
of all the students in the class is 72, then weight of the boys is 2.6 kg more than
what is the average score of the students that of girls. If the average weight of all

r
in A? the boys and girls is 50 kg, then find the
fdlh d{kk ds [kaMA vkSj B ds Nk=kksa dh dqy

si
average weight (in kg) of girls?
la[;k 110 gSA [kaM
A esa Nk=kksa dh la[;kB [kaM
ds ,d d{kk esa] yM+fd;ksa dh la[;k yM+dksa dh la[;k
an by
Nk=kksa dh la[;k ls 10 vf/d gSA fdlh ijh{kk
ds Nk=kksa ds vkSlr izkIrkaad
B esa
A ds Nk=kksa ds vkSlr
ls 60» vf/d gSA yM+fd;ksa dh rqyuk esa yM+dksa dk
vkSlr otu 2-6 fdxzk vf/d gSA ;fn lHkh yM+dksa

n
izkIrkad ls 20» vf/d gSA ;fn lHkh Nk=kksa dk vkSlr vkSj yM+fd;ksa dk vkSlr otu 50 fdxzk gS] rks
izkIrkad 72 gS] A rksds Nk=kksa dk vkSlr izkIrkad yM+fd;ksa dk vkSlr otu (fdxzk esa) fdruk gS\
Kkr djsaA
ja
R s
(a) 48.8 (b) 49.2
SSC CGL 7 June 2019 (Afternoon) (c) 49 (d) 48
a th

(a) 66 (b) 68 66. In a class of 100 students, the average

(c) 63 (d) 70 weight is 30 kg. If the average weight of
63. The total number of students in class A the girls is 24 kg and that of the boys is
ty a

and B is 96. The number of students in 32 kg, then what is the number of girls
A is 40% more than that in B. The in the class?
di M

average weight (in kg) of the students in

100 Nk=kksa dh ,d d{kk esa] vkSlr otu 30 fdxzk
B is 50% more than that of the students
in A. If the average weight of all the gSA ;fn yM+fd;ksa dk vkSlr otu 24 fdxzk gS vkSj
students in A and B taken together is 58 yM+dksa dk 32 fdxzk gS] rks d{kk esa yM+fd;ksa d
kg, then what is the average weight of the la[;k D;k gS\
students in B?
(a) 25 (b) 26
d{kkA vkSj B ds Nk=kksa dh dqy la[;k 96A gSA (c) 27 (d) 28
ds Nk=kksa dh la[;k
B ds Nk=kksa ls 40» vf/d gSA
B 67. Rita buys 5 sarees at an average cost of
d{kk ds Nk=kksa ds vkSlrAotu
ds Nk=kksa ds vkSlr ` 2250. If she buys three more sarees at
otu ls 50» vf/d gSA ;fn A vkSj A nksuksa ds an average cost of ` 2750, what will be
Nk=kksa dk dqy vkSlr otu 58 fdyksxzke BgS] rks the average (in `) of all the sarees she
ds Nk=kksa dk vkSlr otu Kkr djsaA buys?
A

SSC CHSL 2 July 2019 (Evening) jhrk us` 2250 esa vkSlr ewY; ls 5 lkfM+;ka •jhnhA
(a) 72 kg (b) 60 kg ;fn mlus rhu vkSj lkfM+;ka
` 2750 ds vkSlr ewY;
(c) 48 kg (d) 66 kg ls •jhnh rks lHkh lkfM+;ksa dk vkSlr `ewY;
esa) (
64. There are 96 students in a class, out of D;k gksxk\
which the number of girls is 40% more
(a) 2437.5
than that of the boys. the average score
in mathematics of the boys is 40% more (b) 2500
than the average score of girls. If the (c) 2450
average score in mathematics of all the (d) 2332.5

[9]
 ,d nqdkunkj rhu oLrqvksa
X, Y vkSj Z dks cspus
BOWLING AVERAGE BASED ij Øe'k% 21»] 19» vkSj 3» dh gkfu gksrh gSA
QUESTIONS ;fn X vkSjY ij dqy 20-66» rFkk Y vkSjZ ij
dqy 11» dh gkfu gqbZ rks rhuksa oLrqvksa ij gqbZ dq
68. Average run per wicket of a bowler is
11.5. In his next inning bowler took 5 gkfu » Kkr djsaA
wickets and conceded 40 run, thereby he (a) 13.12% (b) 16.16%
reduced his bowling average by 0.5. Find (c) 18.14% (d) 19.27%
the total number of wickets. 72. A shopkeeper sells three items X, Y and
,d xsanckt dk vkSlr ju çfr fodsV 11-5 gksrk gSA Z and incurs a profit of 16%, 19% and
viuh vxyh ikjh esa xsanckt us 5 fodsV fy, vkSj 28% respectively. The overall profit %
40 ju fn,] ftlls mlus vius xsanckth vkSlr esa selling X and Y items is 17% and that of
0-5 dh deh dhA fodsVksa dh dqy la[;k Kkr dhft,A Y and Z items is 22.25%. Find the overall
profit % on selling the three items?
(a) 25 (b) 35
(c) 24 (d) 23 ,d nqdkunkj rhu oLrqvksa
X, Y vkSj Z dks csprk
69. A cricketer whose bowling average is 12.4 gS vkSj mls Øe'k% 16»] 19» vkSj 28» dk ykHk

r
runs per wicket takes 5 wickets for 26 gksrk gSA ;fn
X vkSj Y ij dqy 17» rFkk Y vkSj

si
runs and thereby decreases his average by
Z ij dqy 22-25» dk ykHk gqvk gks rks rhuksa oLrqvksa
0.4 . Find total runs scored by him ?
ij gqbZ dqy ykHk Kkr djsaA
an by
,d fØdsVj ftldk xsanckth vkSlr 12-4 ju çfr
fodsV gS] 26 ju nsdj 5 fodsV ysrk gS vkSj bl
(a) 18.74% (b) 16.24%

n
(c) 20.25% (d) 13.24%
rjg mldk vkSlr 0-4 de gks tkrk gSA mlds }kjk
73. Two types of sugar worth ` 42 per kg and
cuk, x, dqy ju Kkr dhft,\ ` 46 per kg are mixed together with a
ja
R s
(a) 2500 (b) 1050 3rd variety of sugar in the ratio 3 : 3 : 9.
(c) 2400 (d) 1080 If the mixture is worth ` 47 per kg ,then
a th

the price of 3rd variety sugar per kg?

MISCELLANEOUS ` 42 izfr fdxzk vkSj
` 46 izfr fdxzk ds nks izdkj
ds phfu;ksa dks ,d rhljs izdkj ds phuh ds lkFk
70. If a man sells a pen at 21% profit and
ty a

pencil at 48% profit, he earns ` 1890 as vuqikr 3%3 %9 esa fefJr fd;k x;kA ;fn ifj.kkeh
21 feJ.k dk ewY;` 47 izfr fdxzk gS rks rhljs izdkj
di M

profit. But if he sells the pen at % ds phuh dk izfr fdxzk ewY; D;k gS\
4
profit and pencil at 15% loss then he (a) 45 (b) 49
bears no profit no loss. Find the cost (c) 44 (d) 50
price of the pen and pencil ?
74. A shopkeeper mixes 3 varieties of rice
;fn ,d O;fDr 1 isu dks 21» ij csprk gS rks costing ` 20/kg , ` 24/kg and ` 30/kg and
` 1890 dk ykHk dekrk gSA ysfdu ;fn og isu dks sells the mixture at a profit of 10% at
21 ` 27.5. How many kg of the 2nd variety
% ykHk vkSj isafly dks 15» gkfu ij csps rks will be in the mixture if 2kg of the 3rd
4
mls u rks ykHk gksxk u gkfuA isu vkSj isafly dk Ø; variety is there in the mixture?
ewY; Kkr djsaA ,d nqdkunkj pkoy dh rhu fdLeksa` 20 izfr fdxzk]
` 24 izfr fdxzk vkSj ` 30 izfr fdxzk dk feJ.k
A

(a) 10000, 4200

(b) 4000, 1400 djrk gS vkSj feJ.k dks 10» ds ykHk ij ` 27-5
(c) 5000, 1750
izfr fdxzk ij csprk gSA ;fn feJ.k esa rhljh fdLe
(d) 6000, 2100
71. A shopkeeper sells 3 items X, Y and Z
ds 2 fdxzk- pkoy gS rks nwljh fdLe ds fdrus fdxzk-
incurs a loss of 21%, 19% and 3% pkoy feJ.k esa gksaxs\
respectively. The overall loss % on selling (a) 1
X and Y items is 20.66% and that of Y (b) 3
and Z items is 11%. Find the overall (c) 5
loss% on selling three items?
(d) 6

[ 10 ]
 Answer Key
1. (c) 2.(b) 3. (a) 4. (a) 5. (a) 6. (c) 7. (b) 8. (c) 9. (a) 10. (a)

11.(d) 12.(a) 13.(d) 14.(a) 15.(c) 16.(c) 17.(d) 18.(a) 19.(c) 20.(b)

21.(b) 22.(b) 23.(c) 24.(d) 25.(d) 26.(c) 27.(b) 28.(d) 29.(a) 30.(a)

31.(a) 32.(b) 33.(c) 34.(b) 35.(a) 36.(b) 37.(b) 38.(a) 39.(c) 40.(a)

41. (c) 42.(d) 43. (b) 44. (c) 45. (c) 46. (a) 47. (c) 48. (d) 49. (a) 50. (a)

51.(c) 52.(c) 53.(a) 54.(b) 55.(d) 56.(b) 57.(d) 58. (b) 59. (d) 60. (d)

61. (b) 62.(a) 63. (a) 64. (b) 65. (c) 66.(a) 67.(a) 68.(b) 69.(d) 70.(c)

71. (c) 72.(a) 73. (b) 74. (c)

[ 11 ]
 Average

Average/vkSlr
[CLASSROOM SHEET]

TYPE - I (BASIC CONCEPT) 5. The average of 32, 34, 38, 21, 26 and x is
30. What will be the value of x?
1. The weights (in kg) of five girls of a class
are 49, 42, 61, 55 and 58. What is the 32, 34, 38, 21, 26 vkSjx dk vkSlr 30 gSA
x dk
average weight (in kg) of these five girls? eku D;k gksxk\
,d d{kk dh ikap yM+fd;ksa dk otukg
( esa ) 49] SSC CHSL 09/03/2023 (Shift-01)
42] 61] 55 vkSj 58 gSA bu ikap yM+fd;ksa dk vkSlr (a) 31 (b) 29
otu ( kg esa) Kkr djsaA (c) 27 (d) 28
SSC CGL 21/07/2023 (Shift-01) 6. The average of 29.75, 18.25 and number

r
(a) 53 (b) 54 N is 23. What is the value of number N?
la[;k 29-75] 18-25 vkSjN dk vkSlr 23 gSA la[;k

si
(c) 51 (d) 52
2. The daily earnings of a taxi driver during N dk eku D;k gS\

an by
a week are: ` 350, ` 470, ` 510, ` 550, `
560, ` 580 and ` 620. What is his average (a) 23
NTPC CBT-2 17/06/2022 (Shift-01)
(b) 19

n
daily earning (in `) for the week? (c) 17 (d) 21
,d lIrkg ds nkSjku ,d VSDlh pkyd dh nSfud vk;` 7.

ja
A shopkeeper has a sale of `5,445, `5,937,
R s
350, ` 470, ` 510, ` 550, ` 560, ` 580 vkSj` `5,865 and `6,562 for 4 consecutive days.
If he gets an average sale of `6,050 for 5
620 gSA ml lIrkg esa mldh vkSlr nSfud vk; ` esa)
(
a th

days, then his sale on the fifth day is:

fdruh gksxh\ ,d nqdkunkj dh 4 Øekxr fnuksa dh fcØh
`5]445]
ICAR Mains, 10/07/2023 (Shift-2) `5]937] `5]865 vkSj`6]562 gSA ;fn mldh 5 fnuksa
ty a

(a) 490 (b) 520 dh vkSlr fcØh `6]050 gks] rks mldh ikaposa fnu
(c) 530 (d) 510 dh fcØh Kkr dhft,A
di M

3. Find the average of the following sets of SSC CPO 04/10/2023 (Shift-01)
numbers. (a) `6,131 (b) `6,441
fuEufyf[kr la[;k leqPp;ksa dk vkSlr Kkr djsaA (c) `6,231 (d) `6,341
693, 456, 876, 532, 934, 691, 596, 398, 8. A family spends Rs.4,600 Rs.5,600
682 Rs.4,800, Rs.3,800 and Rs.6,000 on
SSC CGL TIER- II 07/03/2023 groceries in the first 5 months of the year.
How much should the family spend in the
(a) 550.50 (b) 750.80
sixth month to make the average
(c) 650.89 (d) 725.90 expenditure of the family on groceries for
4. At a courier shop, the weights of 8 parcels 6 months to Rs.4,500?
were found to be 1.5 kg, 1.25 kg, 1.35 kg,
dksbZ ifjokj o"kZ ds igys 5 eghuksa esa fdjkus ds lkeku
A

750 gm, 950 gm, 0.7 kg, 0.4 kg, and 0.5
kg. Find their average weight. ij 4]600 #i;s] 5]600 #i;s] 4]800 #i;s] 3]800
,d dwfj;j 'kkWi ij] 8 iklZyksa dk otu1.5 kg, #i;s vkSj 6]000 #i;s •pZ djrk gSA fdjkus ds lkeku
1.25 kg, 1.35 kg, 750 gm, 950 gm, 0.7 kg, ij ifjokj ds 6 eghus ds vkSlr •pZ dks 4]500 #i;s
0.4 kg, vkSj0.5 kg ik;k x;kA djus ds fy, ifjokj dks NBs eghus esa fdruk •pZ
mudk vkSlr otu Kkr dhft,A djuk pkfg,\
SSC CPO 03/10/2023 (Shift-02) NTPC CBT-2 12/06/2022 (Shift-01)
(a) 925gm (b) 700gm (a) Rs.2,200 (b) Rs.4,500
(c) 875gm (d) 900gm (c) Rs.3,500 (d) Rs.3,650

Aditya Ranjan (Excise Inspector) 1 Selected gSSelection fnyk,axs

1
 Average

9. The average of 52, 71, 43, 22, a, and b is (a) 75 (b) 70

55 and the average of 42, 45, 49, 51, 42,
(c) 68 (d) 65
c, and d is 53. What is the average of a, b,
c, and d? 14. The average of 25 numbers is 8. If each
number is multiplied by 12, then what will
52] 71] 43] 22] a vkSjb dk vkSlr 55 gS vkSj 42] be the new average be?
45] 49] 51] 42] c, vkSjd dk vkSlr 53 gSAa, b,
25 la[;kvksa dk vkSlr 8 gSA ;fn çR;sd la[;k dks
c, vkSjd dk vkSlr D;k gS\
12 ls xq.kk fd;k tk,] rks u;k vkSlr D;k gksxk\
SSC CGL 11/04/2022 (Shift- 03)
(a) 20 (b) 28
(a) 54.7 (b) 71
(c) 96 (d) 48
(c) 54 (d) 142
15. The average of 10 numbers is 42. If each
10. The average of 15 numbers is 30, while
number is increased by 5 then what will
the average of 13 of these numbers is 32.
be the new average?
If the remaining two numbers are equal,
then what is each of the two numbers? 10 la[;kvksa dk vkSlr 42 gSA ;fn çR;sd la[;k esa
15 la[;kvksa dk vkSlr 30 gS tcfd bu la[;kvksa esa ls 13 5 dh o`f¼ dh tk, rks u;k vkSlr D;k gksxk\

r
la[;kvksa dk vkSlr 32 gSA ;fn 'ks"k nks la[;k,a cjkcj gSa] SSC MTS 02/05/2023 (Shift- 02)

si
rks bu nksuksa la[;kvksa esa ls izR;sd la[;k dk eku D;k gS\(a) 42 (b) 47

an by
SSC CGL 12/04/2022 (Shift- 03) (c) 92 (d) 54
(a) 34 (b) 31 16. The average of 24 numbers is 43. If we

n
(c) 17 (d) 16 subtract a number 'M' from each number,
11. Of the three numbers, second is one-third then the average become 38. What was the

ja
of first and is also three-fourth of the third value of M?
R s
number. If the average of three numbers 24 la[;kvksa dk vkSlr 43 gSA ;fn ge çR;sd la[;k
is 112, then what is the smallest number?
a th

esa ls ,d la[;k 'M' ?kVk nsa] rks vkSlr 38 gks tkrk

rhu la[;kvksa esa ls] nwljh igyh la[;k,d&frgkbZ
dk gSAM dk eku D;k Fkk\
gS vkSj rhljh la[;k dkrhu&pkSFkkbZ gSA ;fn rhuksa la[;kvksa
SSC MTS 04/05/2023 (Shift- 01)
dk vkSlr 112 gS] rks og lcls NksVh la[;k D;k gS\
ty a

(a) 12 (b) 5
SSC CGL 19/04/2022 (Shift- 01)
(c) 7 (d) 10
di M

(a) 63 (b) 45
17. The average of 23 numbers is 81. If each
(c) 84 (d) 189
number is divided by 6 and add 2.5 to each
1 number then what will be the new average
12. If A is of C, and B is twice of A, and the
6
23 la[;kvksa dk vkSlr 81 gSA ;fn çR;sd la[;k
average of A, B and C is 30, then the
difference between A and C is: dks 6 ls foHkkftr fd;k tk, vkSj çR;sd la[;k esa
2-5 tksM+ fn;k tk, rks u;k vkSlr D;k gksxk
1
;fn A, C dk 6 gS]B, A dk nks xquk gS vkSj
A, B (a) 20 (b) 16.5
vkSjC dk vkSlr 30 gS] rksA vkSjC ds chp varj (c) 16 (d) 17
Kkr djsaA 18. Average of 8 values is 36. If 4 is subtracted
from each of the first three values and 5 is
A

SSC CPO 23/11/2020 (Shift-2)

added in the each of dhe next five values,
(a) 60 (b) 40 then what will be the new average?
(c) 80 (d) 50
8 ekuksa dk vkSlr 36 gSA ;fn igys rhu ekuksa esa ls izR;sd
13. The average of 12 numbers is 32. Each esa ls 4 ?kVk fn;k tk, vkSj vxys ik¡p ekuksa esa ls izR;sd
number is multiplied by 2 find the average
of the new set of numbers
esa 5 tksM+ fn;k tk,] rks u;k vkSlr D;k gksxk\
12 la[;kvksa dk vkSlr 32 gSA çR;sd la[;k dks 2 SSC CHSL 17/03/2023 (Shift-03)
ls xq.kk fd;k tkrk gS rks la[;kvksa ds u, lewg dk (a) 34.325 (b) 36.350
vkSlr Kkr djsa (c) 38.325 (d) 37.625

Aditya Ranjan (Excise Inspector) 2 Selected gSSelection fnyk,axs

2
 Average

19. The average of n number is 36. If each of A, B vkSj C dk vkSlr otu 77 fdyksxzke gSA ;fn
75% of the numbers is increased by 6 and A vkSj B dk vkSlr otu 68 fdyksxzke gS vkSjB
each of the remaining numbers is
decreased by 9, then the new average of vkSjC dk vkSlr otu 83 fdyksxzke gS] rksB dk
the number is : otu (fdyks esa) gS%
n la[;kvksa dk vkSlr 36 gSA ;fn bu la[;kvksa ds SSC CPO 04/10/2023 (Shift-3)
75» esa ls izR;sd dks 6 ls c<+k fn;k tk, vkSj
(a) 71 (b) 74
izR;sd 'ks"k la[;k dks 9 ls de dj fn;k tk,] rks
bu la[;kvksa dk u;k vkSlr D;k gksxk\ (c) 67 (d) 73

SSC CHSL 04/07/2019 (Shift- 01) 24. The average weight of A, B and C is 65 kg.
(a) 37.125 (b) 33.75 If the average weight of A and B is 63.5
kg, and the average weight of Aand C is
(c) 38.25 (d) 36.25
67.5 kg. then the weight of A (in kg) is:
20. The average of n numbers is 45. If 60% the
numbers are increased by 5 each and the A, B vkSjC dk vkSlr otu 65 fdxzk gSA ;fnA
remaining numbers are decreased by 10 each, vkSjB dk vkSlr otu 63.5 fdxzk gS vkSj
A vkSjC

r
then what is the average of the numbers so dk vkSlr otu 67.5 fdxzk gS] rks A dk otu
obtained?
(fdxzk esa) Kkr djsaA

si
n la[;kvksa dk vkSlr 45 gSA ;fn 60» la[;kvksa esa
ls izR;sd esa 5 tksM+ fn;k tk, vkSj 'ks"k la[;kvksa esa SSC CPO 23/11/2020 (Shift-1)

an by
ls izR;sd esa ls 10 ?kaVk fy;k tk,] rks bl izdkj (a) 65 (b) 67

n
izkIr la[;kvksa dk vkSlr D;k gksxk\
(c) 60 (d) 68
SSC CGL MAINS 03/02/2022

ja
(a) 42 (b) 43 25. Of the five subjects, the average marks of
R s
Rakesh in first 3 subjects was 75 and the
(c) 46 (d) 44 average marks in the last 3 subjects was
a th

21. The average of 15 results is 21. The 82. If his marks in the third subject was
average of the first 7 of those is 21 and 66, what was his average marks in all the 5
the average of the last 7 is 20. What is subjects?
the 8th result?
ty a

5 fo"k;ksa esa ls jkds'k ds igys 3 fo"k;ksa esa vkSlr vad

15 ifj.kkeksa dk vkSlr 21 gSA muesa ls igys 7 dk
75 Fks vkSj vafre 3 fo"k;ksa esa vkSlr vad 82 FksA ;fn
vkSlr 21 gS vkSj vafre 7 dk vkSlr 20 gSA 8oka
di M

rhljs fo"k; esa mlds vad 66 Fks] rks lHkh fo"k;ksa esa mlds
ifj.kke D;k gS\
vkSlr vad fdrus Fks\
SSC CPO 10/11/2022 (Shift-02)
SSC CHSL 10/03/2023 (Shift-03)
(a) 25 (b) 31
(c) 28 (d) 22 (a) 76 (b) 84
22. The average weight of 100 students is 34 (c) 80 (d) 81
kg. The average weight of first 49 students 26.
In a Hindi test of 100 marks, 11 students
is 34 kg and of last 50 students is 32 kg. got 78 marks, 7 students got 80 marks,
What is the weight of the 50th student? 5 students got 82 marks and 2 students
100 Nk=kksa dk vkSlr otu 34 fdxzk- gSA izFke 49 Nk=kksa
got 86 marks. What was the average marks
dk vkSlr otu 34 fdxzk- vkSj vafre 50 Nk=kksa dk in Hindi?
A

vkSlr otu 32 fdxzk- gSA 50oka Nk=k dk otu D;k gS\ 100 vadksa dh ,d fganh ijh{kk esa 11 fo|kfFkZ;ksa
SSC CHSL 14/03/2023 (Shift-04) dks 78 vad] 7 fo|kfFkZ;ksa dks 80 vad] 5 fo|kfFkZ;ksa
(a) 138 kg (b) 134 kg dks 82 vad rFkk 2 fo|kfFkZ;ksa dks 86 vad çkIr
(c) 130 kg (d) 136 kg gq,A fganh esa vkSlr vad D;k Fks\
23. The average weight of A, B and C is 77 kg. SSC Phase X 04/08/2022 (Shift- 02)
If the average weight of A and B is 68 kg
and that of B and C is 83 kg, then the (a) 84 (b) 80
weight (in kg) of B is: (c) 82 (d) 86

Aditya Ranjan (Excise Inspector) 3 Selected gSSelection fnyk,axs

3
 Average

27. In an examination of 7 papers of 100 ,d O;fDr us Rs. 36 osQ oqQN vke] lHkh ik¡p ef.M;ksa
marks each, there were 3 mathematics ls vyx&vyx Øe'k% Rs.1] Rs. 1-50] Rs. 1-80]
papers, 2 English papers and 2 Hindi
Rs. 2 rFkk Rs. 2-25 çfr vke dh nj ls •jhnsA
papers. D gets average marks of 45, 55 and
60 in mathematics, English and Hindi, rn~uqlkj] çR;sd vke dk vkSlr ewY; fdruk gS\
respectively. What are the average marks NTPC CBT-2 09/06/2022
per paper?
(a) Rs. 1.91 (b) Rs. 2.00
7 isijksa (çR;sd
100 vadksa dk) dh ,d ijh{kk esa xf.kr
(c) Rs. 1.58 (d) Rs. 1.80
ds 3 isij] vaxzsth ds2 isij vkSj fganh ds
2 isij FksA
D
dks xf.kr] vaxzsth vkSj fganh esa45Øe'k%
] 55 vkSj60 31. The average of three-digit numbers 335,
vkSlr vad çkIr gksrs gSaA çfr isij vkSlr vad D;k gSa\ 2x5, x35, 63x and 406 is 411, then find
the average of x – 1, x – 3, x + 3 and x + 5 ?
SSC CGL (PRE) 26/07/2023 (Shift-4)
(a) 56.5 (b) 52.1 rhu vadksa dh la[;k
335, 2x5, x35, 63x vkSj406
dk vkSlr 411 gS] fiQj
x – 1, x – 3, x + 3 vkSjx +
(c) 55.6 (d) 54.1
5 dk vkSlr Kkr djsa\

r
28. In a college in B.Tech. first year there are
three sections A, B and C. If number of (a) 6 (b) 3

si
students in section A, B and C are 95, 209 (c) 4 (d) 5
and 171 respectively and the average marks

an by
of section A, B and C in an exam are 83, 78
and 85 respectively. What is the average
32. If numbers 2 , 3 , 4 and 5 occur (2 + 5k),
(5k – 7), (2k – 3) and (k + 2) times,

n
marks of first year? respectively. The average of the numbers
fdlh dkWyst esa
B.Tech izFke o"kZ esa rhu vuqHkkx
A, is 2.85. Later on, the number 2 was

ja
B vkSjC gSaA ;fn vuqHkkx
A, B vkSjC esa Nk=kksa dh
rerplaced by 6 in all the places. What is the
R s
average of the new numbers?
la[;k Øe'k%95,209 vkSj171 gS vkSj ,d ijh{kk esa
a th

vuqHkkxA, B vkSjC ds vkSlr vad Øe'k%83, 78 ;fn la[;k,¡ 2 ] 3 ] 4 vkSj 5 Øe'k% (2 + 5k), (5k –
vkSj85 gSaA izFke o"kZ dk vkSlr vad D;k gS\ 7), (2k – 3) vkSj(k + 2) ckj vkrh gSaA la[;kvksa dk
(a) 80.66 (b) 81.52 vkSlr 2-85 gSA ckn esa lHkh LFkkuksa ij vad 2 ds LFkku ij
ty a

(c) 81.48 (d) 82.16 6 vafdr dj fn;k x;kA ubZ la[;kvksa dk vkSlr D;k gS\
29. In an examintion, the average score of a
di M

(a) 2.4
student was 67.6. If he would have got 27
more marks in Mathematics, 10 more (b) 3.84
marks in Computer Science,18 more marks (c) 5.25
in History and retained the same marks in
other subjects, then his average score (d) 4.75
would have been 72.6. How many paper 33. Average of the numbers a, b, c and d is
were there in the examination? 2d + 4. Also, the average of the numbers
fdlh ijh{kk esa] fdlh Nk=k ds vkSlr vad 67-6 FksA ;fn a and b, b and c, c and d are 8, 5 and 4
mls xf.kr esa 27 vf/d vad] dEI;wVj foKku esa 10 respectively. If e = a + d – 1, then what is
vf/d vad] bfrgkl esa 18 vf/d vad feyrs vkSj vU; the average of the numbers d and e?
fo"k;ksa esa leku vad feyrs] rks mlds vkSlr vad 72-6 la[;kvksa
a, b, c vkSjd dk vkSlr 2d + 4 gSA lkFk gh]
A

gksrsA ijh{kk esa dqy fdrus isij Fks\ la[;kvksa

a vkSjb, b vkSjc, c vkSjd dk vkSlr Øe'k%
(a) 11 (b) 10 8] 5 vkSj 4 gSA ;fne = a + d – 1, rksd vkSje
(c) 12 (d) 9 la[;kvksa dk vkSlr D;k gS\
30. A person bought a few mangoes of Rs. 36,
separately from all five mandis at the rate (a) 3
of Rs. 1, Rs. 1.50, Rs. 1.80, Rs. 2 and Rs. (b) 8
2.25 per mangoes respectively.
Accordingly, what is the average price of (c) 8.5
each mango? (d) 7

Aditya Ranjan (Excise Inspector) 4 Selected gSSelection fnyk,axs

4
 Average

TYPE - II (INCLUSION) 38. The average of the ages of a group of 65

men in 32 years. If 5 men join the group,
34. The average of two numbers is 46. the average of the ages of 70 men is 34
Together with a third number, the years. Then the average of the ages of
combined average of three numbers
those 5 men joined later (in years) is :
changes to 43. What is the third number?
65 iq#"kksa ds lewg dh vk;q dk vkSlr 32 o"kZ gSA
nks la[;kvksa dk vkSlr 46 gSA ,d rhljh la[;k dks ;fn 5 iq#"k lewg esa 'kkfey gksrs gSa rks 70 iq#"kks
feykus ij] rhuksa la[;kvksa dk la;qÙkQ vkSlr 43 gks
dh vkSlr vk;q 34 o"kZ gks tkrh gSA fiQj ckn esa
tkrk gSA rhljh la[;k Kkr dhft,A 'kkfey gq, mu 5 iq#"kksa dh vk;q dk vkSlr (o"kks±
NTPC CBT-2 12/06/2022 (Shift-02) esa fdruk gS\)
(a) 40 (b) 35 SSC CHSL 19/03/2020 (Shift- 01)
(c) 37 (d) 38 (a) 50 (b) 55
35. The average weight of 49 students is 53 kg. (c) 65 (d) 60
When a new student is admitted to the 39. The average age of 120 members of a society

r
class, the average decreases by 500 g. Find is 62.5 years. By addition of 30 new
members, the average age becomes 58.2

si
the weight of the new student.
years. What is the average age of newly
49 Nk=kksa dk vkSlr otu 53 fdyksxzke gSA tc ,d joined member's:

an by
u, Nk=k dks d{kk esa ços'k fn;k tkrk gS] rks vkSlr ,d lkslk;Vh ds 120 lnL;ksa dh vkSlr vk;q 62-5 o"kZ
500 xzke de gks tkrk gSA u, Nk=k dk otu Kkr gsA 30 u, lnL;ksa dks 'kkfey djus ij vkSlr vk;q 58-

n
dhft,A 2 o"kZ gks tkrh gSA u, 'kkfey gq, lnL;ksa dh vkSlr vk;q
fdruh gS\

ja
SSC CPO 04/10/2023 (Shift-3)
R s
SSC CHSL 09/03/2023 (Shift-02)
(a) 48 kg (b) 18 kg
a th

(a) 40 years (b) 41 years

(c) 28 kg (d) 38 kg (c) 39 years (d) 42 years
36. Average weight of 20 persons is 60 kg. A 40. The average age of a class of 6 girls is x
new person joins the group and average years. Four new girls having ages x – 2, x +
ty a

weight of 21 persons becomes 59 kg. What 4, x + 8 and x – 10 joins the class. What is
will be the weight of new person? the new average age of the class?
di M

20 O;fDr;ksa dk vkSlr Hkkj 60 fdxzk gSA ,d u;k O;fDr ,d d{kk dh 6 yM+fd;ksa dh vkSlr vk;q
x o"kZ gSA pkj
lewg esa 'kkfey gks tkrk gS vkSj 21 O;fDr;ksa dk vkSlrubZ yM+fd;ka ftldh vk;q Øe'k%
x – 2, x + 4, x + 8
Hkkj 59 fd-xzk- gks tkrk gSA u, O;fDr dk Hkkj fdrukrFkkx – 10 o"kZ gS d{kk esa 'kkfey gksrh gSA d{kk dh ubZ
gksxk\ vkSlr vk;q D;k gS\
SSC CHSL 09/03/2023 (Shift-02) SSC CHSL 09/03/2023 (Shift-03)
(a) x – 2 (b) x + 2
(a) 41 kg (b) 29 kg
(c) x + 5 (d) x + 1
(c) 39 kg (d) 40 kg
41. The average weight of 8 students is 48 kg.
37. Ram has an average score of 65 runs in 19 If four students of average weight 44 kg
innings in cricket matches. Find out how and four students of average weight 58 kg
many runs are to be scored by him in the 20th
A

is also added, then find the average weight

innings to raise the average score to 67. of 16 students.
jke dk fØdsV eSpksa dh 19 ikfj;ksa esa vkSlr Ldksj 658 Nk=kksa dk vkSlr otu 48 fdxzk gSA ;fn 44 fdxzk
ju gSA Kkr djsa fd vkSlr Ldksj 67 rd c<+kus ds fy, vkSlr otu okys pkj Nk=kksa] vkSj 58 fdxzk vkSlr
mls 20 oha ikjh esa fdrus ju cukusa gksaxs\ otu okys pkj Nk=kksa dks Hkh 'kkfey dj fy;k tk,]
rks 16 Nk=kksa dk vkSlr otu Kkr djsaA
SSC CGL (PRE) 25/07/2023 (Shift-1)
SSC CPO 05/10/2023 (Shift-01)
(a) 135 (b) 105 (a) 49.5 kg (b) 49 kg
(c) 115 (d) 195 (c) 48.5 kg (d) 48 kg

Aditya Ranjan (Excise Inspector) 5 Selected gSSelection fnyk,axs

5
 Average

42. The average age of 21 students in a class fMohtu A ds 8 Nk=kksa dh vkSlr ÅapkbZ
x gSA ;fn
is 14. If the age of the principal and their vkSlr ÅapkbZ 156 lseh ds 4 Nk=k 'kkfey gks tkrs gSa]
teacher who is 5 years younger than their
principal, is added, the average becomes 2
rks fMohtuA dh vkSlr ÅapkbZ
3
lseh c<+ tkrh gSA
17. Find the age of the principal in years.
,d d{kk esa 21 Nk=kksa dh vkSlr vk;q 14 gSA ;fnfMohtu A esa igys 8 Nk=kksa dh vkSlr ÅapkbZ (lseh
ç/kukè;kid vkSj muds f'k{kd] tks muds ç/kukpk;Z esa) Kkr dhft,A
ls 5 o"kZ NksVs gSa] dh vk;q tksM+ nh tk,] rks vkSlr CRPF HCM 27/02/2023 (Shift - 03)
17 gks tkrk gSA ç/kukpk;Z dh vk;q o"kks± esa Kkr dhft,A 153 2 154
1
(a) (b)
3 3
CRPF HCM 11/03/2023 (Shift - 02)
(c) 154 (d) 153
(a) 51 (b) 53
(c) 46 (d) 48
TYPE - III (EXCLUSION)
43. The average age of a group of friends is 27 46. Average of 15 numbers is 53. A number is
years. If 4 new friends whose average age removed and the average of 14 numbers now
becomes 55. which number was removed ?

r
is 25 years join them, the average age of
the entire group becomes 26 years. How 15 la[;kvksa dk vkSlr 53 gSA ,d la[;k dks fudky

si
many people were there in the group fn;k tkrk gS vkSj vc 14 la[;kvksa dk vkSlr 55 gks
initially? tkrk gSA fuEu esa ls dkSu&lh la[;k fudkyh xbZ\

an by
fe=kksa ds ,d lewg dh vkSlr vk;q 27 o"kZ gSA ;fn 4
u, fe=k ftudh vkSlr vk;q 25 o"kZ gS] muesa 'kkfey (a) 26
SSC CHSL 16/03/2023 (Shift-01)

n
(b) 23
gks tkrs gSa] rks iwjs lewg dh vkSlr vk;q 26 o"kZ (c)
gks 25 (d) 24
tkrh gSA 'kq: esa lewg esa fdrus yksx Fks\

ja
47. The average of five numbers is 30. If one
R s
SSC CGL 20/07/2023 (Shift-01) number is excluded, the average becomes
31. What is the excluded number?
a th

(a) 3 (b) 4
(c) 5 (d) 6 ikap la[;kvksa dk vkSlr 30 gSA ;fn muesa ls ,d
44. th
The average age of 10 class students is 16.5 la[;k fudky nh tk,] rks vkSlr 31 gks tkrk gSA
fudkyh XkbZ la[;k Kkr dhft,A
ty a

years. 15 new students with an average age

of 16 years join the class, thereby decreasing
SSC CGL 13/04/2022 (Shift- 01)
the average age by 0.125 years. The original
di M

strength of the class was: (a) 26 (b) 24

(c) 31 (d) 30
10 oha d{kk ds fo|kfFkZ;ksa dh vkSlr vk;q
16.5 o"kZ gSA
48. There are 15 students in a class. Their
16 o"kZ dh vkSlr vk;q okys
15 u, fo|kFkhZ d{kk esa average weight is 40 kg. When one student
'kkfey gq,] ftlls vkSlr vk;q 0.125 o"kZ de gks xbZA leaves the class, the average weight is 39.5
d{kk esa igys fdrus fo|kFkhZ Fks\ kg. What is the weight of the student who
left the class (where kg means kilogram)?
ICAR Mains, 08/07/2023 (Shift-1)
,d d{kk esa 15 fo|kFkhZ gSaA mudk vkSlr Hkkj
40 kg
(a) 54 gSA tc ,d fo|kFkhZ d{kk NksM+ nsrk gS] rks vkSlr Hkk
(b) 48 39.5 kg gks tkrk gSA d{kk NksM+us okys fo|kFkhZ d
(c) 45 Hkkj fdruk gS (tgk¡
kg dk vFkZ fdyksxzke gS) \
A

(d) 52 SSC CGL 21/07/2023 (Shift-03)

45. The average height of 8 students of (a) 47 kg (b) 42 kg
division A is x. If 4 students of average (c) 52 kg (d) 48 kg
height 156 cm join, the average height of 49. In a hotel, there are 120 staff members.
2 Their average weight is 62.5 kg. When one
division A increases by cm. Find the of the staff members leaves the hotel, the
3
average height (in cm) of the first 8 average weight is reduced by 250 g. Find
students in division A. the weight of the staff member who left
the hotel.

Aditya Ranjan (Excise Inspector) 6 Selected gSSelection fnyk,axs

6
 Average

,d gksVy esa 120 deZpkjh lnL; gSaA budk vkSlr

53. The average weight of 15 persons is
Hkkj 62-5kg gSA tc mu deZpkjh lnL;ksa esa ls increased by 1.2 kg when one of them
whose weight is 51 kg is replaced by a new
dksbZ ,d gksVy NksM+rk gS] rks vkSlr gHkkj 250man. The weight of the new man is:
de gks tkrk gSA ml deZpkjh lnL; dk Hkkj Kkr
dhft,] ftlus gksVy NksM+ fn;kA 15 O;fÙkQ;ksa dk vkSlr Hkkj1.2 rc
kg c<+ tkrk gS]
tc muesa ls ,d O;fÙkQ ftldk Hkkj 51 kg gS] dks
SSC CGL 09/12/2022 (Shift- 01)
,d u, O;fÙkQ ls cny fn;k tkrk gSA u, O;fÙkQ dk
(a) 64.25 kg (b) 78.75 kg Hkkj fdruk \gS
(c) 90.50 kg (d) 92.25 kg
SSC CGL 20/07/2023 (Shift-02)
50. The average score in Mathematics of a
class of 36 students is 60. If the top two (a) 69 kg (b) 70 kg
scores are excluded, the average goes down (c) 65 kg (d) 59 kg
by 2. If the second highest score of the
54. The average weight of three men is
class is 90, find the highest score of the
increased by 4 kg when one of them, whose
class. weight is 100 kg, is replaced by another

r
36 fo|kfFkZ;ksa dh ,d d{kk dk xf.kr esa vkSlr vad man. What is the weight of the new man?
60 gSA ;fn 'kh"kZ nks vadksa dks gVk fn;k tk,] rksrhu O;fDr;ksa ds vkSlr otu esa rc 4 fdxzk dh o`f¼

si
vkSlr 2 de gks tkrk gSA ;fn d{kk dk nwljk mPpre gksrh gS] tc muesa ls ,d O;fDr] ftldk otu 100

an by
vad 90 gS] rks d{kk dk mPpre vad Kkr dhft,A
NTPC CBT-2 17/06/2022 (Shift-2)
fdxzk gS] dks nwljs O;fDr }kjk çfrLFkkfir fd;k tkrk
gSA u, O;fDr dk otu D;k gS\

n
(a) 96 (b) 99 SSC CGL TIER- II 03/03/2023
(c) 98

ja(d) 95 (a) 107 kg. (b) 103 kg.

R s
51. The ages of four members of a family are (c) 104 kg. (d) 112 kg
a th

in the year 2010 are 'x', 'x + 12', 'x + 24'

and 'x + 36'. After some years oldest among 55. Out of 10 teachers of a school, one teacher
them was dead then average reduced by 3. retires and in place of him a new teacher
After how many years form his death, the who is 25 yeas old joins. As a result average
ty a

average age will same as in 2010? age of the teachers reduces by 3 years. Age
of the retired teacher (in yrs.) is :
o"kZ 2010 esa ,d ifjokj ds pkj lnL;ksa dh vk;q
'x', 'x
di M

,d Ldwy ds 10 f'k{kdksa esa ls ,d f'k{kd lsokfuo`Ùk

+ 12', 'x + 24' vkSj'x + 36' gSA dqN o"kks± ds ckn
gks tkrk gS vkSj mlds LFkku ij ,d u;k 25 o"khZ;
muesa ls lcls cM+s dh e`R;q gks xbZ] rks vkSlr 3 de gks
lsok xzg.k dj ysrk gSA ifj.kkeLo:i f'k{kdksa dh
x;kA mldh e`R;q ds fdrus o"kZ ckn] vkSlr vk;q 2010
vkSlr vk;q 3 o"kZ de gks tkrh gSA lsokfuo`Ùk f'k{kd
ds leku gksxh\
dh vk;q fdruh (o"kks± esa) gS\
(a) 2 years (b) 3 years
(a) 55 (b) 65
(c) 4 years (d) 6 years
(c) 45 (d) 67
TYPE- IV (REPLACEMENT)
56. The average weight of 5 men decreases by
52. The average weight of 15 people increases 3 kg when one of them weighing 150 kg
by 3.2 kg when a new person comes in is replaced by another person. Find the
A

place of one of them weighing 52 kg. The

weight of the new person.
weight of the new person is:
5 iq#"kksa dk vkSlr otu kg 3 de gks tkrk gS] tc
15 O;fÙkQ;ksa dk vkSlr otu 3-2 fdyksxzke c<+ tkrk
gStc muesa ls 52 fdyksxzke otu okys ,d O;fÙkQ ds muesa ls ,d 150kg otu okys ,d O;fDr dh txg
LFkku ij ,d u;k O;fÙkQ vkrk gSA u;s O;fÙkQ dk otu gS%nwljs O;fDr dks j[kk tkrk gSA u, O;fDr dk otu Kkr djsaA
SSC CPO 03/10/2023 (Shift-3) SSC CGL 05/12/2022 (Shift- 02)

(a) 96 kg (b) 100 kg (a) 125 kg (b) 100 kg

(c) 52 kg (d) 48 kg (c) 120 kg (d) 135 kg

Aditya Ranjan (Excise Inspector) 7 Selected gSSelection fnyk,axs

7
 Average

57. The average age of a group is increased by ,d f'kfoj esa dqN cPps gSa vkSj mudk vkSlr otu
4 years when a person of whose age is 32 40 fdxzk gSA ;fn 36 fdxzk vkSlr otu okys 5
years was replaced by a person whose age
cPps f'kfoj esa 'kkfey gksrs gSa ;k ;fn 43-2 fdxzk
is 56. Find the number of people in the group
vkSlr otu okys 5 cPps f'kfoj NksM+ nsrs gSa] rks
,d lewg dh vkSlr vk;q esa 4 o"kZ dh o`f¼ rc nksuksa ekeyksa esa cPpksa dk vkSlr otu cjkcj gksrk
gks tkrh gS tc ml lewg esa 32 o"kZ dh vk;q okys gSA f'kfoj esa çkjaHk esa fdrus cPps gSa\
,d O;fDr ds LFkku ij 56 o"kZ dh vk;q okyk dksbZ SSC CGL 23/08/2021 (Shift- 03)
vU; O;fDr 'kkfey gks tkrk gSA lewg ds lnL;ksa
(a) 35 (b) 45
dh la[;k Kkr dhft,A
SSC CHSL 24/05/2022 (Shift- 01) (c) 40 (d) 50

(a) 6 (b) 7 61. The average weight of some girls in a group

is 54.8 kg. When 5 girls of average weight
(c) 8 (d) 9
56.4 kg leave the group and 10 girls of
58. A group of students has an average weight average weight 57.5 kg join the group, then
of 42 kg. One student of weight 48 kg the average weight of the girls in the group
leaves the group and another student of

r
increases by 380 g. The number of girls,
weight 44 kg joins the group. If the new initially, in the group was:

si
average weight becomes 41.6 kg, then how
,d lewg esa dqN yM+fd;ksa dk vkSlr Hkkj 54-8 fdxzk
many students are there in the group?
gSA tc vkSlr otu 56-4 fdxzk dh 5 yM+fd;ka lewg

an by
Nk=kksa ds ,d lewg dk vkSlr otu 42 fdyksxzke gSA
48 fdyksxzke otu okyk ,d Nk=k lewg NksM+ nsrk gS
NksM+ nsrh gSa vkSj vkSlr otu 57-5 fdxzk dh 10
yM+fd;ka lewg esa 'kkfey gks tkrh gSa] rks lewg esa

n
vkSj 44 fdyksxzke otu okyk nwljk Nk=k lewg esa 'kkfeyyM+fd;ksa dk vkSlr otu 380 xzke c<+ tkrk gSA 'kq:
gks tkrk gSA ;fn u;k vkSlr otu 41-6 fdyksxzke gks esa lewg esa yM+fd;ksa dh la[;k Fkh%

ja
R s
tkrk gS] rks lewg esa fdrus Nk=k gSa\
CRPF HCM 26/02/2023 (Shift - 01)
a th

SSC MTS 13/06/2023 (Shift-02)

(a) 50 (b) 45
(a) 15 (b) 10
(c) 8 (d) 12 (c) 55 (d) 40
59. The average weight of some persons in a 62. Average weight of four men A, B, C, D is 68
ty a

group is 76 kg. If 15 persons with average kg. If 5th man E enters the group the average
weight decreases by 2 kg. The average
di M

weight 72 kg join the group or 5 persons

weight becomes 65 kg if a man F comes in
with average weight 84 kg leave the group, place of A and whose weight is 4 kg more
the average weight of the persons in the than weight of E. Find the weight of A.
group in both cases is the same. How many
persons were there in the group, initially? pkj O;fÙkQ;ksa
A] B] C rFkkD dk vkSlr 68 fdyksxzke
,d lewg esa dqN O;fÙkQ;ksa dk vkSlr Hkkj 76 fdxzk gSA tc ,d ikapoka O;fDr
E xzqi esa 'kkfey gksrk gS rks
gSA ;fn 72 fdxzk vkSlr otu okys 15 O;fÙkQ lewg vkSlr Hkkj 2 fdyksxzke de gks tkrkA gSA ds LFkku ij
esa 'kkfey gksrs gSa ;k 5 O;fÙkQ vkSlr otu 84 fdxzk,d u;s O;fDr F ftldk Hkkj E ds Hkkj ls 4 fdyksxzke
lewg NksM+ nsrs gSa] nksuksa ekeyksa esa lewg esa vf/dO;fÙkQ;ksa
gS] ds xzqi esa vk tkus ls vkSlr Hkkj 65 fdyksxzke
dk vkSlr otu leku gSA çkjaHk esa lewg esa fdrus gks tkrk gSA A dk Hkkj D;k gS\
O;fÙkQ Fks\
A

NTPC CBT-2 09/06/2022

SSC Phase IX 2022
(a) 64 kg (b) 74 kg
(a) 50 (b) 30
(c) 45 (d) 25 (c) 60 kg (d) 70 kg
60. There are some children in a camp and 63. A is the average of 10 given numbers. B is
their average weight is 40 kg. If 5 children the average after 2 of the numbers were
with average weight 36 kg join the camp replaced by 3 other different numbers. The
or if 5 children with average weight 43.2
average of the removed numbers is 48 and
kg leave the camp, the average weight of
the average of the newly included numbers is
children in both cases is equal. How many
children are there in the camp, initially? 56. If A + B = 438, then the value of A - B is:

Aditya Ranjan (Excise Inspector) 8 Selected gSSelection fnyk,axs

8
 Average

A nh xbZ 10 la[;kvksa dk vkSlr gSA 2 la[;kvksa dks 360 fo|kfFkZ;ksa dh ,d d{kk20

esa
yM+fd;k¡ gSaA d{kk esa
vU; fHkUu la[;kvksa ls çfrLFkkfir djus dsB ckn yM+dksa dk vkSlr 40 Hkkj
kg gS] tcfd lHkh yM+fd;ksa
vkSlr gSA gVkbZ xbZ la[;kvksa dk vkSlr 48 gS vkSjdk vkSlr Hkkj35 kg gSA laiw.kZ d{kk dk vkSlr Hkkj
ubZ
( kg esa) (nks n'keyo LFkkuksa rd lgh) D;k gS\
'kkfey la[;kvksa dk vkSlr 56 gSAA;fn
$ B ¾ 438 gS]
SSC CGL (PRE) 24/07/2023 (Shift-2)
rksA & B dk eku gS%
(a) 36.67 (b) 38.33
SSC PHASE XI 27/06/2023 (Shift-02) (c) 33.33 (d) 40.67
(a) 21 (b) 14 67. The average marks obtained by 80 students
in an examination is 50. If the average
(c) 12 (d) 26
marks of passed students is 55 and the
TYPE- V (ALLIGATION) number of students who failed the
64. Average of the marks of 132 students of a examination are 30, then what is the
college is 50. If the average of the marks of average marks of students who failed the
the passed students is 55 and the average examination?
of the marks of the failed students is 35, ,d ijh{kk esa 80 Nk=kksa }kjk izkIr fd, x, vkSlr vad
50 gSA ;fn mÙkh.kZ Nk=kksa ds vkSlr vad 55 gSa vkSj ijh

r
then what will be the respective ratio of the
total marks of passed students and the total esa vuqÙkh.kZ gksus okys Nk=kksa dh la[;k 30 gS] rks ijh

si
marks of failed students?
vuqÙkh.kZ Nk=kksa ds vkSlr vad D;k gS\
,d dkWyst ds 132 Nk=kksa ds vadksa dk vkSlr 50 gSA ;fn

an by
SSC CHSL 21/03/2023 (Shift-04)
mÙkh.kZ Nk=kksa ds vadksa dk vkSlr 55 gS vkSj vuqÙkh.kZ
(a) 41.66 (b) 46.66
Nk=kksa ds vadksa dk vkSlr 35 gS] rks mÙkh.kZ Nk=kksa ds dqy

n
(c) 40.33 (d) 52.33
vadksa vkSj vuqÙkh.kZ Nk=kksa ds dqy vadksa 68. dk Øe'k%earned an average of Rs.6250 per
Sunidhi
vuqikr D;k gksxk\

ja
month during the part 12 months. During
R s
the first 10 months her average earnings
SSC CHSL 14/03/2023 (Shift-01) per month was Rs.5800. What was
a th

(a) 1 : 3 (b) 11 : 7 Sunidhi's average earnings per month

(c) 33 : 7 (d) 21 : 8 during the last two months of the period?

65. Rakesh runs a coaching institute having 50 fiNys 12 eghuksa ds nkSjku lqfuf/ us vkSlru 6250
ty a

faculty members. The average monthly #i;s çfr ekg dh dekbZ dhA igys 10 eghus ds nkSjku]
salary of 35 faculty members is Rs. 37,500. mldh vkSlr dekbZ 5800 #i;s çfr ekg FkhA vafre
di M

What will be the average monthly salary (in nks eghuksa dh vof/ ds nkSjku lqfuf/ dh çfr ekg
Rs.) of the other 15 faculty members, if the vkSlr dekbZ fdruh Fkh\
average monthly salary of all the 50 faculty
NTPC CBT-2 12/06/2022 (Shift-02)
members is found to be Rs.30,000?
(a) Rs.8500 (b) Rs.7750
jkds'k ,d dksfpax laLFkku pykrk gS ftlesa 50 ladk; (c) Rs.8750 (d) Rs.8250
lnL; gSaA 35 ladk; lnL;ksa dk vkSlr ekfld osru 69. The average height of girls in a group is 154
cm and the average height of boys in the
37]500 #i;s gSA ;fn lHkh 50 ladk; lnL;ksa dk vkSlr
group is 3 cm more than the average height
ekfld osru 30]000 #i;s ik;k tkrk gS] rks vU; 15 of all the boys and girls in the group. if the
ladk; lnL;ksa dk vkSlr ekfld osru (#i;s esa) D;k number of girls is 25% less than the number
gksxk\ of boys, then what is the average height
A

(in cm) of the boys?

SSC CPO 05/10/2023 (Shift-3)
,d lewg esa yM+fd;ksa dh vkSlr ÅapkbZ
154 lseh gS vkSj
(a) 12,000 (b) 13,000 lewg esa yM+dksa dh vkSlr ÅapkbZ lewg ds lHkh yM+dksa
(c) 12,500 (d) 13,500 yM+fd;ksa dh vkSlr ÅapkbZ 3 lseh
ls vf/d gSA ;fn
66. In a class of 60 students, 20 are girls. The yM+fd;ksa dh la[;k yM+dksa dh la[;k
25%lsde gS] rks
average weight of the boys in the class is yM+dksa dh vkSlr ÅapkbZ (lseh esa) D;k gS\
40 kg, while that of all the girls is 35 kg.
What is the average weight (in kg) of the ICAR Mains, 07/07/2023 (Shift-1)
entire class (correct to two decimal (a) 159 (b) 158
places)? (c) 161 (d) 160

Aditya Ranjan (Excise Inspector) 9 Selected gSSelection fnyk,axs

9
 Average

70. Out of 72 students in a class, the number 74. The average of the marks of 25 students
of boys is 40% more than the number of in a class, in an examination was
girls. The average score of all the students calculated to be 19. Later, the teacher
in a test is 63. If the average score of the realized that the marks of two students
girls is 30% more than that of the boys, were taken as 18 and 19 respectively,
then what is the average score of the girls? instead of 14 and 15. Find the new actual
,d d{kk esa 72 fo|kfFkZ;ksa esa ls] yM+dksa dh la[;k
average marks of the class.
yM+fd;ksa dh la[;k ls 40» vf/d gSA ,d ijh{kk esa ,d ijh{kk eas d{kk ds 25 Nk=kksa ds vadksa dk vkSlr
lHkh fo|kfFkZ;ksa ds vkSlr vad 63 gSaA ;fn yM+fd;ksa
19dsFkkA ckn eas] f'k{kd us eglwl fd;k fd nks
vkSlr vad] yM+dksa dh rqyuk esa 30» vf/d gksa] rksNk=kksa ds vad 14 vkSj 15 ds ctk; xyrh ls Øe'k%
yM+fd;ksa ds vkSlr vad fdrus gSa\ 18 vkSj 19 fy, x, FksA d{kk dk u;k okLrfod
ICAR Mains, 07/07/2023 (Shift-3) vkSlr vad Kkr dhft,A
(a) 71.5 (b) 74.1 SSC CGL 01/12/2022 (Shift- 02)
(c) 72.8 (d) 70.2 (a) 17.43 (b) 16.56

r
TYPE - VI (WRONGLY ENTERED DATA) (c) 18.68 (d) 17.65

si
71. The average of 36 numbers was found to 75. A student finds the average of ten 2-digit
be 45. Later, it was detected that 84 was numbers. While copying numbers by

an by
misread as 48. Find the correct average of
the given numbers.
mistake, he writes one number with its
digits interchanged. As a result his answer

n
is 2.7 less than the correct answer. The
36 la[;kvksa dk vkSlr 45 ik;k x;kA ckn esa ;g ik;k
difference of the digits of the number, in
x;k fd 84 dks xyrh ls 48 i<+ fy;k x;k FkkA nh xbZ

ja
which he made mistake, is :
R s
la[;kvksa dk lgh vkSlr Kkr djsaA ,d fo|kFkhZ 10] 2 vadksa dh la[;kvksa dk vkSlr
a th

SSC CGL 14/07/2023 (Shift-3) fudkyrk gSA mlesa ls ,d la[;k xyrh ls cnys gq,
(a) 58 (b) 48
vadksa ds lkFk fy[k nsrk gS ftlls mldk vkSlr 2-7
(c) 46 (d) 56
de gks tkrk gSA cnyh gqbZ la[;k ds vadksa dk varj
72. The average of 45 numbers was found to
ty a

be 39. Later on, it was detected that a Kkr dhft,A

number 65 was misread as 56. Find the (a) 3 (b) 5
di M

correct average of the given numbers. (c) 4 (d) 2

45 la[;kvksa dk vkSlr 39 ik;k x;kA ckn esa] ;g76. Average marks of 25 students is 40. One
irk pyk fd la[;k 65 dks xyrh ls 56 i<+ fy;k student got 20 marks instead of 60 and
x;k FkkA nh xbZ la[;kvksa dk lgh vkSlr Kkr dhft,A other student got 90 marks in place of 80.
The number of student wrongly read as 25
SSC CPO 05/10/2023 (Shift-02)
instead 20. Find the true average.
(a) 36.2 (b) 37.2
(c) 38.2 (d) 39.2
25 Nk=kksa ds vkSlr vad 40 gSA ,d fo|kFkhZ 60 ds
73. The average of 16 numbers is 35. It was LFkku ij 20 vad izkIr djrk gS vkSj ,d vU; Nk=k
found later that four numbers 18, 17, 24 80 ds LFkku ij 90 vad izkIr djrk gSA Nk=kksa dh
and 35 were taken by mistake. What is the la[;k 20 dh txg xyrh ls 25 i<+h tkrh gSA okLrfod
A

new average after removing these vkSlr Kkr djsaA

numbers'?
(a) 51.5 (b) 52
16 la[;kvksa dk vkSlr 35 gSA ckn esa irk pyk fd pkj
la[;k,¡ 18] 17] 24 vkSj 35 xyrh ls bu la[;kvksa esa (c) 51 (d) 50
'kkfey dj yh xbZ FkhA bu la[;kvksa dks gVkus 77. ds cknIn an exam, the average marks was found to
be 50. After deducing computational errors
u;k vkSlr D;k gS\
the marks of the 100 candidates had to be
SSC CHSL 14/03/2023 (Shift-02) changed from 90 to 60 each and the average
(a) 38.83 (b) 42.33 came down to 45 marks. The total number
(c) 46.66 (d) 33.33 of candidates who took the exam, were :

Aditya Ranjan (Excise Inspector) 10 Selected gSSelection fnyk,axs

10
 Average

,d ijh{kk esa vadksa dk vkSlr 50 Kkr gqvkA dE;wVs'kuy TYPE - VII (AGES)
=kqfV;ka esa dVkSrh djus ds ckn 100 Nk=kksa ds vad cny
81. 5 years ago, the average age of A, B, C and
dj 90 ls 60 dj fn;s x;s ftlds dkj.k vadksa dk D was 45 years. When X is added then the
vkSlr ?kVdj 45 gks x;k rks ijh{kk esa lfEefyr gksus average of all five becomes 49 years. What
okys dqy Nk=kksa dh la[;k Fkh & is the present age of X?
(a) 300 (b) 600 5 o"kZ igysA, B, C, D dh vkSlr vk;q 45 o"kZ
(c) 200 (d) 150
78. Several students have taken an exam.
FkhA
X dks tksM+us ij ik¡pksa dh orZeku vkSlr vk;q
There was an error in the answer key which 49 o"kZ gks tkrh XgSA
dh orZeku vk;q D;k gS\
affected the marks of 48 students, and (a) 64 years (b) 48 years
their average marks reduced from 78 to 66.
(c) 45 years (d) 40 years
The average of remaining students
increased by 3.5 marks. This resulted the 82. The average age of a husband and a wife
reduction of the average of the all students was 27 years when the child was born. The
by 4.5 marks. The number of students that average age of the husband, wife and a new
attended the exam is : born child is 21 years now. The present

r
dbZ Nk=kksa us ,d ijh{kk nh gSA mÙkj dqath esa ,dage
=kqfV
of the child is:

si
Fkh] ftlus 48 Nk=kksa ds vadksa dks izHkkfor fd;k vkSj
ifr ,oa iRuh dh vkSlr vk;q 27 o"kZ Fkh] tc cPps dk
muds vkSlr vad 78 ls ?kVdj 66 gks x;sA 'ks"k Nk=kksatUe gqvk FkkA vc ifr] iRuh ,oa cPps dh orZeku

an by
ds vkSlr esa 3-5 vad dh o`f¼ gqbZA blls lHkh Nk=kksavkSlr vk;q 21 o"kZ gSA cPps dh orZeku vk;q Kkr djsaA
ds vkSlr esa 4-5 vad dh deh vk;hA ijh{kk esa 'kkfey (a) 4 years

n
(b) 3 years
gksus okys Nk=kksa dh la[;k gS %
(c) 2 years (d) 1 years
(a) 96 (b) 84

ja 83. The current average age of a family of five

R s
(c) 93 (d) 100
79. While finding the average marks of a class, members is 24. If the present age of the
a th

Vikas’s marks were wrongly entered as 98 youngest member in the family is 8 years,
in place of 89. Due to this error, the what was the average age of the family
average marks of the class were 0.25 more members just before the birth of this
than the actual average. What is the youngest member?
ty a

number of students in the class? ik¡p lnL;ksa okys ifjokj dh orZeku vkSlr vk;q
,d d{kk ds vkSlr vad Kkr djrs le;] fodkl 24 o"kZ gSA ;fn ifjokj ds lcls NksVs lnL; dh
di M

ds vad 89 ds LFkku ij xyrh ls 98 ds :i eas orZeku vk;q 8 o"kZ gS] rks bl lcls NksVs lnL; ds
ntZ gksx, FksA bl =kqfV ds dkj.k] d{kk ds vkSlr tUe ds Bhd igys ifjokj ds lnL;ksa dh vkSlr
vad] okLrfod vkSlr ls 0-25 vf/d FksA d{kk esa
vk;q D;k Fkh\
Nk=kksa dh la[;k D;k gS\
SSC CGL 08/12/2022 (Shift- 04) SSC MTS 07/07/2022 (Shift- 01)
(a) 32 (b) 38 (a) 24 years (b) 20 years
(c) 34 (d) 36 (c) 28 years (d) 16 years
80. A student‘s marks were wrongly entered as
65 instead of 45. Due to this, the average 84. The average age of Abhay, his wife and Their
child 6 years ago was 12 years and that of
1 his wife and their child 8 years ago was 30
marks for the class got increased by .
A

3 years. Find the present age of Abhay.

The number of students in the class is: vHk;] mldh iRuh vkSj muds cPps dh vkSlr vk;q 6
,d Nk=k ds vad 45 ds LFkku ij xyrh ls 65 ntZ o"kZ iwoZ 42 o"kZ Fkh vkSj 8 o"kZ iwoZ mudh iRuh vksj
dj fn, x,A blds dkj.k d{kk ds vkSlr vad esa cPps dh vkSlr vk;q 30 o"kZ FkhA vHk; dh orZeku vk;q
1 Kkr dhft,A
dh o`f¼ gks xbZA d{kk eas Nk=kksa dh la[;k gSA
3 SSC CHSL 20/03/2023 (Shift-04)
SSC CGL 08/12/2022 (Shift- 03) (a) 68 years (b) 63 years
(a) 40 (b) 20
(c) 64 years (d) 66 years
(c) 60 (d) 30

Aditya Ranjan (Excise Inspector) 11 Selected gSSelection fnyk,axs

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 Average

85. Six years ago, the average of the ages of TYPE - VIII (NUMBERS)
Ravi, Mohan and Govind was 32 years. If
Shyam joins them now, the average of the 88. What is the average of all the natural
ages of all four of them is 36 years. The number from 49 to 125?
present age of Shyam is : 49 ls 125 rd dh lHkh çkÑr la[;kvksa dk vkSlr
Ng lky igys jfo] eksgu vkSj xksfoan dh mez dk D;k gS\
vkSlr 32 lky FkkA vxj ';ke muds lkFk vk tk;s] (a) 85 (b) 87
rks mu pkjksa dh mez dk vkSlr 36 lky gSA ';ke (c) 88 (d) 86
dh orZeku mez gS % 89. What is the average of squares of first 10
CHSL 14/10/2020 (Shift- 01) natural numbers?

(a) 35 years (b) 32 years çFke 10 çkÑfrd la[;kvksa ds oxks± dk vkSlr D;k
(c) 40 years (d) 30 years gS\
86. The average age of 5 children of a family is (a) 55.5 (b) 45.6

r
15 years. Average age of children together (c) 38.5 (d) 40.5

si
with their father and mother is 25 years. If 90. Find the average of square of first 20
the father is older than the mother by 4 natural numbers.

an by
years, then find the age of mother (in years).
igyh 20 çkÑfrd la[;kvksa ds oxZ dk vkSlr Kkr
,d ifjokj ds 5 cPpksa dh vkSlr vk;q 15 o"kZ gSA cPpksadhft,A

n
dh muds firk vkSj ekrk lfgr vkSlr vk;q 25 o"kZ gSA (a) 287 (b) 143.5

ja
;fn firk] ekrk ls 4 o"kZ cM+s gSa] rks ekrk dh vk;q (o"kks±
R s
(c) 387 (d) 193.5
esa) Kkr dhft,A 91. Find the average of cube of first 10 natural
a th

SSC CHSL 15/03/2023 (Shift-01) numbers?

(a) 44 (b) 48 çFke 10 çkÑr la[;kvksa ds ?ku dk vkSlr Kkr dhft;s\
ty a

(c) 46 (d) 52 (a) 302.5 (b) 301.5

87. 6 years ago, the average age of the four (c) 225.5 (d) 120.5
di M

members of a family was 15 years. In the 92. Find the average of cubes of first 49
meantime, two children were born in that positive integers.
family. However, the present average age
igys 49 /ukRed iw.kkZadksa ds ?ku dk vkSlr Kkr
of the members of that family is still the
same as it was 6 years ago. If there is a dhft,A
difference of 2 years in the ages of the (a) 30625 (b) 1225
children, then what is the age of the elder (c) 30125 (d) 6235
child?
93. Find the average of first 50 even numbers.
6 o"kZ iwoZ ,d ifjokj ds pkj lnL;ksa dh vkSlr vk;q igyh 50 le la[;kvksa dk vkSlr Kkr dhft,A
15 o"kZ FkhA blh chp ml ifjokj esa nks cPpksa dk(a) 47 (b) 49
A

tUe gqvkA gkyk¡fd] ml ifjokj ds lnL;ksa dh orZeku

(c) 51 (d) 53
vkSlr vk;q vHkh Hkh ogh gS tks 6 o"kZ igys FkhA ;fn
94. What is the sum of all two digit even
cPpksa dh vk;q esa 2 o"kZ dk varj gS] rks cM+s cPpsnumbers?
dh
vk;q D;k gS\ nks vadksa dh lHkh le la[;kvksa dk ;ksx fdruk gksrk gS\
CRPF HCM 23/02/2023 (Shift - 01) SSC CHSL 15/03/2023 (Shift-01)
(a) 5 years (b) 2 years (a) 2520 (b) 2470
(c) 4 years (d) 3 years (c) 2430 (d) 2410

Aditya Ranjan (Excise Inspector) 12 Selected gSSelection fnyk,axs

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 Average

95. The average of odd numbers upto 100 is 101. 10 Consecutive numbers are given. If the
average of the two numbers given in the
100 rd dh fo"ke la[;kvksa dk vkSlr gS&
middle is 13.5, then what is the sum of the
(a) 50.5 (b) 50 first 6 numbers?
(c) 49.5 (d) 49 10 Øec¼ la[;k,¡ nh xbZ gSA ;fn chp esa nh xbZ nks
96. The average of the first eight odd natural la[;kvksa dk vkSlr 13-5 gS] rks igyh 6 la[;kvksa dk
numbers is: ;ksx D;k gS\
igyh vkB fo"ke izkÑr la[;kvksa dk vkSlr Kkr dhft,A SSC CHSL 14/03/2023 (Shift-03)
SSC Phase X 01/08/2022 (Shift- 03) (a) 58 (b) 55
(a) 8 (b) 11 (c) 67 (d) 69
(c) 9 (d) 10 102. The average of 7 consecutive natural
numbers is K, then what will be the average
97. What is the average of the first six prime
of next 7 consecutive natural numbers?
numbers?
7 Øekxr çkÑfrd la[;kvksa dk vkSlrk gS rks

r
çFke Ng vHkkT; la[;kvksa dk vkSlr D;k gS\
vxyh Øekxr 7 çkÑfrd la[;kvksa dk vkSlr D;k

si
SSC CPO 05.10.2023 (Shift-3)
gksxk\

an by
2 5
(a) 6 (b) 6 (a) K (b) K + 7
3 6
(c) K + 1 (d) K + 49

n
1 1
(c) 6 (d) 6 103. The average of five consecutive natural
6 3

ja
numbers is 12. What will be the average of
R s
98. The average of all prime numbers between the seven numbers if the next two natural
32 and 69 is: numbers are also included?
a th

32 vkSj 69 ds chp dh lHkh vHkkT; la[;kvksa dk ik¡p Øekxr çkÑfrd la[;kvksa dk vkSlr 12 gSA ;fn
vkSlr _______ gksxkA vxyh nks çkÑfrd la[;kvksa dks Hkh 'kkfey dj fy;k
tk, rks lkr la[;kvksa dk vkSlr D;k gksxk\
ty a

SSC CGL (PRE) 27/07/2023 (Shift-3)

(a) 52.5 (b) 60 NTPC CBT-2 15/06/2022 (Shift-1)
di M

(c) 51 (d) 56.5 (a) 14 (b) 13

99. The average of a set of 18 consecutive (c) 15 (d) 13.5
integers is 22.5. What is the largest integer 104. The average of nine consecutive numbers
in the set? is n. If the next two numbers are also
18 Øfed iw.kk±dksa ds ,d leqPp; dk vkSlr
22.5 gSA included the new average will
fuEu esa ls dkSu&lk leqPp; dk lcls cM+k iw.kk±d gS\ 9 Øekxr la[;kvksa dk vkSlrn gSA ;fn vxyh nks
SSC CGL 18/04/2022 (Shift- 03) la[;kvksa dks Hkh 'kkfey fd;k tkrk gS rks u;k vkSlr
(a) 13 (b) 17 D;k gksxk\
(c) 31 (d) 14 (a) Increase by 2/2 ls c<s+xk
A

100. Average of 17 consecutive natural numbers (b) Remain the same/leku jgsxk
is 41. What is the smallest number among
(c) Increase by 1.5/1-5 ls c<+sxk
these numbers?
17 Øekxr izkÑr la[;kvksa dk vkSlr 41 gSA bu la[;kvksa (d) Increase by 1/1 ls c<s+xk
esa lcls NksVh la[;k D;k gS\ 105. The average of 5 consecutive natural
SSC CHSL 10/03/2023 (Shift-04) numbers is M. If the next three natural
numbers are also included, How much
(a) 27 (b) 29 more than M will the average of these 8
(c) 39 (d) 33 numbers be ?

Aditya Ranjan (Excise Inspector) 13 Selected gSSelection fnyk,axs

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 Average

5 Øekxr la[;kvksa dk vkSlrM gSA ;fn vxyh 6 Øekxr le la[;kvksa dk vkSlr 35 gSA bu 6 la[;kvksa
rhu çkÑfrd la[;kvksa dks Hkh 'kkfey fd;k tkrk esa lcls NksVh vkSj lcls cM+h la[;k dk ;ksx fdruk
\ gksxk
gS rks bu 8 la[;kvksa dk vkSlr
M dh rqyuk esa SSC CHSL 14/03/2023 (Shift-04)
fdruk vf/d gksxk\ (a) 68 (b) 72
(a) 2 (b) 1 (c) 70 (d) 66
(c) 1.4 (d) 1.5 111. If the average of 7 consecutive even
number is 84. Find the difference between
106. The average of eleven consecutive positive
integers in increasing order is 251. If the first and last number.
next four odd numbers are included, then ;fn 7 Øekxr le la[;kvksa dk vkSlr 84 gSA igyh
what is the average of all the numbers? vkSj vafre la[;k ds chp dk varj Kkr dhft,A
vkjksgh Øe esa] X;kjg Øekxr /u iw.kkZadksa dk vkSlr(a) 12 (b) 14
251 gSA ;fn vxyh pkj fo"ke la[;kvksa dks lfEefyr
(c) 16 (d) 84
fd;k tk,] rks lHkh la[;kvksa dk vkSlr fdruk gksxk\
112. The average of 5 consecutive even numbers
(a) 253 (b) 253.4

r
is A. If next 5 even numbers are also
(c) 254 (d) 252.6 included, then what is the average of these

si
107. The sum of eight consecutive even numbers 10 numbers?
of set-A is 376. What is the sum of different 5 Øekxr le la[;kvksa dk vkSlrA gSA ;fn vxyh 5

an by
set of five consecutive whose lowest number
is 15 more than the mean of set-A?
le la[;kvksa dks Hkh 'kkfey dj fy;k tk,] rks dqy 10
la[;kvksa dk vkSlr fdruk gksxk\

n
,d lewg&A dh vkB yxkrkj le la[;kvksa dk ;ksx SSC CHSL 21/03/2023 (Shift-02)
376 gSA ,d vU; lewg dh ikap yxkrkj la[;kvksa dk

ja
R s
(a) A + 7 (b) A + 2
;ksx D;k gksxk ftldh lcls NksVh la[;k dk eku lewg
(c) A + 9 (d) A + 5
A ds ekè; ls 15 vf/d gS \
a th

113. The average of 44 consecutie odd numbers

(a) 296 (b) 320
is 144. What is the largest number?
(c) 324 (d) 284
44 Øekxr fo"ke la[;kvksa dk vkSlr 144 gSA lcls
ty a

108. The average of 10 consecutive integers is cM+h la[;k dkSu lh gS\

di M

33 (a) 189 (b) 191

. What is the average of first three
2 (c) 187 (d) 193
integers?
114. The sum of four consecutive odd number
33 is 30 more than the average of these
10 Øekxr iw.kk±dksa dk vkSlr
2
gSA igys rhu iw.kk±dksa
numbers. What is the first of these no.s?
dk vkSlr D;k gS\
pkj yxkrkj fo"ke la[;kvksa dk ;ksx bu la[;kvksa
SSC CHSL 13/03/2023 (Shift-01)
ds vkSlr ls 30 vf/d gSA bu uacjksa esa ls igyk
(a) 12 (b) 13 D;k gS\
(c) 15 (d) 11
(a) 7 (b) 14
109. The average of 35 consecutive even
A

(c) 17 (d) 21
numbers is 44. Find the smallest number.
115. The sum of 5 consecutive odd numbers
35 yxkrkj le la[;kvksa dk vkSlr 44 gSA lcls
is 525. What will be the sum of the next
NksVh la[;k Kkr djsaA set of 5 consecutive odd numbers?
(a) 8 (b) 12
5 Øekxr fo"ke la[;kvksa dk ;ksx 525 gSA 5 Øekxr
(c) 10 (d) 14
fo"ke la[;kvksa ds vxys lewg dk ;ksx D;k gksxk\
110. Average of 6 consecutive even numbers is 35.
what will be the sum of smallest and largest (a) 625 (b) 575
even number among these 6 nubers ? (c) 525 (d) 600

Aditya Ranjan (Excise Inspector) 14 Selected gSSelection fnyk,axs

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 Average

116. Average of 9 consecutive odd numbers is 120. The arithmetic mean of the following
27. If the previous and next odd number to numbers:
these 9 odd numbers are also included, then fuEufyf•r la[;kvksa dk vadxf.krh; ekè; gS%
what will be me new average?
1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6,
9 Øec¼ fo"ke la[;kvksa dk vkSlr 27 gSA ;fn bu 9 6, 6, 6, 6, 6 and 7, 7, 7, 7, 7, 7, 7 is
fo"ke la[;kvksa dh fiNyh vkSj vxyh fo"ke la[;k dks (a) 4 (b) 5
(c) 14 (d) 20
Hkh 'kkfey dj fy;k tk, rks u;k vkSlr D;k gksxk\ 121. The average of four consecutive even
SSC CHSL 09/03/2023 (Shift-04) numbers and four consecutive odd
numbers is 14.5. If the average of the given
(a) 32 (b) 28 four odd numbers is 14, find the average
(c) 29 (d) 27 of the given four even numbers.
117. The average of 35 consecutive natural pkj yxkrkj le la[;kvksa vkSj pkj yxkrkj fo"ke
number is N. Dropping the first 10 numbers la[;kvksa dk vkSlr 14-5 gSA ;fn nh xbZ pkj fo"ke
and including the next ten numbers the la[;kvksa dk vkSlr 14 gS] rks fn, x, pkj le
average is changed to M. If the M2 – N2 = la[;kvksa dk vkSlr Kkr dhft,A

r
600. Then find M and N? (a) 12 (b) 15

si
35 Øekxr çkÑr la[;kvksa dk vkSlr N gSA igyh 10 (c) 20 (d) 16
122. The Sum of 8 consecutive odd Numbers
la[;kvksa dks NksM+us vkSj vxyh nl la[;kvksa dks feykdj

an by
is 656. Also average of four consecutive
vkSlr M esa cny tkrk gSA ;fn
M2 – N2 = 600 gSA rks even numbers is 87. What is the sum of
M vkSjN Kkr dhft,\ the Smallest Odd number and second

n
largest even number ?
(a) 15, 25 (b) 20, 30
8 yxkrkj fo"ke la[;kvksa dk ;ksx 656 gSA pkj
(c) 35, 45

ja (d) 35, 25
yxkrkj la[;kvksa dk vkSlr Hkh 87 gSA lcls NksVh
R s
118. The average of 7 even consecutive natural fo"ke la[;k vkSj nwljh lcls cM+h la[;k dk ;ksx
a th

number is N. Dropping the first 2 even D;k gS\

Numbers and including the next 2 even
(a) 165 (b) 175
numbers the average is changed to M. If
(c) 163 (d) 156
the value of M2 – N2 = 160. Then Find M
ty a

and N?
TYPE-IX (CRICKET)
123. A cricket batsman had a certain average of
7 yxkrkj le çkÑfrd la[;kvksa dk vkSlrN gSA igys
di M

runs for his 11 innings. In the 12th

2 le la[;kvksa dks NksM+us vkSj vxys 2 le la[;kvksainnings, he made a score of 90 runs after
that his average run is decreased by 5. Find
dks 'kkfey djus ls vkSlrM esa cny tkrk gSA ;fn
his average of runs after 12th innings.
M2 – N2 = 160 gSA rksM vkSjN Kkr djsa\
,d cYysckt dh 11 ikfj;ksa dk ,d fuf'pr vkSlr
(a) 22, 18 (b) 20, 30 ju gSA 12oha ikjh esa] og 90 ju cukrk gS ftlds
(c) 35, 45 (d) 35, 25 dkj.k mldk vkSlr 5 de gks tkrk gSA 12oha ikjh ds
119. The average of 7 consecutive odd numbers ckn u;k vkSlr ju Kkr djsaA
is A. If next 3 and previous 2 odd numbers (a) 155 (b) 150
to these 7 odd numbers are also included, (c) 145 (d) 140
then what is the new average of these 12 124. A batsman made certain average of runs in
16 innings. He made 85 runs in his 17th
A

consecutive odd numbers?

innings there after his average runs is
7 yxkrkj fo"ke la[;kvksa dk vkSlrA gSA ;fn bu 7 increased by 3 runs. Find the average runs
fo"ke la[;kvksa esa vxyh 3 vkSj fiNyh 2 fo"ke la[;kvksa after 17 innings.
th

dks Hkh 'kkfey dj fy;k tk,] rks bu 12 yxkrkj fo"ke ,d cYysct us 16 ikfj;ksa esa juksa dh ,d fuf'pr vkSlr
la[;kvksa dk u;k vkSlr D;k gS\ cuk;hA viuh 17oha ikjh esa mlus 85 ju cuk;s ftlls
mlds juksa dh vkSlr esa 3 dh o`f¼ gks x;hA crk,¡
SSC MTS 16/06/2023 (Shift-01)
17oha ikjh ds ckn mlds juksa dh vkSlr D;k Fkh\
(a) A + 1 (b) A – 2 (a) 37 (b) 34
(c) A + 2 (d) A + 3 (c) 36 (d) 38

Aditya Ranjan (Excise Inspector) 15 Selected gSSelection fnyk,axs

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 Average

125. Average of 64 innings of a player is 62 129. The average of 33 numbers is 74. The
runs, difference between his maximum and average of the first 17 numbers is 72.8
minimum score is 180 runs. If these two and that of the last 17 numbers is 77.2.
innings are excluded then the average of If the 17th number is excluded, then what
remaining innings is 60 runs. Then his will be the average of the remaining
maximum score is : numbers (correct to one decimal place)?
,d fØdsV ds f[kykM+h dh 64 ikfj;ksa dk vkSlr 62 33 la[;kvksa dk vkSlr 74 gSA igyh 17 la[;kvksa
ju gSA mldk vf/dre Ldksj mlds U;wure Ldksj ls
dk vkSlr 72-8 gS rFkk vafre 17 la[;kvksa dk vkSlr
180 ju T;knk gSA mu nks ikfj;ksa dks NksM+dj mldh
77-2 gSA ;fn 17oha la[;k gVk nh tk,] rks 'ks"k la[;kvksa
'ks"k ikfj;ksa dk vkSlr 60 ju vkrk gSA rnuqlkj ml
dk vkSlr D;k gksxk\ (,d n'keyo LFkku rd)
f[kykM+h dk vf/dre Ldksj fdruk gS\
(a) 180 (b) 209 SSC CGL Tier-II 12/09/2019
(c) 212 (d) 214 (a) 72.9 (b) 73.4
126. The bowling average of cricketer is 12.4. (c) 71.6 (d) 70.8
He improves his bowling average by 0.2 130. The average of 21 numbers is 44. The
points when he takes 5 wickets for 26 runs

r
average of first 11 numbers is 48 and that
in his last match. The number of wickets of last 11 numbers is 42. If 11th number

si
taken by him before the last match is :
is excluded, what is the average of the
,d xsanckt dk vkSlr 12-4 gSA og viuh xsanckth remaining number?

an by
dk vkSlr 0-2 ls lq/kjrk gS] tc og vafre eSp esa
26 ju nsdj 5 fodsV ysrk gSA vafre eSp ls igys
21 la[;kvksa dk vkSlr 44 gSA igyh 11 la[;kvksa
dk vkSlr 48 rFkk vafre 11 la[;kvksa dk vkSlr

n
fy;s x;s fodsVksa dh la[;k Kkr djsaA
42 gSA ;fn 11oha la[;k dks gVk fn;k tk,] rks 'ks"k
(a) 125 (b) 150
la[;kvksa dk vkSlr D;k gksxk\

ja
R s
(c) 175 (d) 200
127. A cricketer whose bowling average is SSC MTS 20/08/2019 (Shift- 02)
a th

11.125 runs per wicket. he takes 7 wickets (a) 43 (b) 42

for 38.5 runs and thereby decrease his
average by 1.125. The number of wickets (c) 42.9 (d) 43.5
taken by him till last matches was: 131. Average of 6 natural number is 50. If the
ty a

,d fØds Vj ftldh x s a nckth dk vkS lr average of first 3 natural number is 40 and

11-125 ju izfr fodsV gSA 38-5 ju nsdj og 7 fodsV the 4th number is 10 less than the 5th
di M

number and 20 less than 6th number. Then

ysrk gS] ftlls mldk vkSlr ju 1-125 ?kV tkrk gSA
find the 4th number?
vafre eSp rd mlds }kjk fy;s x;s fodsVksa dh la[;k
crk,¡A 6 izkÑr la[;kvksa dk vkSlr 50 gSA ;fn izFke 3
(a) 35 (b) 18 izkÑr la[;kvksa dk vkSlr 40 gS vkSj pkSFkh la[;k
(c) 28 (d) 38 5oha la[;k ls 10 de vkSj NBh la[;k ls 20 de
TYPE - X (MISCELLANEOUS) gks rks pkSFkh la[;k Kkr djsaA
128. The average of a series of 21 numbers is (a) 60 (b) 50
equal to 43. The average of the first eleven (c) 55 (d) 45
of them is 33. The average of the last 132. The average of 38 numbers is 51. The
eleven number is 53. The eleventh number average of the first 24 numbers is 45, and
A

of the series is : that of the last 5 numbers is 60. What is

21 la[;kvksa dh ,d Ük`a[kyk dk vkSlr 43 ds cjkcj the average of the remaining numbers?
gSA buesa ls igyh X;kjg la[;kvksa dk vkSlr 33 gSA
38 la[;kvksa dk vkSlr 51 gSA igyh 24 la[;kvksa dk
vafre X;kjg la[;kvksa dk
vkSlr 53 gSA bl Ük`a[kyk vkSlr 45 gS] vkSj vafre 5 la[;kvksa dk vkSlr 60 gSA
dh 11oha l[;k gS% 'ks"k la[;kvksa dk vkSlr D;k gS\
SSC CHSL 11/07/2019 (Shift- 02)
NTPC CBT-2 14-06-2022 (Shift- 02)
(a) 43 (b) 47
(a) 59 (b) 60
(c) 33 (d) 46
(c) 62 (d) 61

Aditya Ranjan (Excise Inspector) 16 Selected gSSelection fnyk,axs

16
 Average

133. The average of 25 numbers is 55. The 25 la[;kvksa dk vkSlr 64 gSA igyh 13 la[;kvksa dk
average of first 11 numbers is 51 and the vkSlr vkSj vafre 13 la[;kvksa dk vkSlr Øe'k% 62-8
average of last 10 numbers is 56. What is
the average of 66, 70 and the remaining 4
vkSj 72-2 gSA ;fn 12oha la[;k 61 gS] vkSj ;fn 12oha
numbers out of given 25 numbers? vkSj 13oha la[;k dks fudky fn;k tk,] rks 'ks"k la[;kvksa
dk vkSlr (n'keyo ds ,d LFkku rd) Kkr dhft,A
25 la[;kvksa dk vkSlr 55 gSA igyh 11 la[;kvksa dk
SSC CGL MAINS 03/02/2022
vkSlr 51 gS vkSj vafre 10 la[;kvksa dk vkSlr 56 (a) 59.2 (b) 62.2
gSA nh xbZ 25 la[;kvksa esa ls 66] 70 vkSj 'ks"k(c) 4 60.2 (d) 61.5
la[;kvksa dk vkSlr D;k gS\ 137. A librarian purchased 60 Story books for
NTPC CBT-2 15.06.2022 (Shift-2) his library. But he found that he could get
4 extra books by spending Rs.336 more and
(a) 68 (b) 65
then the overall average price per book
(c) 66 (d) 64 would be reduced by Rupees 1. find the
134. Average of 8 numbers is 44. The average previous average price of each book?
of first three numbers is 50 and the ,d iqLrdky;kè;{k us vius iqLrdky; ds fy, 60

r
average of next two numbers is 52. If the dgkuh dh iqLrdsa •jhnhaA ysfdu mlus ik;k fd og 336

si
sixth number is 6 and 8 less than seventh #i;s vf/d •pZ djds 4 vfrfjÙkQ iqLrdsa çkIr dj
and eighth number respectively, then what ldrk gS vkSj fiQj çfr iqLrd dk dqy vkSlr ewY; 1

an by
is the value of eighth number? #i;s de gks tk,xkA çR;sd iqLrd dk fiNyk vkSlr
8 la[;kvksa dk vkSlr 44 gSA igyh rhu la[;kvksa dk ewY; Kkr dhft,\

n
vkSlr 50 gS vkSj vxyh nks la[;kvksa dk vkSlr 52 (a) 100 (b) 120
gSA ;fn NBh la[;k lkroha vkSj vkBoha la[;k ls Øe'k% (c) 90 (d) 108

ja
6 vkSj 8 de gS] rks vkBoha la[;k dk eku D;k gS\138. Out of the 3 natural numbers, if the average
R s
of 2 numbers is added to the third number
a th

SSC MTS 16/05/2023 (Shift-01)

then 24, 20, 18 is obtained, find out all the
(a) 36 (b) 32 natural numbers.
(c) 40 (d) 56 rhu çkÑfrd la[;kvksa esa ls] ;fn nks la[;kvksa ds vkSlr
dks rhljh la[;k esa tksM+k tkrk gS rks 24] 20 vkSj 18
ty a

135. The average of thirteen numbers is 47. The

average of the first three number is 39 and çkIr gksrs gSA lHkh çkÑfrd la[;kvksa dk irk yxk;sA
that of the next seven number is 49. The
di M

(a) 5, 8, 19 (b) 5, 9, 17
11th number is two times the 12th num-
ber and 12th number is 3 less than the (c) 6, 8, 17 (d) 7, 9, 18
13th number. What is the average of 11th 139. There are four natural numbers. The
and 13th number? average of any three numbers is added in
the fourth number and in this way, the
13 la[;kvksa dk vkSlr 47 gSA igyh rhu la[;kvksa numbers 29, 23, 21 and 17 are obtained.
dk vkSlr 39 gS rFkk vxyh lkr la[;kvksa dk vkSlr One of the numbers is:
49 gSA 11oha la[;k 12oha la[;k ls nksxquh gS rFkk
fdlh Hkh pkj çkÑfrd la[;kvksa esa] ;fn rhu la[;kvksa
12oha la[;k 13oha la[;k ls 3 de gSA 11oha vkSj ds vkSlr dks pkSFks uacj esa tksM+ fn;k tkrk gS vkSj bl
13oha la[;kvksa dk vkSlr Kkr djsaA rjg ls la[;k, 29] 23] 21 vkSj 17 çkIr dh tkrh gSA
SSC CGL Tier-II 11/09/2019 rks mues ls ,d la[;k gS%
A

(a) 54.5 (b) 57 (a) 11 (b) 24

(c) 56 (d) 55.5 (c) 21 (d) 10
140. Average age of 7 students of a class is 28
136. The average of 25 numbers is 64. The
years. Average age of first three students
averages of the first 13 numbers and that
is 30 years. Age of fourth student is 4 years
of the last 13 numbers are 62.8 and 72.2, less than the age of fifth student. Ages of
respectively. If the 12th number is 61, and last two students is same and is 5 more
if the 12th and 13th numbers are excluded, than the average age of first three
then what is the average of the remaining students. What is the average age of fourth
numbers (correct to one decimal place)? and fifth student?

Aditya Ranjan (Excise Inspector) 17 Selected gSSelection fnyk,axs

17
 Average

,d d{kk eas 7 Nk=kksa dh vkSlr vk;q 28 o"kZ 144.gSA

There were 54 students in a hostel. Due
izFke rhu Nk=kksa dh vkSLkr vk;q 30 o"kZ gSAtopkSFks the admission of 9 new students, the
expenses of the mess were increased by `
Nk=k dh vk;q ik¡posa
Nk=k dh vk;q ls 4 o"kZ de gSA 540 per day while the average expenditure
vafre nks Nk=kksa dh vk;q leku gS rFkk izFke rhu per head diminished by ` 3. What was the
Nk=kksa dh vkSlr vk;q ls 5 o"kZ
vf/d gSA pkSFks original expenditure (in `) of the mess?
rFkk ik¡posa Nk=k dh vkSlr vk;q fdruh gS\ ,d Nk=kkokl esa54 fo|kFkhZ 9 FksA
u, Nk=kksa ds ukekadu
SSC CGL MAINS 08/08/2022 ds dkj.k] esl dk [kpZ izfrfnu` 540 ?kV x;k] rFkkfi
(a) 20 years (b) 18 years izfr O;fDr vkSlr [kpZexpenditure per head
diminished by ` 3 de gks x;kA esl dk ewy [kpZ
(c) 36 years (d) 16 years
( ` esa) fdruk Fkk\
141. Eleven friends spent Rs 18 each on a tour
ICAR Mains, 10/07/2023 (Shift-1)
and the twelfth friend spent Rs 11 less (a) 4374 (b) 4419
than the average expenditure of all twelve (c) 4616 (d) 4518
of them. What is the total money spent by 145. The average weight of students of section

r
twelve friends? A and B having 40 students each is 45.5
X;kjg nksLrksa esa ls çR;sd us ,d nkSjs ij 18 #i;s •pZ kg and 44.2 kg respectively. Two students

si
of section A having average weight 48.75
fd, vkSj ckjgosa nksLr us mu lHkh ckjg nksLrksa kg ds were shifted B and 2 students of
vkSlr •pZ ls 11 #i;s de •pZ fd,A ckjg fe=kksa

an by
}kjk •pZ fd;k x;k dqy /u fdruk gS\
section B were shifted to section A,
marking the average weight of both the

n
SSC MTS 02/05/2023 (Shift-02) section equal. What is the average weight
(in kg) of the students who were shifted
(a) Rs.204 (b) Rs.215

ja
from section B to section A?
R s
(c) Rs.212 (d) Rs.208 oxZA vkSjB ds Nk=kksa dk vkSlr otu] ftuesa çR;sd
esa 40 Nk=k gSa] Øe'k% 45-5 fdxzk vkSj 44-2 fdxzk gS
a th

142. 20 Students of a college went to a hotel. 19

of them spent Rs 175 each on their meal
and the 20th student spent Rs 19 more than
oxZA ds nks Nk=kksa ftudk vkSlr otu 48-75 fdyksxzke
the average of all the 20. Find the total Fkk] mUgsaB oxZ
esa vkSj oxZ
B ds 2 Nk=kksa dksA oxZ
money spent by them. esa LFkkukarfjr dj fn;k x;k] ftlls nksuksa oxksaZ dk
ty a

,d dkWyst ds 20 fo|kFkhZ ,d gksVy esa x,A muesa ls 19vkSlr otu cjkcj gks x;kA oxZ B ls oxZA esa f'kÝV
esa ls izR;sd us vius Hkkstu ij 175 #i;s [kpZ fd, vkSj fd, x, Nk=kksa dk vkSlr otu (fdxzk eas) D;k gS\
di M

20osa fo|kFkhZ us lHkh 20 ds vkSlr ls 19 #i;s vf/d SSC CGL 23/08/2021 (Shift-02)
[kpZ fd,A muds }kjk [kpZ dh xbZ oqQy jkf'k Kkr dhft,A(a) 34.5 (b) 35
SSC CGL 17/07/2023 (Shift-04) (c) 35.75 (d) 34.25
(a) Rs 3490 (b) Rs 3540 146. The batting average for 27 innings of a
(c) Rs 3520 (d) Rs 3500 cricket player is 47 runs. His highest score
in an innings exceeds his lowest score by
143. There were 70 students in a hostel. After
157 runs. If these two innings are
admission of 14 new students, the
excluded, the average score of the
expenses of mess increases by Rs. 28 per
remaining 25 innings is 42 runs. Find his
day while the average expenditure per head
diminished by Rs.1. What was the orginial highest score in an innings.
27 ikfj;ksa ds fy, fdlh fØdsV f[kykM+h dk cYysckth
A

expenditure of the mess?

vkSlr
,d Nk=kkokl esa 70 Nk=k FksA 14 u, Nk=kksa ds ços'k ds 47 ju gSA ,d ikjh esa mldk mPpre Ldksj]
ckn] esl dk •pZ 28 #i;s çfr fnu ls c<+ tkrk gSA mlds fUkEure Ldksj ls 157 ju vf/d gSA ;fn ;s
tcfd çfr O;fÙkQ vkSlr O;; 1 #i;s de gks x;kA nks ikfj;k¡ gVk nh tk,¡] rks 'ks"k 25 ikfj;ksa dk
esl dk ewy O;; D;k Fkk\ vkSlr Ldksj 42 ju gSA ,d ikjh esa mldk mPpre
CRPF HCM 26/02/2023 (Shift - 03)
Ldksj Kkr dhft,A
SSC CGL 01/12/2022 (Shift- 01)
(a) Rs.550 (b) Rs.560 (a) 176 (b) 188
(c) Rs.565 (d) Rs.652 (c) 186 (d) 174

Aditya Ranjan (Excise Inspector) 18 Selected gSSelection fnyk,axs

18
 Average

147. The average monthly expenditure of a (a) 25 (b) 29

family was Rs 18,600 during the first three (c) 27 (d) 26
months, Rs 21,750 during the next four 151. In an exhibition in the month of December
months and Rs 22,840 during the last five starting with Thursday, the average
months of a year. If the total savings during
number of visitors on saturday is 254. The
the year was Rs 1,43,020, then the average
average number of visitors on Sunday is
monthly income (in Rs) of the family was: 625 and an average number of a visitors
igys rhu eghuksa ds nkSjku] fdlh ifjokj dk vkSlr ekfld on other days of the month is x. If the
[kpZ #- 18]600 Fkk] vxys pkj eghuksa ds nkSjku #- 21]750average number of visitors, per day, for
vkSj o"kZ ds vkf[kjh ikap eghuksa #- ds 22]840
nkSjkuFkkA the whole month is 238, then what is the
value of x ?
;fn o"kZ ds nkSjku dqy cpr 1]43]020
#- Fkh] rks ifjokj
dh vkSlr ekfld vk; (#- eas) fdruh Fkh\ ,d izn'kZuh esa] xq#okj ls 'kq: gksus okys fnlacj ekg esa
SSC CHSL 12/04/2021 (Shift- 03) 'kfuokj dks vkxarqdksa dh vkSlr la[;k 254 gS] jfookj
(a) 32,225 (b) 34,115 dks vkxarqdksa dh vkSlr la[;k 625 gS vkSj eghus ds vU;
(c) 35,333 (d) 33,335 fnuksa esa vkxarqdksa dh vkSlrx gSA
la[;k;fn iwjs ekg esa
148. The average expenditure of a man for the izfrfnu vkxarqdksa dh vkSlr la[;k 238 jgh gks]
x dkrks

r
first five months is ` 7,200 and for the next
eku fdruk gksxk\
seven months is ` 7,600. If he saves `

si
36,800 during the year, then his average ICAR Mains, 07/07/2023 (Shift-3)
income per month (in `) is: (a) 163 (b) 166

an by
izFke ik¡p eghuksa ds fy, ,d O;fDr dk vkSlr [kpZ
7,200 gS vkSj vxys lkr eghuksa ds`fy,
`
7,600 gSA152.
(c) 165 (d) 164
According to Raghav, his weight is more

n
than 64 kg but less than 74 kg. His sister
;fn og o"kZ ds nkSjku
` 36,800 cpkrk gS] rks mldh
does not agree with Raghav and she thinks
izfr ekg vkSlr vk; ( ` esa) fdruh gksxh\

ja
that his weight is more than 60 kg but less
R s
ICAR Mains, 10/07/2023 (Shift-2) than 69 kg. His mother's view is that his
(a) 11,000 (b) 12,000 weight cannot be more than 68 kg. His
a th

(c) 10,500 (d) 11,500 father's view is that his weight cannot be
149. The average temperature of a particular more than 67 kg. If all are them are correct
week between Monday and Friday is noted in their estimation, then what is the
to be 30.2º C and the average temperature average of different probable weights of
ty a

from Tuesday to Friday is found to be 30ºC Raghav measured (in kg)?

and the temperature of Monday is 2 more than
jk?ko ds vuqlkj mldk otu 64 kg ls T;knk ysfdu
di M

that of Friday. Find the temperature on Friday.

lkseokj vkSj 'kqØokj ds chp ,d fo'ks"k lIrkg dk 74 kg ls de gSA mldh cgu] jk?ko dh ckr ls
vkSlr rkieku 30-2 fMxzh lsfYl;l vkSj eaxyokj ls lger ugha gS vkSj og lksprh gS fd mldk otu 60
'kqØokj rd vkSlr rkieku 30 fMxzh lsfYl;l ik;k kg ls T;knk gS ysfdu69 kg ls de gSA mldh ek¡
tkrk gS vkSj lkseokj dk rkieku 'kqØokj dh rqyuk esa dk ekuuk gS fd mldk otu 68 kg ls T;knk ugha
2 vf/d gksrk gSA 'kqØokj dk rkieku Kkr dhft,A gks ldrkA mlds firk dk ekuuk gS fd mldk otu
CRPF HCM 27/02/2023 (Shift - 02) 67 kg ls T;knk ugha gks ldrkA ;fn os lHkh vius
(a) 32ºC (b) 29ºC vuqeku esa lgh gSa] rks jk?ko ds ekis x, fofHkUu laHkkfo
(c) 31ºC (d) 30ºC
150. The average sale of cars per day by a dealer otuksa dk vkSlr kg
( esa) D;k gS\
in the month of April is 28. The average SSC CGL 18/07/2023 (Shift-03)
sale of cars on Saturday is 30 and the (a) 66 (b) 67
A

average sale of cars on Fridays is 37. What (c) 68 (d) 65

is the average sale of cars on the other
153. In Shiva’s opinion, his weight is greater
days of the month if the month starts on
a Tuesday? than 65 kg but less than 72 kg. His sister
vçSy ekg esa ,d Mhyj }kjk izfrfnu dkjksa dh fcØh dk does not agree with Shiva, and she thinks
that Shiva’s weight is greater than 60 kg
vkSlr 28 gSA 'kfuokj dks dkjksa dh vkSlr fcØh 30 vkSj but less than 70 kg. His father’s view is that
'kqØokj dks dkjksa dh vkSlr fcØh 37 gSA ;fn ekg dh his weight cannot be greater than 68 kg. If
'kq:vkr eaxyokj ls gqbZ gks rks ekg ds vU; fnuksa esa dkjksa
all of them are correct in their estimation,
dh vkSlr fcØh fdruh gksxh\ then the average of the different probable
ICAR Mains, 07/07/2023 (Shift-2) weights (in kg) of Shiva is:

Aditya Ranjan (Excise Inspector) 19 Selected gSSelection fnyk,axs

19
 Average

f'ko dh jk; esa mudk otu 65 fdyks ls T;knk ysfdu jke] ';ke] jksgwu] jhrk vkSj eqds'k ,d ifjokj ds ikap
72 fdyks ls de gSA mldh cgu f'ko ls lger ugha lnL; gSa ftudk otu yxkrkj fd;k tkrk gS vkSj çR;sd
gS] vkSj og lksprh gS fd f'ko dk otu 60 fdyks ls lnL; dk otu djus ds ckn muds vkSlr otu dh
vf/d ysfdu 70 fdyks ls de gSA muds firk dk x.kuk dh tkrh gSA ;fn çR;sd ckj vkSlr Hkkj fdxzk c<+
ekuuk gS fd mudk otu 68 fdyks ls T;knk ugha gks tkrk gS 2] rks eqds'k] jke ls fdruk Hkkjh gS\
(a) 14 kg (b) 18 kg
ldrkA ;fn os lHkh vius vuqeku esa lgh gSa] rks f'ko (c) 16 kg (d) 12 kg
ds fofHkUu laHkkfor otu (fdxzk esa) dk vkSlr gS%155. One page is torn from a booklet whose pages
CRPF HCM 28/02/2023 (Shift - 01) are numbered in the usual manner starting
(a) 67 from the first page as 1. The sum of the
(b) 68 numbers on the remaining pages is 195.
(c) 66 The torn page contains which of the
(d) 69 following numbers?
154. Ram, Shyam, Rohan, Reeta and Mukesh are ,d iqfLrdk ls ,d i`"B iQkM+k tkrk gS ftlds i`"Bksa ij
five members of a family who are weighed igys i`"B ls çkjaHk djrs gq, lkekU; rjhds ls 1 Øekafdr
fd;k x;k gSA 'ks"k i`"Bksa dh la[;kvksa dk ;ksx 195 gSA

r
consecutively and their average weight is
calculated after each member is weighed. iQVs gq, i`"B esa fuEufyf•r esa ls dkSu lh la[;k,¡ gSa\

si
If the average weight increases by 2 kg each
UPSC CSAT 2020
time, how much heavier is Mukesh than

an by
(a) 5, 6 (b) 7, 8
Ram? (c) 9, 10 (d) 11, 12

n
ANSWER KEY
ja
R s
1.(a) 2.(b) 3.(c) 4.(a) 5.(b) 6.(d) 7.(b) 8.(a) 9.(b) 10.(c)
a th

11.(a) 12.(d) 13.(b) 14.(c) 15.(b) 16.(b) 17.(c) 18.(d) 19.(c) 20.(d)

21.(c) 22.(b) 23.(a) 24.(b) 25.(d) 26.(b) 27.(b) 28.(b) 29.(a) 30.(c)
ty a

31.(d) 32.(c) 33.(d) 34.(c) 35.(c) 36.(c) 37.(c) 38.(d) 39.(b) 40.(b)
di M

41.(a) 42.(a) 43.(b) 44.(c) 45.(c) 46.(c) 47.(a) 48.(a) 49.(d) 50.(c)

51.(b) 52.(b) 53.(d) 54.(d) 55.(a) 56.(d) 57.(a) 58.(b) 59.(c) 60.(b)

61.(b) 62.(b) 63.(b) 64.(c) 65.(c) 66.(b) 67.(a) 68.(a) 69.(c) 70.(c)

71.(c) 72.(d) 73.(a) 74.(c) 75.(a) 76.(a) 77.(b) 78.(c) 79.(d) 60.(c)

81.(c) 82.(b) 83.(b) 84.(a) 85.(d) 86.(b) 87.(c) 88.(b) 89.(c) 90.(b)

91.(a) 92.(a) 93.(c) 94.(c) 95.(b) 96.(a) 97.(a) 98.(c) 99.(c) 100.(d)
A

101.(d) 102.(b) 103.(b) 104.(c) 105.(d) 106.(b) 107.(b) 108.(b) 109.(c) 110.(c)

111.(a) 112.(d) 113.(c) 114.(a) 115.(b) 116.(d) 117.(d) 118.(a) 119.(a) 120.(b)

121.(b) 122.(a) 123.(c) 124.(a) 125.(d) 126.(c) 127.(a) 128.(a) 129.(a) 130.(c)

131.(b) 132.(c) 133.(b) 134.(a) 135.(b) 136.(c) 137.(a) 138.(b) 139.(c) 140.(b)

141.(a) 142.(c) 143.(b) 144.(a) 145.(c) 146.(b) 147.(d) 148.(c) 149.(b) 150.(d)

151.(d) 152.(a) 153.(a) 154.(c) 155.(b)

Aditya Ranjan (Excise Inspector) 20 Selected gSSelection fnyk,axs

20
 Average

Average/vkSlr
(Practice Sheet With Solution)
1. The average of x, 11, 23, 17, is 15 and the av- 4. The average of odd numbers up to 100 is:
erage of x, y, 12, 25 is 16. The value of y is: 100 rd dh lHkh fo"ke la[;kvksa dk vkSlr gksxk&
x, 11, 23, 17, dk vkSlr 15 gS vkSj
x, y, 12, 25 dk (a) 50.5 (b) 50
vkSlr 16 gSA rks
y dk eku gS% (c) 49.5 (d) 49
1 1 Sol: (b)
(a) (b) The number of odd numbers from 1 to 100 = 50
3 2
(c) 16 (d) 18 Sum of 'n' of odd numbers = n2
Sol: (d)
502

r
Average of x, 11, 23, 17 = 15 Average of nos. from 1 to 100 = = 50
Sum = x + 11 + 23 + 17 = 15 × 4 50

si
x + 51 = 60 5. The average of 37 consecutive numbers is 54.
x=9 The largest of these numbers is:
a n by
Average of x, y, 12, 25 = 16 37 yxkrkj la[;kvksa dk vkSlr 54 gSA bu la[;kvksa esa l
x + y + 12 + 25 = 16 × 4 cM+k la[;k D;k gS\
x + y + 37 = 64
x + y = 64 – 37
n (a) 74
(c) 72
(b) 73
(d) 71
ja
y = 27 – 9
R s

Sol: (c)
y = 18
Average of 37 consecutive no = 54
a th

2. What is the difference between the average of

Now, 1st term, 2nd term, ......
first 148 even positive numbers and the aver-
age of first 129 odd positive numbers? 19th term
çFke 148 le /ukRed la[;kvksa ds vkSlr rFkk çFke 129 ......,
54
,....., Last term
ty a

fo"ke /ukRed la[;kvksa ds vkSlr ds chp fdruk varj gS\ 36, 37, ......54,............,72
(a) 21 (b) 19 Largest of these numbers is 72
di M

(c) 20 (d) 23 6. The average of the 9 consecutive positive in-

Sol: (c) tegers is 63. The product of the largest and
Average of first 148 even positive no = 149 smallest integer is
Average of first 129 odd positive no = 129
9 yxkrkj /ukRed iw.kkZdksa dk vkSlr 63 gSA lcls cM+
their difference = 149 – 129 = 20
3. The average of square of natural numbers from
lcls NksVs iw.kkZad dk xq.kuiQy Kkr djsaA
1 to 71 is? (a) 3935 (b) 3953
1 ls 71 rd çkÑr la[;kvksa ds oxks± dk vkSlr D;k gS\ (c) 3853 (d) 3845
(a) 1616 (b) 1716 Sol: (b)
(c) 1728 (d) 1692 Average of 9 consecutive positive integer is 63
Sol: (b) So, the numbers will be 59, 60, 61, 62, 63, 64,
Average of square of 'n' natural number 65, 66, 67
A

Now,
n + 12n +1 The product of largest and smallest integer
=
6 = 67 × 59 = 3953
ATQ,
7. Average of all even numbers between 104 and
Average of square of natural numbers from 148 is......
71 +12 × 71 + 1 104 vkSj 148 ds chp dh lHkh le la[;kvksa dk vkSlr
1 to 71 =
6 fdruk gksxk\
72 143 (a) 128 (b) 130
= = 1716 (c) 124 (d) 126
6

Aditya Ranjan (Excise Inspector) Selected gSSelection fnyk,axs1

 Average
Sol: (d) 12. The average of 126 numbers is 951. If each
All even no between 104 and 148 is = 106, 108, number is multiplied by 0.2 and added to 3.6,
110, 112, 114,......., 144, 146 the average of the new set of numbers is:
Sum of all no between 104 and 148 is = 2646
126 la[;kvksa dk vkSlr 951 gSA ;fn çR;sd la[;k dks 0-2 l
Average of all the nos. =
2646
= 126 xq.kk fd;k tk, vkSj 3-6 esa tksM+ fn;k tk,] rks la[;kvksa
21 u, lsV dk vkSlr Kkr djsa\
8. If the average of 14 consecutive even numbers
is 107. Then, find the smallest number? (a) 193.8 (b) 28.8
;fn 14 yxkrkj le la[;kvksa dk vkSlr 107 gS rks lcls NksVh (c) 479.1 (d) CND
la[;k Kkr djsa\ Sol: (a)
(a) 93 (b) 94 When we change in a set of number, similarly
(c) 92 (d) 89 that change will be in average of that number
Sol: (b) 2
Required average = 951 × + 3.6 = 193.8
94......6 no.....,106,107,108,.....,118 10
 13. The average of the squares of four consecutive
Average

r
odd natural numbers is 201. The average of 7
So, 94 is the smallest number.
times of the largest number and 3 times of the
9. The average of the first 1234 .........numbers is

si
equal to 1234. smallest number is:
çFke 1234 -------------la[;kvksa dk vkSlr 1234 ds cjkcj gSApkj Øekxr fo"ke çkÑfrd la[;kvksa ds oxks± dk vkSlr 201
a n by
(a) Odd (b) Even gSA buesa ls lcls cM+h la[;k ds 7 xqus vkSj lcls NksVh
(c) Prime (d) Natural ds 3 xqus dk vkSlr Kkr djsaA
Sol: (a)

n
The average of n odd number is n
(a) 72 (b) 78
ja
(c) 76 (d) 66
R s

So, Average of first 1234 Odd number is equal

to 1234 Sol: (c)
We know,
a th

10. The average of first 101 ..........number is equal

to 102. greatest number always greater than average
çFke 101 -----------la[;kvksa dk vkSlr 102 ds cjkcj gSA A.T.Q,
(a) Natural (b) Odd Let that four numbers are 11, 13, 15, 17
ty a

(c) Even (d) Perfect square Required average = 17 × 7 + 11 ×3

Sol: (c)
di M

Average of n even number is (n +1) 152

119 + 33 = = 76
So, the average of first 101 Even number is 2
equal to (101 + 1) = 102 14. If the average of P numbers is Q2 and the aver-
11. If average of 20 observations x1, x2, ..., x20 is y, age of Q numbers is P2, then the average of (P +
then the average of x1 – 101, x2 – 101, x3 – 101,
Q) numbers will be?
..., x20–101 is
20 ekiuksax1, x2, ..., x20 dk vkSlr y gS A rc](x1 – 101), ;fn P la[;kvksa dk vkSlr Q2 gS vkSj
Q la[;kvksa dk vkSlr
(x2 –101), (x3 – 101), ..., (x20–101) dk vkSlr Kkr P 2
gS] rks (
P + Q ) la[;kvksa dk vkSlr gksxk\
djsa\ (a) P – Q (b) P + Q
(a) y – 20 (b) y – 101 (c) PQ (d) 2PQ
(c) 20y (d) 101y Sol: (c)
Sol: (b) Average of P numbers = Q2
A

Given that, Average of Q numbers = P2

x1 + x 2 + x 3 + x 4 .....x 20 Required average
=y
20
Q2 × P + Q × P 2 PQ P + Q 
then, average of required series = = = PQ
P+Q P+Q
x1 + x 2 + .....x 20 – 101 × 20
15. The average of 7 consecutive natural numbers is
20
K. The next three natural numbers are also in-
20y – 101 × 20 cluded, how much more than K will the average
= = y – 101 of these 10 numbers be?
20

Aditya Ranjan (Excise Inspector) Selected gSSelection fnyk,axs2

 Average

7 çkÑfrd la[;kvks dk vkSlrK gS ;fn vxyh 3 çkÑfrd Sol: (d)

la[;kvks dks Hkh lfEefyr dj fy;k tk; rks u;k vkSlr
K ls Number Average
fdruk vf/d gksxk\ 
(a) 1 (b) 1.5 35  N
(c) 2 (d) 2.5 35  M
Sol: (b) A.T.Q,
When we add the next natural number in a M – N = 10
series average of that series will be increased Given that,
by 0.5 (M + N) (M – N) = 600
A.T.Q, M + N = 60
New average increased by = 0.5 × 3 = 1.5 M = 35
16. The average of five consecutive even number N = 25
is M. If the next five even number are also in- 35 × 3 + 5 × 25
cluded, the average of ten numbers will be:- Required average =
2
ik¡p Øekxr le la[;kvksa dk vkSlrM gSA ;fn vxyh ik¡p

r
105 ×125 230
le la[;k,¡ Hkh 'kkfey dj yh tkrh gS] rks bl 10 la[;kvksa = = = 115
2 2

si
dk vkSlr D;k gksxk\
19. If the average of the 3-digit numbers 335, 2x5,
(a) M+5 (b) 11
a n by
x35, 63x and 406 is 411, then what will be the
(c) 10 (d) M+10 average of x-1, x-3, x+3 and x+5?
Sol: (a) 3 vad okyh la[;kvksa
335, 2x5, x35, 63x vkSj406 dk

n
When we add the next even natural number in
a series, average of that series will be
vkSlr 411 gS] rks
djsa A
x-1, x-3, x+3 vkSjx+5 dk vkSlr Kkr
ja
R s

increased by 1
(a) 6 (b) 3
A.T.Q,
(c) 5 (d) 4
a th

old average = M Sol: (c)

New average = M + 1 × 5 = M + 5 Unit digit of average = 1
17. The average of four consecutive even num- then, unit digit of sum = 1 × 5
ty a

bers is 27. By adding which number does the Solve by unit digit
average become 28? 5+5+5+x+6=5
di M

pkj Øekxr le la[;kvksa dk vkSlr 27 gSA blesa fdl la[;k 21 + x = 5 [Unit digit of 21 is 1]
dks tksM+us ls vkSlr 28 gks tk,xk\ 1+x=5
(a) 32 (b) 30 x=4
(c) 33 (d) 29 Required average
Sol: (a) 3 +1 + 7 + 9 20
= = =5
Average of 4 numbers = 27 4 4
Average of 5 numbers = 28 20. The average monthly expenditure of a man is
then fifth number = 28 + 1 × 4 = 32 2,400 during the first three months, 3,500
18. The average of 35 consecutive natural nubers during the next five months and 4,800 for the
is N. Dropping the first 10 numbers and remaining four months. If his total saving is
inculding the next 10 numbers, the average is 3,500 during the entire year, then what is his
A

changed to M. If the value of M2 – N2 = 600, average monthly income (in Rs)?

then the average of 3 M and 5 N is: fdlh vkneh dk vkSlr ekfld •pZ] igys rhu eghuksa ds
Øekxr 35 çkÑfrd la[;kvksa dk vkSlr N gSA vxj igyh 10 nkSjku 2]400 gS] vxys ikap eghuksa ds nkSjku 3]500 v
la[;kvksa dks fudky fn;k tk, vkSj vkxs dh 10 la[;kvksa dks pkj eghuksa ds nkSjku 4]800 gSA ;fn iwjs o"kZ ds nkS
'kkfey dj fy;k tk,] rks ;g vkSlr M gks tkrk gS] ;fnM2 dqy cpr 3]500 gS] rks mldh vkSlr ekfld vk; (# esa) Kkr
– N2 = 600 gS rks 3 M vkSj5 N dk vkSlr gksxkA djsaA
(a) 4,550 (b) 4,100
(a) 90 (b) 120
(c) 3,700 (d) 3,950
(c) 100 (d) 115

Aditya Ranjan (Excise Inspector) Selected gSSelection fnyk,axs3

 Average

Sol: (d) Sol: (b)

Expenditure for 3 months = 2400 × 3 = 7200
Number Average Sum
Expenditure for next 5 months = 3500 × 5 = 17500
35 22 770
Expenditure for next 4 months = 4800 × 4 = 19200
Income for 1 year = 7200 + 17500 + 19200 + 17 19 323
3500 = 47400 17 20 340
47400 18th Number = 770 – (323 + 340)
Average monthly income = = Rs 3950 = 770 – 663 = 107
12
23. The average of 65 numbers is 137.8. The aver-
21. The average monthly expenditure of a family
age of first 32 numbers is 132.6 and average
was Rs. 18,800 during the first three months, of last 32 numbers is 140.5. Find the 33th num-
Rs. 21,750 during the next four months and ber?
Rs. 22,840 during the last five months of a year.
If the total savings during the years was Rs.
65 la[;kvksa dk vkSlr 137-8 gSA igyh 32 la[;kvksa d
1,43,020, then the average monthly income vkSlr 132-6 gS vkSj vafre 32 la[;kvksa dk vkSlr 140-5 g
(in Rs.) of the family was : 33oha la[;k Kkr djsa\
igys rhu eghuksa ds nkSjku] fdlh ifjokj dk vkSlr ekfld (a) 215.4 (b) 217.8

r
•pZ 18]800 #- Fkk] vxys pkj eghuksa ds nkSjku 21]750 #- (c) 213.5 (d) 219.6

si
Sol: (b)
vkSj o"kZ ds vkf•jh ikap eghuksa ds nkSjku 22]840 #- FkkA ;fn
o"kZ ds nkSjku dqy cpr 1]43]020 #- Fkh] rks ifjokj dh Number Average Sum
a n by
vkSlr ekfld vk; (#- esa) fdruh Fkh\ 65 137.8 8957
(a) 33,385 (b) 34,115 32 132.6 4243.2
(c) 35,333
Sol: (a)
n(d) 32,225 32 140.5 4496
ja
33th Number = 8957 – (4243.2 + 4496)
R s

Let, = 8957 – 8739.2 = 217.8

Average expenditure for 12 months = 20000 24. The average of 40 numbers is 36. The average
a th

Original average expenditure of the first 25 numbers is 31 and the average

of last 16 numbers is 43. Find the 25th num-
–1200 × 3 +1750 × 4 + 2840 × 5 ber.
=
12
40 la[;kvksa dk vkSlr 36 gSA igyh 25 la[;kvksa dk vkS
ty a

 –3600 + 7000 + 14200  31 ,oa vafre 16 la[;kvksa dk vkSlr 43 gSA 25oha la[;k K
= 20000 +
dhft,A
di M

12
(a) 23 (b) 24
17600  (c) 21 (d) 22
= 20000 +
12 Sol: (a)
Expenditure for 1 year = 20000 × 12 + 17600
Number Average Sum
= 240000 + 17600
= 257600 40 36 1440
Income for 1 year = 257600 + 143020 25 31 775
= 400620 16 43 688
400620 25th Number = (688 + 775) – (1440)
Income for 1 month = = Rs 33385 = 1463 – 1440 = 23
12
25. The average daily income of Shyam Lal during
A

22. If the average of 35 numbers is 22, the aver-

the month of February 2020 was 560. The aver-
age of the first 17 numbers is 19, and the aver-
age income for the first 16 days was 590 and
age of the last 17 numbers is 20, then the 18 for the last 16 days it was 500 . What was his
number is: average income for 14th, 15th and 16th Febru-
;fn 35 la[;kvksa dk vkSlr 22 gS] igyh 17 la[;kvksa dk ary?
vkSlr 19 gS] vkSj vafre 17 la[;kvksa dk vkSlr 20 gS] rks 18 iQjojh 2020 ds nkSju] ';ke yky dh vkSlr nSfud vk; 560
oha la[;k Kkr djs A FkhA igys 16 fnuksa ds fy, vkSlr vk; 590 Fkh vkSj vaf
(a) 133 (b) 107 16 fnuksa ds fy, vkSlr vk; 500 FkhA 14] 15 vkSj 16 iQjojh
(c) 132 (d) 108 dks mldh vkSlr vk; Kkr djsaA

Aditya Ranjan (Excise Inspector) Selected gSSelection fnyk,axs4

 Average

(a) 545 (b) 400 ,d Nk=kkokl esa 90 Nk=k gSaA u, ços'kksa ds dkj.k] 30
(c) 590 (d) 587 Hkkstuky; esa 'kkfey gksrs gSa vkSj Hkkstuky; ds nSfud
Sol: (b) 560 dh o`f¼ gksrh gS] tcfd çfr Nk=k vkSlr O;; 10 # rd
Average income for 14th, 15th & 16th february de gks tkrk gSA Hkkstuky; dk ewy nSfud O;; (# esa) fdru
Days Average Sum Fkk\
(a) 4,280 (b) 5,280
29 560 29 × 560 (c) 3,680 (d) 4,980
16 590 16 × 590 Sol: (b)
16 500 16 × 500 Let,
Average expenditure = x
90x + 560 = (x – 10)120
16 590 + 500 – 29 × 560 90x + 560 = 120x – 1200
=
3 30x = 1760
Initial expenditure
16 1090 – 29 × 560 17440 – 16240 = 90x = Rs 5280
= = 28. The average height of 5 boys is 175 cm. A sixth
3 3
boy joined the group and the average height of
all the boys in the group now increased by one

r
1200
= = 400 centimetre. The height of the sixth boy is:
3 ,d lewg esa 5 yM+dksa dh vkSlr ÅapkbZ 175 lseh gSA ,d

si
26. Four numbers are such that if the average of yM+dk lewg esa 'kkfey gks x;k vkSj lewg ds lHkh yM+
three of them is added to fourth number the vkSlr ÅapkbZ vc ,d lsaVhehVj c<+ xbZA NBs yM+ds d
a n by
sum obtained 206, 210, 212, 214 respectively. gS%
What is the average of original four numbers. (a) 180 cm (b) 181 cm

n
pkj la[;k,¡ ,slh gSa fd ;fn muesa ls rhu dk vkSlr pkSFkh (c) 179 cm (d) 175 cm
Sol: (b)
la[;k esa tksM+k tk, rks ;ksx Øe'k% 206] 210] 212] 214 çkIr Height of 6th no boy = 176 + 1 × 5 = 181 cm
ja
gksrk gSA ewy pkj la[;kvksa dk vkSlr D;k gSA
R s

29. The average age of 35 persons is 40 years. 5

(a) 105.25 (b) 105 new persons with an average age of 35 years
a th

joined them. The average age of all the per-

(c) 106.25 (d) 106 sons is :
Sol: (a) 35 O;fÙkQksa dh vkSlr vk;q 40 o"kZ gSA muesa 35 o"k
Let, vk;q okys 5 u, O;fDr vkSj 'kkfey gksrs gSaA lHkh O;fDr
four numbers are a, b, c, d vkSlr vk;q fdruh gksxh\
ty a

A. T. Q, 3 1
(a) 39 years (b) 39 years
di M

a+b+c 8 8
+ d = 206
3 7 5
(c) 39 years (d) 39 years
8 8
b+c+d Sol: (c)
+ a = 210
3 Person Average
c+d+a 35 40
+ b = 212
3 5 35
By alligation
d+a+b
+ c = 214
3 35 40
6(a+b+c+d) = (206 + 210 + 212 + 214)3
2(a+b+c+d) = 842 x
A

a + b + c + d = 421
421 5 35
Average = =105.25 1 : 7
4
27. There are 90 students in a hostel. Due to new
35 ×1 + 40 × 7
admissions, 30 new students join the mess and Overall average age (x) =
the daily expenses of the mess increases by 8
560, while the average expenditure per head
35 + 280 315 3
diminishes by 10. What was the original daily = = = 39 years
expenditure (in Rs) of the mess? 8 8 8

Aditya Ranjan (Excise Inspector) Selected gSSelection fnyk,axs5

 Average

30. The average weight of some students in a class Sol: (a)

was 58.4 kg, when 5 students having the aver-
age weight 62.8kg joined the class, the aver- 65 – 60.5 8
age weight of all the students is increases by The no of student initially =
0.9
0.55 kg. The number of students initially in
the class were: 4.5 × 8
=
,d d{kk esa dqN Nk=kksa dk vkSlr otu 58-4 fdykxzke Fkk] 0.9
= (40 – 8) = 32
tc vkSlr otu 62-8 fdyksxzke okys 5 Nk=k d{kk esa 'kkfey
33. The average of n observations is 40. If one ob-
gq,] rks lHkh Nk=kksa dk vkSlr otu 0-55 fdyksxzke c<+ tkrk
servation of value 80 is added, then the aver-
gSa d{kk esa 'kq: esa Nk=kksa dh la[;k Fkh% age of all the observation is 41. What is the
(a) 30 (b) 35 value of n?
(c) 25 (d) 40
n i;Zos{k.kksa dk vkSlr 40 gSA ;fn ,d i;Zos{k.k ftldk ek
Sol: (b)
80 gS] 'kkfey fd;k tkrk gS rks lHkh i;Zos{k.kksa dk vkS
62.8 – 58.4 × 5 gks tkrk gSA
n dk eku Kkr dhft,A
The no of student initially =
0.55
(a) 43 (b) 38

r
4.4 (c) 40 (d) 39
= × 5 = (40 – 5) = 35
.55 Sol: (d)

si
31. The average weight of the students in a group
75.4 kg. Later on, four students having weights 80 – 40
a n by
Value of n = = (40 – 1) = 39
72.9 kg, 73.8 kg, 79.5 kg and 87.4 kg joined 1
the group. As a result, the average weight of 34. Given that the mean of five numbers is 28. If

n
the students in the group increased by 240 gm.
one of them is excluded, the mean gets reduced
What was the number of students in the group
by 5. Determine the excluded number.
ja
initially?
R s

,d lewg esa fo|kfFkZ;ksa dk vkSlr75.4

otu kg FkkA ckn esa ikap la[;kvksa dk ekè; 28 gSA ;fn muesa ls ,d la[;k dk
2.9 kg, 73.8 kg, 79.5 kg vkSj87.4 kg otu okys 4 fudky fn;k tk,] rks ekè; esa 5 dh deh gks tkrh gSA fudkyh
a th

fo|kFkhZ lewg esa 'kkfey gks x,A ifj.kke Lo:i] lewg ds lHkhxbZ la[;k Kkr dhft,A
fo|kfFkZ;ksa dk vkSlr otu
240 gm c<+ x;kA izkjaHk esa lewg (a) 46 (b) 48
esa fo|kfFkZ;ksa dh la[;k fdruh Fkh\ (c) 47 (d) 45
ty a

(a) 46 (b) 36 Sol: (b)

(c) 50 (d) 48
Mean of five nos. is 28
di M

Sol: (a)
Total sum of five nos. = 28 × 5 = 140
Initially average weight = 75.4 kg
Average weight of 4 student Let, the number excluded be 'x'
A.T.Q,
72.9 + 73.8 + 79.5 + 87.4
= = 78.4 140 – x = (28 – 5) × 4
4
The number of student initially x = 48
35. The average of 33 numbers is 74. The average
78.4 – 75.4 4
3 × 4 × 100
of the first 17 numbers is 72.8 and that of the
= = = (50 – 4) = 46
.24 24 last 17 numbers is 77.2. If the 17th number is
32. The average weight of some students in a class excluded, then what will be the average of the
was 60.5 kg. When 8 students, whose average remaining numbers (correct to one decimal
weight was 65 kg, joined the class, then the
A

place)?
average weight of all the students increased
by 0.9 kg. The number of students in the class, 33 la[;kvksa dk vkSlr 74 gSA igys 17 la[;kvksa dk vkS
initially, was: 72-8 gS vkSj vafre 17 la[;kvksa dk vkSlr 77-2 gS vkSj va
,d d{kk esa dqN fo|kfFkZ;ksa dk vkSlr otu 60-5 fdyks gSA17 la[;kvksa dk vkSlr 77-2 gSA ;fn 17 oha la[;k dks ckg
tc 65 fdxzk vkSlr otu okys 8 fo|kfFkZ;ksa ds vk tkus ls j[kk x;k gS] rks 'ks"k la[;kvksa dk vkSlr (,d n'keyo LFkk
vkSlr otu esa 0-9 fdxzk dh o`f¼ gks tkrh gSA d{kk esads fy, lgh) D;k gksXkk\
fo|kfFkZ;ksa dh vkjfEHkd la[;k fdruh Fkh\ (a) 72.9 (b) 71.6
(a) 32 (b) 37
(c) 70.8 (d) 73.4
(c) 42 (d) 40

Aditya Ranjan (Excise Inspector) Selected gSSelection fnyk,axs6

 Average

Sol: (a) Sol: (c)

Total sum of 33 numbers = 74 × 33 = 2442 Sum of 25 numbers = 64 × 25 = 1600
Sum of first 17 numbers = 72.8 × 17 = 1237.6 Sum of 1st 13 and last 13 numbers
Sum of last 17 numbers = 77.2 × 17 = 1312.4 = (62.8 × 13) + (72.2×13) = 1755
Let, the 17th number be x 13th number = 1755 – 1600 = 155
A.T.Q, 12th number is 61
2442 + x = 1237.6 + 1312.4 Average of remaining no
2442 + x = 2550
1600 – (155 + 61)
x = 108 = = 60.2
23
Average of remaining nos.
38. The average weight of a certain number of stu-
2442 – 108 dents in a group is 72 kg. If 10 students having
= = 72.9
32 an average weigt of 78 kg leave and 4 students
OR having an average weight of 80 kg join the
group, the average weight of the students in
Using Deviation the decreases by 0.7 kg. The number of students
72.8 – 74 = – 1.2 and 77.2 – 74 = + 3.2 initially in the group is:

r
Total deviation = 3.2 – 1.2 = +2 ,d lewg esa Nk=kksa dh ,d fuf'pr la[;k dk vkSlr otu 72
17th number = 74 + 17 × (+2) = 108 fdyksxzke gSA vxj 10 Nk=k ftudk vkSlr otu 78 fdyksxzxk

si
Average of remaining nos. gS NksM+dj pys tkrs gS vkSj 4 Nk=k ftudk vkSlr otu
fdyksxzke gS u, 'kkfey gksrs gS] rks Nk=kksa dk vkSlr
a n by
74 × 33 – 108
= = 72.9
32 7 fdyksxzke de gks tkrk gSA lewg esa 'kq: esa Nk=kksa

n
36. The average of 28 numbers is 77. The average gS%
of first 14 numbers is 74 and the average of (a) 44 (b) 46
ja
last 15 numbers is 84. If the 14th number is (c) 54 (d) 56
R s

excluded, then what is the average of remain- Sol: (b)

ing numbers? (correct to one decimal places)
a th

28 la[;kvksa dk vkSlr 77 gSA igyh 14 la[;kvksa dk vkSlr Student Average weight

74 vkSj vafre 15 la[;kvksa dk vkSlr 84 gSA 14oha la[;k dks x 72
Left
gVk fn, tkus ij 'ks"k la[;kvksa dk vkSlr (,d n'keyo 10 78 –6×10 +4×8
LFkku rd lgh) Kkr djsaA
ty a

Joined
4 80
(a) 77 (b) 74.7
Difference = – 60 + 32 = – 28 kg
di M

(c) 76.9 (d) 73.3

Sol: (d) 28
No. of student initially = = 40 + 6 = 46
74 – 77 = – 3 and 84 – 74 = 10 .7
Total deviation = 7 39. The average of the marks of 30 boys is 88, and
14th number = 77 + (14 × 7) = 175 when the top two scores were excluded, the
Average of remaining no average marks reduced to 87.5. If the top
scores differ by 2, then the highest mark is:
77 × 28 – 175
=
27
= 73.3 30 yM+dksa ds vadksa dk vkSlr 88 gS] vkSj tc 'kh"kZ n
37. The average of 25 numbers is 64. The averages dks ckgj dj fn;k x;k] rks vkSlr vad ?kVdj 87-5 jg x,A
of the first 13 numbers and that of the last 13 ;fn 'kh"kZ Ldksj 2 ls fHkUu gS] rks mPpre vad gS%
numbers are 62.8 and 72.2, respectively. If the (a) 90 (b) 94
12th number is 61, and if the 12th and 13th
A

(c) 92 (d) 96
numbers are excluded, then what is the aver- Sol: (d)
age of the remaining numbers (correct to one Average marks of 30 boys = 88
decimal place)?
Deviation of marks on 28 boys = 0.5 × 30 = 15
25 la[;kvksa dk vkSlr 64 gSA igyh 13 la[;kvksa dk vkSlr Sum of marks of 2 boys = 87.5 + 87.5 + 15 = 190
vkSj vafre 13 la[;kvksa dk vkSlr Øe'k% 62-8 vkSj 72_2 gSAA.T.Q,
;fn 12oha vkSj 13oha la[;k dks fudky fn;k tk,] rks 'ks"k Top two scores differ by 2
la[;kvksa dk vkSlr (n'keyo ds ,d LFkku rd) Kkr dhft,A So, one number will be 96 and other number
(a) 59.2 (b) 62.2 is 94
(c) 60.2 (d) 61.5  The highest marks is = 96

Aditya Ranjan (Excise Inspector) Selected gSSelection fnyk,axs7

 Average
40. The average weight of a class of 20 students fdlh lewg esa dqN O;fDr;ksa dk vkSlr otukg72gS tc 66-
is 45 kg. A new student whose weight is 40 kg 6 kg vkSlr otu okys 5 O;fDr lewg esa 'kkfey gksrs gSa v
replaces an old student of this class. Hence, the
average weight of the whole class decreased by 75 kg vkSlr otu okys 13 O;fDr lewg NksM+rs gSa] rks lew
1 kg. The weight of the replaced student is: O;fDr;ksa ds vkSlr otu esa 1-65 dh deh gksrh gSaA 'kq: es
20 Nk=kksa dh ,d d{kk dk vkSlr Hkkj 45 fdxzk gSA ,d u;kesa fdrus O;fDr Fks\
Nk=k ftldk otu 40 fdxzk gS] bl d{kk ds ,d iqjkus Nk=k dh (a) 40 (b) 44
txg ysrk gSA blfy,] iwjh d{kk vkSlr otu 1 fdxzk de gks (c) 38 (d) 48
tkrk gSA cnys x, Nk=k dk otu gS% Sol: (d)
(a) 55 kg (b) 50 kg Total no of persons initially
(c) 60 kg (d) None of these |72 – 66.6|5+|72 – 75|13
Sol: (c) = +8
1.65
Weight of the replaced student
= 40 + 20 × 1 = 40 + 20 = 60 kg  27 + 39   66 
=  + 8 =  + 8 = 48
41. In a combined family the average age of 4  1.65  1.65 
males and 7 females is 42 and 20 years respec-
tively. If two persons whose average age is 13 44. The average height of a certain number of stu-

r
years have left the family and other three dents in a group is 155.6 cm. If 12 students
people joined the family whose respective ages having an average height of 150.5 cm join the

si
are 11, 15 and 28 years, then the average age group and 7 students having an average height
of the new family is increased by: of 159 cm leave the group, the average height
a n by
,d la;qDr ifjokj esa 4 iq#"kksa vkSj 7 efgykvksa dh vkSlrof the students in the group will decrease by
vk;q Øe'k% 42 vkSj 20 o"kZ gSA ;fn nks O;fDr ftudh vkSlr34 mm. What is the number of students, ini-

n
tially, in the group?
vk;q 13 o"kZ gS] ifjokj NksM+ pqds gSa vkSj vU; rhu O;fDr
ftudh vk;q Øe'k% 11] 15 vkSj 28 o"kZ gS] ifjokj esa 'kkfey fdlh lewg esa Nk=kksa dh fuf'pr la[;k dh vkSlr ÅapkbZ 1
gks x, gSa] rks u, ifjokj dh vkSlr vk;q fdruh c<+ tkrh gS% 6 lseh gSA ;fn 150-5 lseh vkSlr ÅapkbZ okys 12 Nk=k
ja
R s

(a) 4 years (b) 1 year esa 'kkfey gksrs gSa vkSj 159 lseh vkSlr ÅapkbZ oky
lewg NksM+ nsrs gS] rks lewg esa Nk=kksa dhmm vkSlr Å
a th

(c) 3 years (d) No change

Sol: (d) rd de gks tkrh gSA lewg esa Nk=kksa dh vkjafHkd la[
42 × 4 + 20 × 7 168 +140 djsaA
1st Case = = (a) 30 (b) 25
11 11
ty a

(c) 40 (d) 20
308 Sol: (d)
= = 28
di M

11 Total no of students initially

28 ×11 – 26 + 54 336
= = 28 |155.6 – 150.5|12+|155.6 – 159|7
2nd Case = = –5
12 12 3.4
42. The average weight of 8 persons is increased
by 2.5 kg when one of them who weights 56 kg 61.2 + 23.8
= –5
is replaced by a new man. Find the weight of 3.4
new man.
= (25 – 5) = 20
8 O;fDr;ksa dk vkSlr otu 2-5 fdyks c<+ tkrk gS tc 5645. The average weight of some students in a class
fdyks okys O;fDr dh txg u;k O;fDr vk tkrk gSA u, O;fr was 69.5. When 10 students of average weight
dk otu Kkr djsa\ 68 kg joined the class, and 6 students of aver-
(a) 73 kg (b) 76 kg age weight 60 kg left the class, it was noted
(c) 86 kg (d) 82 kg that the average weight of the new group of
A

Sol: (b) students increased by 2 kg. How many students

Weight of new person = (56 + 2.5 × 8) are there in the class now?
= (56 + 20) = 76 kg fdlh d{kk esa dqN Nk=kksa dk vkSlr otukg69-5FkkA tc
43. The average weight of some person in a group 68 kg vkSlr otu okys 10 Nk=k d{kk esa 'kkfey gksrs gSa
is 72 kg. When 5 persons with average weight 60 kg vkSlr otu okys 6 Nk=k d{kk NksM+rs gS] rks ;g
66.6 kg join and 13 persons with average
weight 75 kg leave the group, the average
x;k fd Nk=kksa ds u, lewg ds vkSlr otu esa
kg 2
dh o`f¼
weight of the persons in the group decreases gqbZ gSA vc d{kk esa fdrus Nk=k gSa\
by 1.65 kg. How many persons were there in (a) 19 (b) 21
the group initially? (c) 29 (d) 26

Aditya Ranjan (Excise Inspector) Selected gSSelection fnyk,axs8

 Average

Sol: (b) 48. Mr. Kishor calculated the average of 10,'three

Total no of student now digit numbers'. But due to mistake he reversed
69.5 – 6810 + 69.5 – (60) 6 the digits of a number and thus his average
= increased by 19.8. The difference between the
2 unit digit and hundreds digit of that number
1.510 + 9.5 6 is:
=
2 Jh fd'kksj us 10] ^rhu vadksa dh la[;k* ds vkSlr dh x.ku
|15 – 57| 42 dhA ysfdu xyrh ds dkj.k mlus ,d la[;k ds vadksa dks myV
= = = 21
2 2 fn;k vkSj bl izdkj mldk vkSlr 19-8 c<+ x;kA ml la[;k
46. The average weight of some students in a group ds bdkbZ vad vkSj lkS vad ds chp dk varj gS%
is 58 kg. If 8 students of average weight 54 kg
leave the group, and 3 students weighing 53.6 (a) 8 (b) 4
kg, 54 kg and 57.4 kg join the group. then the (c) 2 (d) Can't be determined
average weight of the remaining students in Sol: (c)
the group will increase by 575 g.The number Difference in average = 19.8
of students, initially, in the group is:
fdlh lewg esa dqN Nk=kksa dk vkSlr otu 58 fdxzk gSA ;fn 54Difference in total = 19.8 × 10 = 198
fdxzk vkSlr otu okys 8 Nk=k lewg NksM+ nsrs gSa vkSj Let, 53-6 the number be xyz whose digits are

r
fdxzk] 54 fdxzk vkSj 57-4 fdxzk otu okys 3 Nk=k lewg esa reversed.
'kkfey gksrs gSa] rks lewg esa 'ks"k Nk=kksa ds vkSlr otu 100x
esa 575
+ 10y + z – (100z + 10y + x) = 99x – 99z

si
xzke dh o`f¼ gksxhA lewg esa Nk=kksa dh vkjafHkd la[;k fdruh – z)
= 99 (x
Fkh\ 99(x – z) = 198
a n by
(a) 40 (b) 45 x–z=2
(c) 35 (d) 50 49. Smriti was asked to find the average of N con-

n
Sol: (b) secutive natural numbers startin from 1. By
Total no of student initially = |(58 – 53.6) + (58 mistake, he added a number twice but he didn't
ja
– 54) + (58 – 57.4) + (58 – 54) 8| notice it. As a result he obtained a wrong aver-
R s

|4.4 + 4 + .6 – 32| 11
= +5 age of 45
a th

575 . Find the number she added twice.

18
|9 – 32| Le`fr dks 1 ls 'kq: gksus okyh
N yxkrkj izzkd`frd la[;kvksa
= + 5 = 45
.575 dk vkSlr [kkstus ds fy, dgk x;k FkkA xyrh ls] mlus nks ck
ty a

47. There are some children in a camp and their

average weight is 40 kg. If 5 children with av- ,d la[;k tksM+ nh ysfdu mlus bl ij è;ku ugha fn;kA
erage weight 36 kg join the camp or if 5 chil- 11
ifj.kkeLo:i mls 45 dk xyr vkSlr izkIr fd;kA mlds
di M

dren with average weight 43.2 kg leave the

camp, the average weight of children in both 18
cases is equal. How many children are there in }kjk nks ckj tksM+ xbZ la[;k Kkr dhft,A
the camp, initially?
(a) 8 (b) 11
,d f'kfoj esa dqN cPpksa dk vkSlr otu 40 fdxzk gSA ;fn 36 (c) 10 (d) 18
fdxzk vkSlr otu okys 5 cPps f'kfoj esas 'kkfey gks tk,a ;k
Sol:
43-2 fdxzk vkSlr otu okys 5 cPps f'kfoj ls pys tk,a] rks (c)
nksuksa fLFkfr;ksa esa cPpksa dk vkSlr otu leku jgsxkA vkjaHk esa N +1
f'kfoj esaa fdrus cPps Fks\ Average of N Consecutive numbers =
2
(a) 34 (b) 45
Let the number added be x
(c) 40 (d) 50
Sol: (b) 1  x  x
number 11
A

n Wrong Average is 45
18
+5 Correct Average could be 45 or 45.5
Case-I If average = 45
–5 3.2 × 5 = 16
N +1
20 16 = 45  N = 89
40 – = 40 – 2
n+5 n–5
Sum = 89 × 45 = 4005
 5n – 25 = 4n + 20
n = 45 11
45 × 89  integer
18

Aditya Ranjan (Excise Inspector) Selected gSSelection fnyk,axs9

 Average

Case-II If average = 45.5 (a) 63.9 (b) 64.5

(c) 64.7 (d) 64.1
N +1
= 45.5  N = 90 Sol: (d)
2
Student Average
Sum = 45.5 × 90 = 4095
50 65
11
45 × 90 = 4105 Correct data Wrong data
18
x = 4105 – 4095 = 10 38 83
50. The average of the marks of 25 students in a
class, in an examination was calculated to be
difference = – 45
19. Later, the teacher realized that the marks
of two students were taken as 18 and 19 re- 45
spectively, instead of 14 and 15. Find the new Correct average = 65 – =65 – 0.9 = 64.1
50
actual average marks of the class. 53. In a class, the average score of thirty students
,d ijh{kk esa ,d d{kk ds 25 Nk=kksa ds vadksa dk vkSlr 19in a test is 69. Later on, it was found that the
FkkA ckn esa] f'k{kd us eglwl fd;k fd nks Nk=kksa ds vad score
14 of one student was wrongly read as 88
instead of 58. The actual average score is:
vkSj 15 ds ctk; xyrh ls Øe'k% 18 vkSj 19 fy, x, FksA

r
,d d{kk easa] ,d ijh{kk esa rhl Nk=kksa dk vkSlr Ldksj 6
d{kk dk u;k okLrfod vkSlr vad Kkr dhft,A ckn esa ;g ik;k x;k fd ,d Nk=k ds Ldksj dks 58 ds ctk;

si
(a) 17.43 (b) 16.56 88 ds :i esa xyr rjhds ls i<+k x;k FkkA okLrfod vkSlr
(c) 18.68 (d) 17.65 Ldksj gS%
a n by
Sol: (c) (a) 88 (b) 68
Total error = (18 + 19) – (14 + 15) = 8 (c) 58 (d) 69

n
Actual average = 19 –
8
= 19 – 0.32 = 18.68
Sol: (b)
Student
ja
25 Average
R s

51. Mean marks of 50 students were found to be 30 69

78.4. But later it was detected that 95 was mis-
a th

Correct data Wrong data

read as 59 and 25 was misread as 52. What is
the difference between correct mean and in- 58 88
correct mean?
50 Nk=kksa ds vkSlr vad 78-4 ik, x,A ysfdu ckn eas irk
ty a

difference = –30
pyk fd 95 dks xyr rjhds ls 59 vkSj 25 dks xyr rjhds 30
ls 52 i<+k x;kA lgh ekè; vkSj xyr ekè; esa D;k varj gS\ Correct average = 69 – = 68
di M

30
(a) .04 (b) 0.08 54. The average marks of 40 students was found
(c) 0.12 (d) 0.18 to be 68. If the marks of two students were in-
Sol: (d) correctly entered as 48 and 64 instead of 84
Student Average and 46 respectively, then what is the correct
50 78.4 average?
Wrong data Correct data 40 fo|kfFkZ;ksa ds vkSlr vad 68 gSA ;fn nks fo|kFkhZ d
59 95 84 vkSj 46 ds LFkku ij xyrh ls Øe'k% 48 vkSj 64 ntZ gk
52 25 x, gks rks lgh vkSlr vad D;k gksxh\
difference = (95 + 25) – (59 + 52) (a) 68.15 (b) 68.25
(c) 68.35 (d) 68.45
= (120 – 111) = 9
Sol: (d)
9 Student Average
A

Average difference = = 0.18

50 40 68
52. The average marks of 50 students in an exami- Correct data Wrong data
nation was 65. It was later found that the marks 84 48
of one student had been wrongly entered as 83 46 64
instead of 38. The correct average is?
difference = (84 + 46) – (48 + 64)
50 Nk=kksa ds fdlh ijh{kk esa vkSlr vad 65 FksA ckn esa=,slk
(130 – 112) = 18
irk pyk dh fdlh Nk=k ds vad 38 ds ctk; 83 tksM+ fn;k
x, FksA lgh vkSlr D;k gksXkk\ 18 4.5
Correct average = 68 + = 68 + = 68.45
40 10

Aditya Ranjan (Excise Inspector) Selected gSSelection fnyk,axs10

 Average

55. The average of 100 numbers is 63, but it was 57. While tabulation of marks scored in an exami-
found that 2 numbers 37 & 76 are mistakenly nation by the students of a class, by mistake
calcultated as 73 & 67 respectively. Find his the marks scored by one student got recored
correct average if it was also found that total as 93 in place of 63, and thereby the average
numbers are only 90. marks increased by 0.5. What was the number
100 la[;kvksa dk vkSlr 63 gS] ysfdu ;g ik;k x;k fd 2 of students in the class?
la[;kvksa ftudk eku 37 vkSj 76 gS] bu la[;kvksa dks xyrh ,d d{kk ds Nk=kksa }kjk ijh{kk esa izkIr fd, x, vadks
ls Øe'k% 73 vkSj 67 ds :i esa x.kuk dh xbZA ;fn lkFk gh rkfydk cukrs le;] xyrh ls ,d Nk=k }kjk izkIr fd, x,
;g Hkh ik;k x;k fd dqy la[;k,a dsoy 90 Fkh rks lgh vkSlr
vadksa dks 63 ds LFkku ij 93 fy[k fn;k x;k] ftlds
Kkr dhft,\
(a) 70.3 (b) 62.7
ifj.kkeLo:i vadksa ds vkSlr esa 0-5 dh o`f¼ gks xbZA
(c) 63.3 (d) 69.7 esa fo|kfFkZ;ksa dh la[;k fdruh Fkh\
Sol: (d) (a) 20 (b) 60
Number Average Sum (c) 30 (d) 15
Sol: (b)
100 63 6300

r
Person Average
Correct data Wrong data 63 93

si
+ 37 73
+
76 67 difference = 30
a n by
30

n
Difference = (37+76) – (73+67) Total no of student = = 60
0.5
= 113 – 140 = – 27
58. The average score of Shubman Gill in 10 in-
ja
R s

6300 – 27 nings was 77 runs. In the 11th innings he had

Correct average = = 69.7
90 scored zero runs. The overall average score of
a th

56. The average age of a number of persons in a Shubman Gill in all the 11 innings was:
group was calculated as 35 years, which was 10 ikfj;ksa esa 'kqceu fxy dk vkSlr Ldksj 77 ju FkkA 11
2.5 years more than the correct average as ikjh esa mUgksaus 'kwU; ju cuk, FksA lHkh 11 ikfj;ksa e
there was an error in recording the age of two
dk dqy vkSlr Ldksj Fkk%
ty a

persons as 38.5 and 40 years instead of 29

years and 22 years respectively. The number (a) 77 (b) 7.7
di M

of persons in the group was? (c) 11 (d) 70

,d lewg essa dbZ O;fDr;ksa dh vkSlr vk;q 35 o"kZ Fkh] tks fd
Sol: (d)
lgh vkSlr ls 2-5 o"kZ vf/d Fkh D;ksafd 29 vkSj 22 ds ctk;
Innings Average Total Run
38-5 o"kZ vkSj 40 o"kZ ds :i esa nks O;fDr;ksa dh vk;q ntZ djus
esa =kqfV gqbZ Fkh Øe'k% o"kZA lewg esa O;fDr;ksa dh la[;k 10fdruh 77 770
th
Fkh\ 11 x 0
(a) 11 (b) 12
(c) 15 (d) 13 770
Average score of total innings = = 70
Sol: (a) 11
59. The bowling average of a cricketer was 12.5.
Person Average
He improves his bowling average by 0.5 when
x
A

35 he takes 5 wickets for 26 runs in his last match.

Correct data Wrong data The number of wickets taken by him before the
last match was?
29 38.5
+
22 40
+ ,d fØdsVj dk xsanckth vkSlr 12-5 FkkA tc og fiNys eSp
esa 26 ju nsdj 5 fodsV ysrk gS rks mlds xsanckth vkSlr es
Difference = |(29 + 22) – (38.5 + 40)|
= |(51 – 78.5)| = 27.5 5 dk lq/kj gksrk gS] fiNys eSp ls igys mlds }kjk fy, x,
fodVksa dh la[;k Fkh\
27.5
Total no of person = = 11 (a) 65 (b) 68
2.5
(c) 85 (d) 70

Aditya Ranjan (Excise Inspector) Selected gSSelection fnyk,axs11

 Average

Sol: (b) Sol: (a)

By alligation Innings Average Run Sum
26 24 x 24 x
12.5
5 25th 100
Average run before the 25th innings
12 = 100 – (25 × 1.4)
= (100 – 35) = 65
6.8 .5 63. A batsman in his 13th inning makes a score of
97 runs, thereby increasing his average score
Given that, 0.5 unit = 5 by 5. What is his average score after the 13th
inning?
5
then, 6.8 unit = × 6.8 = 68 ,d cYysckt }kjk viuh 13oha ikjh esa 97 ju cukus ij mlds
0.5
vkSlr Ldksj esa 5 o`f¼+ gks tkrh gSA 13oha ikjh ds ckn
60. The batting average for 27 innings of a cricket vkSlr Ldksj gksxk gS\
player is 47 runs. His highest score in an in- (a) 37 (b) 77
nings exceeds his lowest score by 157 runs. If (c) 67 (d) 57
these two innings are excluded, the average Sol: (a)
score of the remaining 25 innings is 42 runs.

r
Average score after the 13th innings = [97 – (5 × 12)]
Find his highest score in an innings. = 97 – 60 = 37

si
27 ikfj;ksa ds fy, fdlh fØdsV f[kykM+h dk cYysckth vkSlr
64. A cricket batsman had a certain average of runs
47 ju gSA ,d ikjh esa mldk mPpre Ldksj] mlds fUkEure in his 91 innings. In the 92th inning, he made
a n by
a score of 54 runs and thereby his average of
Ldksj ls 157 ju vf/d gSA ;fn ;s nks ikfj;k¡ gVk nh tk,¡] runs was decreased by 0.75. His average of runs
rks 'ks"k 25 ikfj;ksa dk vkSlr Ldksj 42 ju gSA ,d ikjh esaafter 92th innings is:

n
mldk mPpre Ldksj Kkr dhft,A ,d fØdsV cYysckt uss viuh 91 ikfj;ksa esa fuf'pr vkSlr ju
(a) 176 (b) 188 cuk;s Fks 92oha ikjh esa mUgksaus 54 jukas dk Ldksj cu
ja
(c) 186 (d) 174 rjg muds juksa dk vkSlr 0-75 de gks x;kA 92 juksa dh ik
R s

Sol: (b) ds ckn mudk vkSlr gS%

(a) 122.25 (b) 123.75
a th

Innings Average Run Sum (c) 123 (d) 121.5

27 47 1269 Sol: (a)
2 219 Innings Average Run Sum
25 42 1050
ty a

91 x 91 × x
2 Innings = 219 th
92 54
Inning of highest run = 31 + 157 =188
di M

61. A batsman scores 92 runs in his 15th innings, His average of runs after 92th innings
which increases his batting average by 4. What = 54 + (91 × 0.75)
will be his batting average after the 15th in- = 54 + 68.25
nings = 122.25
65. A cricketer had a certain average of runs for
,d cYysckt 15oha ikjh esa 92 ju cukrk gS] ftlls mlds his 64 innings. In his 65th innings, he is bowled
vkSlr esa 4 dh o`f¼ gks tkrh gSA 15oha ikjh ds ckn mldkout for no score on his part. This brings down
his average by 2 runs. His new average of runs
vkSlr D;k gS\ is:
(a) 32 (b) 36 ,d fØdsVj ds ikl viuh 64 ikfj;ksa esa juksa dk ,d fuf'pr
(c) 40 (d) 35 vkSlr FkkA viuh 65oha ikjh esa og fcuk dksbZ Ldksj
Sol: (b) vkmV gks x,A blls mldk vkSlr 2 ju de gks tkrk gSA mud
Average after 15th innings = 92 – (14 × 4) juksa dk u;k vkSlr gS%
A

= 92 – 56 = 36 (a) 130 (b) 128

62. A batsman makes 100 runs in the 25th match (c) 70 (d) 68
of his career. His average runs per match in- Sol: (b)
creases by 1.4. Find his average before the 25th
match. Innings Average Run Sum
,d cYysckt vius dfj;j ds 25osa eSp esa 100 ju cukrk gSA 64 x 64 x
mlds ju dk vkSlr çfr eSp vkSlr 1-4 c<+ tkrs gSaA 25osa eSp 65th 0 64 x + 0
ls igys mldk vkSlr D;k gS\
His new average of runs = 0 + 64 × 2 = 128
(a) 65 (b) 55
(c) 75 (d) 45

Aditya Ranjan (Excise Inspector) Selected gSSelection fnyk,axs12

 Average

66. A batsman scores certain runs in 72 innings. ,d fØdsV f•ykM+h dh 40 ikfj;ksa ds fy, cYysckth vkSlr
In next two innings he scores 24 and 36 re- 50 ju gSA mudk mPpre Ldksj muds lcls de Ldksj 172 ju
spectively. Therefore, decreases his average by ls vf/d gSA vxj bu nksuksa ikfj;ksa dks NksM+ fn;k tk, r
3 runs. Find his average after 74th innings. 38 ikfj;ksa dk vkSlr 48 ju gSA f•ykM+h dk mPpre Ldksj g
,d cYysckt us 72 ikkfj;ksa esa dqN ju cuk,A vxyh nks (a) 165 runs (b) 170 runs
(c) 172 runs (d) 174 runs
ikkfj;ksa esa mUgksaus Øe'k% 24 vkSj 36 dk Ldksj fd;kA
Sol: blfy,
(d)
mudk vkSlr 3 ju de gks tkrk gSA 74 oha ikjh ds ckn mudk Innings Average Score Sum
vkSlr Kkr djsa\ 40 50 2000
(a) 151 (b) 153 2 176
38 48 1824
(c) 138 (d) 155
 4 
Heighest score = 172 +  = 174
Sol: (c)
 2
Innings Average Run Sum 69. Average of 65 innings of a batsman is 50 runs.
72 x 72x His lowest score is 255 runs less than his high-
est score. If these two innings are excluded,
Next innings the average of remaining innings is 47 runs.

r
72x + 24 + 36 = (x – 3)74 Find the lowest score of player?
,d cYysckt dh vkSlr 65 ikfj;ksa esa 50 ju gSaA mudk lcl

si
72x + 60 = 74x – 222
2x = 222 + 60
de Ldksj muds mPpre Ldksj ls 255 ju de gSA vxj bu nksuk
ikfj;ksa dks NksM+ fn;k tk, rks 'ks"k ikfj;ksa dk vkSlr
a n by
2x = 282 gSA f•ykM+h dk fuEure Ldksj Kkr dhft;s\
x = 141 (a) 17 (b) 11

n
Average after 74th innings = (141 – 3) = 138 (c) 15 (d) 19
67. A batsman scores 556 run in 26th, 27th, 28th Sol: (a)
ja
and 29th innings together and now his average
R s

Innings Average Score Sum

increases by 4 runs. Find average run after 29th
65 50 3250
a th

match. 2 289
63 47 2961
,d cYysckt vius 26oha] 27oha 28oha vkSj 29 oha ikjh esa dqy
Heighest score + Lowest score = 289
feykdj 556 ju cukrk gS vkSj rc mlds vkSlr esa 4 juksa dh Lowest score = 17
o`f¼ gksrh gSA 29osa eSp ds ckn vkSlr ju Kkr dhft;s\70. A bowler, whose bowling average is 24.85 runs
ty a

(a) 107 (b) 110 per wicket. In next match he takes 5 wickets
for 52 runs and thereby decreases his average
di M

(c) 114 (d) 106 by 0.85. The number of wickets taken by him
Sol: (b) till the last match is?
,d xsanckt] ftldk xsanckth vkSlr 24-85 ju çfr fodsV gSA
Innings Average Run Sum vxys eSp esa mUgksaus 52 ju nsdj 5 fodsV fy, vkSj bl rj
25 x 25x mudk vkSlr 0-85 de gks x;kA vkf•jh eSp rd mlds }kjk
26 , 27 , 28th , 29th
th th
556 fy, x, fodsVksa dh la[;k fdruh gS\
(a) 80 (b) 75
Average run before last 4 innings (c) 85 (d) 90
Sol: (c)
556 – 116 By alligation
= 556 – (29 × 4) =
4
24.85 52
A

440 5
= = 110
4
Average run after 29th innings = (110 + 4) = 114 24
68. The batting average for 40 innings of a cricket
player is 50 runs. His highest score exceeds 13.6 .85
his lowest score by 172 runs. If these two in- 80 5
nings are excluded, the average of the remain-
5 unit = 5
ing 38 innings is 48 runs. The highest score of
80 unit = 80
the player is:
Required wicket = (80 + 5) = 85

Aditya Ranjan (Excise Inspector) Selected gSSelection fnyk,axs13

 Average

71. The bowling average of a cricketer was 12.4. 74. The average of the ages of a group of 65 men is
He improves his bowling average by 0.2 points 32 years, If 5 men join the group, the average
when he takes 5 wickets for 26 runs in his last of the ages of 70 men becomes 34 years. Then
match. The number of wickets taken by him the average of the ages of those 5 men joined
before the last match was: later (in years) is:
65 iq:"kksa okysa lewg dh vkSlr vk;q 32 o"kZ gSA ;fn
,d fØdsVj dk xsanckth vkSlr 12-4 FkkA mUgksaus vius xsanckth
vkSlr esa 0-2 dk lq/kj fd;k tc mUgksaus vius vkf•jh eSp iq:"k bl lewg esa 'kkfey gksrs gS rks 70 iq:"kksa dh vkSlr
esa 26 ju nsdj 5 fodsV fy,A vafre eSp ls igys muds }kjk 34 o"kZ gks tkrh gSA rks ckn esa tqM+us okys 5 iq:"kk
vk;q Kkr djsaA
fy, x, fodsVksa dh la[;k Fkh&
(a) 50 (b) 65
(a) 125 (b) 150
(c) 65 (d) 60
(c) 175 (d) 200 Sol. (d)
Sol: (c)
 65 × 2 
Average age of 5 new persons = 34 + 
12.4 5.2  5 
= 34 + 26 = 60 years
12.2
75. A SSC aspirant appears for a certain number of

r
tests. His average score increases by 1 if the
first 10 test are not considered and decrease

si
7 .2
by 1 if the last 10 are not considered .If his
0.2 unit = 5 average scores for the first 10 and the last 10
a n by
5 × 7 ×10 tests are 20 and 30 respectively. Then the to-
7 unit = = 175 tal number of tests taken by him is:
2

n
,d ,l,llh mEehnokj ,d fuf'pr la[;k esa ijh{k.kksa ds
72. In a village the average age of n people is 42
years. But after the verification it was found
fy, mifLFkr gksrk gSA ;fn igys 10 ijh{k.kksa ij fopkj ug
fd;k tkrk gS rks mldk vkSlr Ldksj 1 ls c<+ tkrk gS vkSj ;fn
ja
that the age of a person had been considered
R s

20 years less than the actual age, so the new vafre 10 ij fopkj ugha fd;k tkrk gS rks 1 ls de gks tkrk
gSA ;fn igys 10 vkSj vafre 10 ijh{k.kksa ds fy, mldk
a th

average, after the correction, increased by 1.

The value of n is: vkSlr Ldksj Øe'k% 20 vkSj 30 gSaA rks mlds }kjk fy,
,d xkao esan yksxksa dh vkSlr vk;q 42 o"kZ gSA ysfdu lR;kiuijh{k.kksa dh dqy la[;k gS%
ds ckn ;g ik;k x;k fd ,d O;fÙkQ dh vk;q okLrfod vk;q (a) 53 (b) 57
ty a

ls 20 o"kZ de ekuh xbZ Fkh] blfy, lq/kj ds ckn u, vkSlr (c) 60 (d) 63
Sol. (c)
esa 1 dh o`f¼ gqbZA
n dk eku D;k gksxkA
di M

Let the total number of tests be x and their

(a) 21 (b) 20 average be A.
(c) 22 (d) None of these Ax – 20 × 10 = (A + 1) (x – 10)
Sol. (b) Ax – 200 = Ax – 10A + x – 10
Required number 10A – x = 190
Age difference 20 Ax – 30 × 10 = (A – 1) (x – 10)
= difference in average = 1 = 20 Ax – 300 = Ax – 10A – x + 10
10A + x = 310
73. The average of the ages of sonu, Hari and 10A + x = 310 ........(i)
Govind is 30 years. If their ages are in the ra- 10A + x = 310 ........(ii)
tio of 4:5:6, respectively, then the difference Using (1) and (ii), we get
between the ages of sonu and govind is: 20A = 500 = A = 25
lksuw] gfj vkSj xksfoan dh vk;q dk vkSlr 30 o"kZ gSA ;fn mudh
from (1) , 10 × 25 + x =310
A

vk;q Øe'k% 4% 5% 6 ds vuqikr esa gS] rks lksuw vkSj xksfoan250dh+ x = 310 = x = 60
vk;q ds chp dk varj gS % 76. If a & b are non-negative real numbers such
(a) 18 years (b) 21 years that a + 2b = 6, then the average of the maxi-
mum & minimum possible values of (a+b)
(c) 15 years (d) 12 years
Sol. (d)
;fn a vkSjb xSj ½.kkRed okLrfod la[;k,a gSa tSls
a+ fd
2b = 6, rks(a+b) ds vf/dre vkSj U;wure laHko ekuksa dk
Given that,
vkSlr
15x = 30 × 3
(a) 1.5 (b) 2.5
x=6
(c) 3.5 (d) 4.5
Required difference = 2x = 12 years

Aditya Ranjan (Excise Inspector) Selected gSSelection fnyk,axs14

 Average

Sol. (d) 6 la[;kvksa esa ls] igyhs 5 la[;kvksa dk ;ksx 6oha la[;k d
a + 2b = 6 xquk gSA ;fn mudk vkSlr 136 gS] rks 6 oka uacj gS\
a+b=6–b (a) 102 (b) 84
(a + b) max when b = 0 (c) 96 (d) 116
a=6 Sol. (a)
(a + b) min when a = 0 Let, the six numbers are a, b, c, d, e, f
0+b=6–b A.T.Q,
2b = 6 = b = 3 a + b + c + d + e = 7f
then (a + b) min = 6 – 3 = 3 Given that,
6+3 9 7f + f
Average = = = 4.5 = 136
2 2 6
77. The average of 29 numbers is zero out of them, f = 102
how many be greater than zero at most? 80. The average of the first four numbers is three
29 la[;kvksa dk vkSlr 'kwU; gS] muesa vf/dre fdruh la[;k, times the fifth number. If the average of all
'kwU; ls vf/d gksaxh\ the five number is 85.8, then the fifth number

r
is?
(a) 27 (b) 28
igyh pkj la[;kvksa dk vkSlr] ik¡poha la[;k dk rhu xquk g

si
(c) 29 (d) 0
Sol. (b) ;fn mu lHkh ik¡p la[;kvksa dk vkSLkr 85-8 gS] rks ik
la[;k crkb,A
a n by
28 numbers can be greater than zero.
Let the sum of 28 numbers be x then the 29th (a) 33 (b) 29

n
number will be – x. (c) 39 (d) 34
78. The average of three numbers a, b and c is 2 Sol. (a)
ja
more than c. The average of a and b is 48. If d Let,
R s

is 10 less than c, then the average of c and d the five numbers are a, b, c, d, e
is: A.T,Q,
a th

a, b vkSjc rhu la[;kvksa dk vkSlr c ls 2 vf/d gSA a vkSj

a+b+c+d
b dk vkSlr 48 gSA ;fnd, c ls 10 de gS] rksc vkSjd dk = 3e
4
vkSlr Kkr dhft,A a + b + c + d = 12e
ty a

(a) 36 (b) 40 Given that,

(c) 35 (d) 38
di M

Sol. (b) 12e + e

= 85.8
A.T.Q, 5
e = 6.6 × 5
a+b+c
= c + 2 ......(i) e = 33
3 81. The average of x, y and z is 45. x is as much
a+b more than the average as y is less than the
= 48 ......(ii) average. Find the value of z.
2
x, y vkSjzz dk vkSlr 45 gSAx vkSlr ls ftruk vf/d gS
c – d = 10 ......(iii)
mruky vkSlr ls de gSAzz dk eku Kkr dhft,\
frome eq. (i)
(a) 45 (b) 25
a + b + c = 3c + 6
(c) 35 (d) 15
a + b – 2c = 6
A

Sol. (a)
2c = 90
c = 45 x +y+z
= 45
d = 35 3
45 + 35 80 Given that,
Average of c and d = = = 40 x – 45 = 45 – y
2 2
x + y = 90
79. Out of 6 numbers, the sum of the first 5 num-
90 + z = 45 × 3
bers is 7 times the 6th number. If their aver-
age is 136, then the 6th number is? 90 + z = 135
z = 45

Aditya Ranjan (Excise Inspector) Selected gSSelection fnyk,axs15

 Average

82. A student appeared in 6 papers. The maximum 19x + 30 × 24 = 1043

marks are the same for each paper. His marks 19x = 1043 – 720
in these papers are in the proportion of
19x = 323
5:6:7:8:9:10. Overall he scored 60%. In how
x = 17
many number of papers did he score less than
60% of the maximum marks? y=7
,d Nk=k 6 isijksa esa mifLFkr gqvkA çR;sd isij ds fy, vf/dre Required difference = (x – y) = (17 – 7) = 10
vad leku gSaA bu isijksa esa mlds vad 5%6%7%8%9%10 84. dsThe average of weight of 30 persons of group A
vuqikr
is 3 kg more than the average weight of 25per-
esa gSaA dqy feykdj mUgksaus 60» vad çkIr fd,A mlus fdrus sons group B. The average weight of 25 persons
isijksa esa vf/dre vadksa ds 60» ls de vad çkIr fd,\ of group B is 2.5kg more than the average weight
(a) 2 (b) 3 of 20 persons of group C. If the total weight of
(c) 4 (d) 5 30 persons of group A is 1725 kg. then what will
Sol. (b) be average weight of the persons of group A and
group C taken together (in kg)?
Let, maximum marks of each paper are = 100
marks obtained by the student lewgA ds 30 O;fÙkQ;ksa dk vkSlr otu]
B ds 25 O;fÙkQ;ksa ds
vkSlr otu ls 3 fdxzk vf/d gSA lewgB ds 25 O;fÙkQ;ksa dk

r
600 × 60
=
100
= 360 vkSlr otu] lewg C ds 20 O;fÙkQ;ksa ds vkSlr otu ls 2-5

si
fdxzk vf/d gSa ;fn lewgA ds 30 O;fÙkQ;ksa dk dqy otu
Let,
1725 fdxzk gS] rks lewg
A vkSj lewgC ds O;fÙkQ;ksa dk dqy
a n by
Obtain marks in each subject
5x, 6x, 7x, 8x, 9x, 10x vkSlr otu (fdxzk) esa fdruk gksxk\

n
45x = 360, x = 8 (a) 55.3 (b) 55.4
5 × 8, 6 × 8, 7 × 8, 8 × 8, 9 × 8, 10 × 8 (c) 55.1 (d) 55
ja
40, 48, 56, 64, 72, 80 Sol. (a)
R s

Marks obtain less than 60% = 3 papers

Group Person Average
83. There are 3 groups of persons-male, female and
a th

children. There are 20 males and the number 1725

A 30
of females and children taken together is 4 30
more than that of the males. The average 1725
B 25 –3
weight of males is 54 kg, that of females is 49
ty a

30
kg and that of children is 30 kg. If the average 1725
weight of the whole group is 48.25 kg, then C 20 – 5.5
30
di M

what is the difference between the number of

females and the number of children? Average weight of group C = (57.5 – 5.5)
O;fÙkQ;ksa ds rhu lewg gSa& iq#"k] efgyk vkSj cPps A iq#"k
Total20weight of group C = (57.5 – 5.5) × 20
gSa rFkk efgykvksa vkSj cPpksa dh dqy la[;k] iq#"kksa dh la[;k = 52 × 20 = 1040
ls 4 vf/d gSA iq#"kksa dk vkSlr otukg54] efgykvksa dk 1040 + 1725 2765
=
vkSlr otu 49 kg vkSj cPpksa dk vkSlr otu 30
kg gSA vxj Required average =
50 50
rhuksa lewgksa dk vkSlrkg48-25
gks] rks efgykvksa dh la[;k
vkSj cPpksa dh la[;k esa fdruk varj gS\ 5530
= = 55.3
(a) 17 (b) 10 100
(c) 7 (d) 14 85. A library has an average of 265 visitors on Sun-
days and 130 visitors on other days. The aver-
A

Sol. (b)
Let, No of female = x, No of boy = y age number of visitors per day in a month of
20 × 54 + x × 49 + y × 30 = 48.25 × 44 30 days beginning with a Monday is:
1080 + 49x + 30y = 11 × 193 ,d iqLrdky; esa jfookj dks vkSlru 265 rFkk vU; fnuksa e
49x + 30y = 2123 – 1080 vkSlru 130 yksx vkrs gSA lkseokj ls 'kq: gksus okys 30
49x + 30y = 1043 ds ,d eghus esa çfr fnu vkus okys n'kZdksa dh vkSlr la[
We know D;k gksxh\
x + y = 24 (a) 148 (b) 135
19x + 30x + 30y = 1043 (c) 165 (d) 129

Aditya Ranjan (Excise Inspector) Selected gSSelection fnyk,axs16

 Average

Sol. (a) Sol. (c)

A.T.Q, Let, total number = 100
Total no of sunday = 4 A.T.Q,
Remaining days = 26 Number Average
100 58
4 × 265 + 26 × 130
Required average = Sum = (65 × 16) – (35 × 9)
30
= (1040 – 315)
1060 + 3380 4440 = 725
= = = 148
30 30 725
New average = 58 + = 65.25
86. In a class of 80 students, 60% participate in 100
games and the rest do not. The average weight 88. In AKGEC college in B.Tech. ECE branch there
of the former group is 5% more than that of are three sections A, B and C. If number of stu-
the latter. If the average weight of all the stu- dents in section A, B and C are 95, 209 and
1 171 respectively and the average marks of sec-
dents is 51 kg then what is the average tion A, B and C in an exam are 83, 78 and 85
2
weight (in kg) of the former group? respectively. What is the average marks of ECE

r
branch?
80 fo|kfFkZ;ksa dh d{kk esa 60» fo|kFkhZ •sy esa Hkkx ysrs gSa
AKGEC dkWyst esaB. Tech. ECE 'kk•k esa rhu vuqHkkx

si
vkSj ckdh ugha •syrs gSaA igys okys lewg dk vkSlr otu ckn
A, B vkSjC gSaA ;fn vuqHkkx
A, B vkSjC esa Nk=kksa dh la[;
okys lewg dh rqyuk esa 5» vf/d gSA vxj lHkh fo|kfFkZ;ksa dk
a n by
Øe'k% 95] 209 vkSj 171 gS vkSj ,d ijh{kk esa vuqHkk
A,
1
vkSlr otu 51 kg gS rks igys okys lewg dk vkSlr otu B vkSjC ds vkSlr vad Øe'k% 83] 78 vkSj 85 gSaA
ECE
2

n
'kk•k dk vkSlr vad D;k gS\
D;k gS\
(a) 80.66 (b) 81.52
(a) 57.6 (b) 54.5
ja
(c) 81.48 (d) 82.16
R s

(c) 60 (d) 52.5

Sol. (b)
Sol. (d)
a th

Average marks in branch (ECE)

By alligation
95 × 83 + 209 × 78 + 171 × 85

21x 20x 95 + 209 + 171
ty a

38722
= = 81.52
51.5 475
di M

89. The average of 18 numbers is 37.5. If six num-

3 2 bers of average x are added to them, then the
average of all the numbers increases by one.
Let, average weight of former group = 21x
The value of x is:
Average weight of later group = 20x
21x × 3 + 20x × 2 = 51.5 × 5
18 la[;kvksa dk vkSlr 37-5 gSA ;fn 6 la[;k;s ftudk vkSlr
x gS dks mu lHkh la[;kvksa esa tksM+k tkrk gS] rks lHk
63x + 40x = 257.5
103x = 257.5 esa 1 dh c<+ksrjh gks tkrh
x dk
gSA
eku D;k gS\
(a) 42 (b) 40
257.5 (c) 38.5 (d) 41.5
x = = 2.5
103 Sol. (d)
Required average weight = 2.5 × 21 = 52.5 kg Average of 6 numbers
A

87. The average of n numbers is 58. If each of 65%

 18 
of the numbers is increased by 16 and each of = 38.5 +  = (38.5 + 3) = 41.5
the remaining numbers is decreased by 9, then
 6 
the new average of the numbers: 90. In an examination, the average score of a
n la[;kvksa dk vkSlr 58 gSA ;fn 65» la[;kvksa esa ls çR;sd student was 67.6. If he would have got 27 more
la[;k esa 16 tksM+ fn;k tk, vkSj 'ks"k la[;kvksa esa ls çR;sdmarks
esa in Mathematics, 10 more marks in
Computer Science, 18 more marks in History
ls 9 ?kVk fn, tk,a rks la[;kvksa dk u;k vkSlr D;k gksxk\ and retained the same marks in other subjects,
(a) 67.125 (b) 64.75 then his average score would have been 72.6.
(c) 65.25 (d) 66.5 How many papers are there in the examination?

Aditya Ranjan (Excise Inspector) Selected gSSelection fnyk,axs17

 Average

fdlh ijh{kk esa] fdlh Nk=k ds vkSlr vad 67-6 FksA ;fn mls rhu la[;k,a bl çdkj gS] fd ;fn muesa fdlh nks dk vkSlr
xf.kr esa 27 vf/d vad] dEI;wVj foKku esa 10 vf/d vad] rhljssa uacj esa tksM+k tkrk gS] rks çkIr la[;k,a de'k% 16
bfrgkl esa 18 vf/d vad feyrs] vkSj vU; fo"k;ksa esa leku vkSj 180 gSA rhuksa ewy la[;kvksa dk vkSlr D;k gS\
(a) 86 (b) 87
vad feyrs] rks mlds vkSlr vad 72-6 gksrsA ijh{kk esa dqy(c) 89 (d) 84
fdrus isij Fks\ Sol. (b)
(a) 11 (b) 10 Let, 3 numbers a, b, c
(c) 12 (d) 9 A.T.Q,
Sol. (a)  4 (a + b + c) = 2 (168 + 174 + 180)
No of papers in examination  4 (a + b + c) = 2(522)
a+b+c = 261
27 + 10 + 18 55
= = = 11 261
72.6 – 67.5 5 Average of 3 numbers = = 87
3
91. The average age of 24 students is 15.5 years. 94. The average of eleven numbers is 68. The av-
The age of the teacher is 24 years more than erage of the first four numbers is 78 and that
the average age of all the students and teacher. of the next four numbers is 63. The 9th num-

r
What is the age (in years) of the teacher? ber is two times the 11th number and the 10th
number is 4 less than the 11th number. What
24 fo|kfFkZ;ksa dh vkSlr vk;q 15-5 o"kZ gSA f'k{kd dh vk;q]

si
is the average of the 9th and 11th numbers?
lHkh fo|kfFkZ;ksa vkSj f'k{kd dh vkSlr vk;q
o"kZls
vf/d
24 X;kjg la[;kvksa dk vkSlr 68 gSA igyh pkj la[;kvksa d
a n by
gSA f'k{kd dh vk;q (o"kkZs esa) fdruh gS \ vkSlr 78 vkSj mlls vxyh pkj la[;kvksa dk vkSlr 63 gSA
(a) 40 (b) 41.4 9oha la[;k 11oha la[;k ls nksxquh gS vkSj 10oha la[;k

n
(c) 42 (d) 40.5 la[;k ls 4 de gSA 9oha vkSj 11oha la[;kvksa dk vkSlr K
Sol. (d) dhft, A
ja
(a) 72.6 (b) 70.1
R s

 24 
Age of teacher = 15.5 +  + 24 (c) 72.2 (d) 70.5
 24 
a th

Sol. (d)
= (16.5 + 24) = 40.5 Number Average Sum
92. 30 people went to a restaurant for a dinner 11 68 748
party. 20 of them paid Rs. 880 and each of the
ty a

4 63 252
rest of them paid Rs. 110 more than the aver-
age of the total expenses. What was the total 4 78 312
di M

expense (in Rs.) for the dinner? Sum of remaining 3 numbers

,d fMuj ikVhZ ds fy, 30 yksx fdlh jsLVksjsUV esa x,A muesa= 748 – (252 + 312)
ls 20 us çR;sd # 880 dk Hkqxrku fd;k vkSj 'ks"k yksxksa esa(748
ls – 564) = 184
Let, 11th number is x
çR;sd us dqy •pks± ds vkSlr ls # 110 vf/d Hkqxrku fd;kA 9th 10th 11th
fMuj ds fy, dqy •pZ (# esa ) fdruk Fkk \ 2x x–4 x
(a) 27,840 (b) 29,360 4x – 4 = 184
(c) 24,580 (d) 28,050 4x = 188
Sol. (d) x = 47
9th 10th 11th
Total expenditure for dinner
94 43 47
 110 ×10 
= 880 +
A

 × 30 94 + 47 141
 20  Required average =
2
=
2
= 70.5

= (880 + 55)30 95. The Average of twelve numbers is 56.5, The

(935 × 30) = Rs 28050 average of first four numbers is 53.4 and that
93. Three numbers are such that if the average of of next four numbers is 54.6 The 10th number
any two of them is added to the third number, is greater than the 9th number by 3 but less
the sums obtained are 168, 174 and 180 than 11th and 12th numbers by 2 and 3, respec-
respectively. What is the average of the origi- tively, what is the average of the 10th and the
nal three numbers? 12th numbers?

Aditya Ranjan (Excise Inspector) Selected gSSelection fnyk,axs18

 Average

ckjg la[;kvksa dk vkSlr 56-5 gSA igyh pkj la[;kvksa dk = (6 + 4 + 5)unit = 165
vkSlr 53-4 gS vkSj vxyh pkj la[;kvksa dk vkSlr 54-6 gSA 1 unit = 11
10 oha la[;k 9 oha la[;k ls 3 vf/d gS] ysfdu 11 oha vkSj sum of 22nd and 24th = 66 + 55 = 121
12 oha la[;k ls Øe'k% 2 vkSj 3 de gSA 10 oha vkSj 12 oha Required average = 121 = 60.5
la[;kvksa dk vkSlr D;k gS\ 2
(a) 62.5 (b) 58 97. The average weight of 3 men A, B and C is 84
(c) 56 (d) 57.5 kg. Another man D joins the group and the av-
erage now becomes 80 kg. If another man E
Sol. (a) whose weight is 3 kg more than that of D, re-
Number Average Sum places A, then the average weight of B, C, D
and E becomes 79 kg. Then weight of A is:
12 56.5 678.0
3 iq#"kksa
A, B vkSjC dk vkSlr otu 84 fdyksxzke gSA ,d
4 53.4 213.6 vkSj vknehD lewg esa 'kkfey gks x;k vkSj vkSlr vc 80
4 54.6 218.4 fdyksxzke gks x;kA ;fn dksbZ nwljk E vkneh
ftldk otu D
Sum of remaining 4 numbers dh rqyuk esa 3 fdyks vf/d gS]
A dh txg ysrk gS] rksB, C,
= 678 – (213.6 + 218.4) D vkSjE dk vkSlr otu 79 fdyksxzke gks tkrk gSA A dk
rks
= 678 – (432) otu D;k gS\

r
= 246 (a) 72 kg (b) 74 kg
Given that, (c) 75 kg (d) 76 kg

si
9th 10th 11th 12th Sol. (c)
x x+3 x+5 x+6 Weight of D = 80 – (4 × 3) = 68 kg
a n by
4x + 14 = 246 Weight of E = (68 + 3) = 71 kg
4x = 232 Given that,

n
x = 58 B + C + D + E = 79 × 4
B + C = 316 – (71 + 68)
61 + 64 125
ja
Required average = = = 62.5 B + C = (316 – 139)
R s

2 2 B + C = 177
96. The average of 24 number is 56. The average Given that,
a th

of the first 10 numbers is 71.7 and that of the A + B + C = 84 × 3 = 252

next 11 numbers is 42. The next three num- then,
bers (i.e., 22nd, 23rd and 24th) are in the ra-
weight of A = (252 – 177) = 75 kg
1 1 5 98. The average of A, B and C is 18 and that of C, D
ty a

tio : : nd
what is the average of the 22 and
2 3 12 and E is 12 and that of E and F is 6.5 and that
24th numbers? of E and C is 3.5. What is the average of A, B, C,
24 la[;kvksa dk vkSlr 56 gSA igyh 10 la[;kvksa dk vkSlr D, E and F?
di M

71-7 gS vkSj vxyh 11 la[;kvksa dk vkSlr 42 gSA vxyh rhu A, B vkSjC dk vkSlr 18 rFkkC, D vkSjE dk vkSlr 12
1 1 5 rFkkE vkSjF dk vkSlr 6-5 rFkkE vkSjC dk vkSlr 3-
la[;kvksa dk vuqikr2 : 3 : 12 gSA 22 oh vkSj 24 oh 5 gS rks
A, B, C, D, E vkSjF dk vkSlr D;k gS\
la[;kvksa dk vkSlr D;k gS \ (a) 24 (b) 16
(c) 18 (d) 22
(a) 60.5 (b) 58 Sol. (b)
(c) 55 (d) 49.5 A + B + C = 18 × 3
Sol. (c) A + B + C = 54 ...(i)
C + D + E = 36 ...(ii)
Numbers Average Sum E + F = (6.5) × 3
24 56 1344 E + F = 13 ...(iv)
A

10 71.7 717 E + C = 7 ...(v)

11 42 462 A + B + C + C + D + E + E + F + E + C = 54 + 36
+ 23 + 13 + 7
Sum of remaining 3 number = A + B + 3C + D + 3E +F = 110
1344 – (717 + 462) = A + B + 3(C + E) + D + F = 110
(1344 – 1179) = 165 A + B + 21 + D + F = 110
Given that, A + B + D + F = (110 – 21)
A + B + C + D + F = 89
 1 1 5 
 + +
 2 3 12  unit = 165 96
= 16
Required average = 89 + 7 =
6

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 Average

99. The average weight of 11 players of Indian 100. Which digit is missing in the average of num-
cricket team is increased by 1 kg, when one bers 9,99, 999, 9999, ..........999999999?
player of the team weighting 55 kg replaced by la[;kvks 9]99]999]-------- ]999999999 ds vkSlr esa dkS
a new player . The weight of the new player is:
vad mifLFkr ugha gS \
Hkkjrh; fØdsV Vhe ds 11 f•ykfM+;ksa dk vkSlr otu 1 (a) 0 (b) 1
fdyks c<+ tkrk gS] tc Vhe ds 55 fdyks otu okys ,d (c) 2 (d) 3
f•ykM+h dks ,d u, f•ykM+h ls cny fn;k tkrk gSA u, Sol: (a)
f•ykM+h dk otu D;k gksxkA Sum = 9 (1+11+111+11111 ....... +111111111)
(a) 55 kg (b) 64 kg 9(1 +11 +111 +1111....... +111111111)
(c) 66 kg (d) None of these Average =
9
Sol. (c)
= 123456789
The weight of new player = (55 + 11 × 1) = 66 kg

r
si
a n by
n
ja
R s
a th
ty a
di M
A

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SIMPLIFICATION/ljyhdj.k
[CLASSROOM SHEET]
CONCEPT-01 20
(a) 20 (b)
(BODMAS Rule) 3
25
This rule is the basic principle of solving (c) (d) 25
algebraic or numerical expressions. 3
4. Simplify
;g fu;e chtxf.krh; ;k la[;kRed O;atdksa dks gy djus fuEufyf[kr dk eku Kkr djsaA
dk ewy fl¼kar gSA 2.5 × [144 ÷ 198 × {121 × 81 ÷ (11 × 9)}]
Order to solve/gy djus ds Øe SSC CGL 17/07/2023 (Shift-01)

r
(a) 180 (b) 175
B  Bracket (dks"Bd)
(c) 185 (d) 190

si
O  of (dk) 5. Simplify./fuEu dk eku Kkr djsaA
D  Division an by
M  Multiplication
(Hkkx)
(xq.kk)
325 + 276 ÷ [150 – {9 × 9 + (83 – 4 × 15)}]
SSC CGL 20/07/2023 (Shift-03)

n
(a) 332 (b) 333
A  Addition (tksM+) (c) 334 (d) 331
ja (?kVko) 6. If (48 ÷ 72 × 3) – [15 ÷ 8 × (40 – 32) – 10] + 2P
R s
S  Subtraction
= 6 ÷ 2, then find the value of P?
Types of Bracket & Solving order
a th

;fn (48 ÷ 72 × 3) – [15 ÷ 8 × (40 – 32) – 10] +

dks"Bd ds çdkj ,oa gy djus ds Øe
2P = 6 ÷ 2, rksPdk eku Kkr dhft,\
(i)  Vinculum/Line/Bar bracket (js[kk SSC CPO 03/10/2023 (Shift-3)
ty a

dks"Bd) (a) 2 (b) 4

(c) 1 (d) 3
(NksVk dks"Bd)
di M

(ii) ( )  Small bracket

7. Find the value of the given expression.
(iii) { }  Curly bracket (ea>yk dks"Bd) uhps fn, x, O;atd dk eku Kkr dhft,A
(iv) [ ]  Square bracket (cM+k dks"Bd)
 1 1 4 3  1 1
1. The value of 11 × 11 + 11 ÷ 11 – 11 × 11 + 11  4 3  3 3  1 5  3 4  1 2  1 3  
+ 11 × 11 – 11 – 11 × 11 is:
2 5 2
11 × 11 + 11 ÷ 11 – 11 × 11 + 11 + 11 × 11 –    
3 6 3
11 – 11 × 11 dk eku D;k gS\
SSC CPO 03/10/2023 (Shift-01) SSC CHSL 10/08/2023 (Shift-2)
(a) 121 (b) 0 3 3
(c) 11 (d) 1 (a) 11 (b) 10
8 8
A

2. Evaluate the following 5 – [96 ÷ 4 of 3 – (16 –

55 ÷ 5)]. 3 5
(c) 14 (d) 16
5 – [96 ÷ 4 of 3 – (16 – 55 ÷ 5)] dk eku Kkr dhft,A 8 8
(a) 0 (b) 3 8. Simplify the following expression
(c) 2 (d) 4
fn, x, O;atd ljy dhft,A
3. Simplify the given expression.
fn, x, O;atd dk eku Kkr dhft,A  
25 – 16 – 14 – 18 – 8  3 
  
18 ÷ 3 of 2 × 5 + 72 ÷ 18 of 2 × 3 – 4 ÷ 8 × 2
(a) 16 (b) 18
SSC CGL 14/07/2023 (Shift-4) (c) 15 (d) 20

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9. Simplify: 13. Simplify the given expression.

fuEu dk eku Kkr dhft,A fn, x, O;atd dk lyhdj.k djsaA
1  1  1 1 1   (326  222)2  (326  222)2
3  4   3  2    (326  222)
3  3  3 3 3  
SSC CGL 18/07/2023 (Shift-01)
SSC CPO 04/10/2023 (Shift-01)
(a) 1 (b) 4
8 1 (c) 3 (d) 2
(a) – (b) 
3 3 14. The value of/dk eku Kkr djasA
2 1 0.325 × 0.325 + 0.175 × 0.175 + 25 × 0.00455 0.5
(c) (d) +
3 3 5 × 0.0065 × 3.25 – 7 × 0.175 × 0.025 1.5
1 1 47 47 SSC CPO 24/11/2020 (Shift-1)
10. If A = 3 4 ÷ 34 –  and B = 11
4 4 32 16 (a) (b) 3
3
1 1 11
2 5 ÷ 55 – then what is the value of 7

r
2 2 10 (c) 0 (d)
3
A – B?

si
15. The value of
1 1 47 47
;fn A = 3 4 ÷ 34 –
an by  rFkkB = 4.669  4.669 – 9  (0.777)²
4 4 32 16 is (1 – k),
(4.669)²  (2.331)²  14(0.667)(2.331)
1 1 11

n
2  5 ÷ 55 – gks] rks
A – B dk eku D;k gS\ where k = ?
2 2 10
4.669  4.669 – 9  (0.777)²
5 ja dk eku (1
R s
(a) (b) 1 (4.669)²  (2.331)²  14(0.667)(2.331)
8
– k) gS] ftlesak = ?
a th

3
(c) 0 (d) SSC CPO 11/12/2019 (Shift-02)
8 (a) 0.666 (b) 0.647
CONCEPT-02 (c) 0.467 (d) 0.768
ty a

(A) (0.13)²  (0.21)²

16. The value of
2
a² + b² = (a + b) – 2ab (0.39)²  81(0.07)²
di M

a² + b² = (a – b)2 + 2ab (2.4)4  3  (11.52)  9

 lies between:/dk
(2.4)6  6(2.4)4  3  (17.28)
a² – b² = (a + b)(a – b)
eku fdlds chp fLFkrgS\
11. Simplify the following expression. SSC CPO 12/12/2019 (Shift-01)
fuEufyf[kr O;atd dk eku Kkr dhft,A (a) 0.7 and 0.8 (b) 0.4 and 0.5
(c) 0.6 and 0.7 (d) 0.5 and 0.6
7.35  7.35  2.25  2.25
0.24
(B)
a + b = (a + b)(a – ab + b2)
3 3 2
SSC CGL 27/07/2023 (Shift-3)
a3 – b3 = (a – b)(a2 + ab + b2)
(a) 204 (b) 320 17. Simplify the given expression.
A

(c) 225 (d) 304 fn, x, O;atd dk ljyhdj.k djsaA

12. Simpify:
432  432  247  247  432  247
fuEu dks ljy dhft,A 432  432  432  247  247  247
(379  276)2  (379 – 276)2 SSC CGL 19/07/2023 (Shift-01)
379  379  276  276 1 1
(a) (b)
SSC CHSL 11/08/2023 (Shift-2) 259 185
(a) 2 (b) 655 1 1
(c) (d)
(c) 103 (d) 1 679 450

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(0.83)3 – (0.1)3 23. Simplify/ljy djsa%

18. Simplify: =?
(0.83)2  0.083  0.01 (3.321)3  (2.681)3  (1.245)3
(3.321)2  (2.681)2  (1.245)2
(0.83)3 – (0.1)3
lehdj.k (0.83)2  0.083  0.01 = ? 3  3.321  2.681  1.245
 (3.321  2.681)  (2.681  1.245)  (1.245  3.321)
SSC CHSL 14/08/2023 (Shift-2) SSC CHSL 04/08/2023 Shift-01
(a) 0.98 (b) 0.27 (a) 6.125 (b) 8.645
(c) 0.93 (d) 0.73 (c) 7.247 (d) 10.245
24. Simplify the given expression.
19. The value of/dk eku Kkr dhft,A

(0.013)³  (0.007)(0.000049) (80  80  80)  (70  70  70)  (50  50  50) – 840000

6400  4900  2500 – 5600 – 3500 – 4000
(0.007)²  0.013(0.013 – 0.007)
fn, x, O;atd dks ljy dhft,A
SSC CPO 13/12/2019 (Shift-02) SSC CHSL 10/08/2023 (Shift-01)

r
(a) 0.07 (b) 0.02 (a) 100 (b) 200
(c) 0.06 (d) 0.04 (c) 400 (d) 300

si
25. Simplify the following.
675  675  675  325  325  325 fuEufyf[kr dk ljyhdj.k dhft,A
20. an by
67.5  67.5  32.5  32.5 – 67.5  32.5
to:
is equal
0.01  0.01  0.01  0.003  0.003  0.003

n
0.05  0.05  0.015  0.05  0.015  0.015
675  675  675  325  325  325
SSC CGL 24/07/2023 (Shift-3)
ja
67.5  67.5  32.5  32.5 – 67.5  32.5
R s
13 13
fuEufyf[kr esa ls fdlds cjkcj gS% (a)  103 (b)  10 3
25 15
a th

(a) 100 (b) 10,000

(c) 1,000 (d) 1,00,000 13 13
(c)  103 (d)  10 3
15 25
2513  2493
ty a

21. The value of CONCEPT-03

25.1  25.1 – 624.99  24.9  24.9
is 5 × 10k, where the value of k is ____. (Bar Type Questions/ckj okys iz'u
)
di M

26. Convert 0.7777.........  into fraction

2513  2493 n'keyo 0.7777.........  dks fHkUu esa cnysa
dk eku 5 × 10k,
25.1  25.1 – 624.99  24.9  24.9
7 7
gS] tgk¡
k dk eku ____ gSA (a)
9
(b)
3
(a) 4 (b) 5
7 77
(c) 3 (d) 6 (c) (d)
10 99
(C) 27. Convert 0.535353............into fraction
If a + b + c = 0 n'keyo 0.535353............ dks fHkUu esa cnysa
53 53
then  a³ + b³ + c³ = 3abc (a)
99
(b)
49
What is the value of/dk eku Kkr dhft,A
A

22. 53 53
(c) (d)
100 59
0.74  1.23  0.13 28. Convert it into vulgar fraction
(0.37)3  (0.41)3 – 8(0.39)3
0.5 87
SSC CPO 11/12/2019 (Shift-01) CISF HCM 30/10/2023 Shift-01
–1 93 97
(a) (b) 1 (a) (b)
3 167 165
1 95 91
(c) –1 (d) (c) (d)
3 167 165

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29. Correct expression of 0.0654 . (the bar 35. Find the value of/dk eku Kkr dhft;s
indicates repeating decimal)
0.2  0.3  0.32
0.0654 dk lgh O;atd gS (ckj n'keyo dh iqujko`frÙk (a) 0.77 (b) 0.82
dks n'kkZrk gS)%
(c) 0.86 (d) 0.87
NTPC CBT-2 19/01/2017 (Shift-1)
36. Find the value of/dk eku Kkr dhft;s
654 654
(a) (b) 324.786 – 10.193
1000 10000

18 18 (a) 314.59345 (b) 314.59445

(c) (d)
275 277
(c) 314.59345 (d) 314.59445
30. Correct expression of 1.427 . (the bar indicates
37. If A = 0.312 , B = 0.415 and C = 0.309 , then
repeating decimal)
what is the value of A + B + C?
1.427 dk lgh ljyhdj.k gS (ckj n'keyo dh iqujko`fÙk
;fn A  0.312 , B  0.415 rFkk C  0.309 gS] rks

r
dks n'kkZrk gS)%
A  B  C dk eku fdruk gS\

si
NTPC CBT-2 17/01/2017 (Shift-3)
1211 1043
(a)
1427
1000
an by (b)
157
110
(a)
1100
(b)
1100

n
1427 157 1097 1141
(c) (d) (c) (d)
10000 111 1100 1100
ja Find the value of/dk eku Kkr dhft;s
R s
31. 2.8768  ? 38.
a th

878 9 22.4  11.567 – 33.59

(a) 2 (b) 2
999 10 SSC CGL TIER - II 11/09/2019
(a) 0.412 (b) 0.31
ty a

292 4394
(c) 2 (d) 2 (c) 0.412 (d) 0.32
333 4995
di M

32. Find the Value of x/x dk eku Kkr dhft;s 39. Find the value of/dk eku Kkr dhft;s

0.3  0.4  0.5  0.6  x 0.57 – 0.432  0.35

SSC CGL TIER - II 16/11/2020
(a) 3 (b) 5
(a) 0.494 (b) 0.498
(c) 2 (d) 8
33. The value of 0.56  0.43  0.89 is (c) 0.498 (d) 0.494

dk eku gS 40. Find the value of/dk eku Kkr dhft;s

0.56  0.43  0.89
NTPC CBT-1, 23/02/2021 (Shift-01) 0.47  0.503 – 0.39  0.8
SSC CGL TIER - II 13/09/2019
(a) 1.98 (b) 1.87
A

(a) 0.615 (b) 0.615

(c) 1.89 (d) 1.88
(c) 0.625 (d) 0.625
34. 3.245  1.234  2.12 is equal to: 41. Find the value of/dk eku Kkr dhft;s
3.245  1.234  2.12 cjkcj gS & 0.56 – 0.723  0.39  0.7
ICAR Mains, 08/07/2023 (Shift-3) SSC CGL TIER - II 12/09/2019
(a) 2.358 (b) 2.437 (a) 0.154 (b) 0.154
(c) 2.243 (d) 2.536 (c) 0.158 (d) 0.158

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42. Find the value of/dk eku Kkr dhft;s 48. Which of the following is the largest fraction?
fuEu esa ls lcls cM+h fHkUu dkSu lh gS\
 2.4  0.6  3  0.16    0.27   0.83  0.16  
8 6 4 13
SSC CGL TIER - II 15/11/2020 , , ,
9 11 9 15
(a) 0.814 (b) 0.11
8 6
(c) 1.1 (d) 1.36 (a) (b)
9 11
43. 2.75  3.78
4 13
(a) 1.03 (b) 1.53 (c) (d)
9 15
(c) 4.53 (d) 5.53 LCM Method
5 49. Find the greatest among
44. If 0. ab  0. ba  , find the value of a + b.
9 fuEufyf•r fHkUuksa esa ls lcls cM+h fHkUu Kkr dhft,A
5
;fn 0. ab  0. ba  ] rksa + b dk eku Kkr dhft;sA 1 5 3 6
9 , , &
2 7 4 7

r
(a) 5 (b) 6
(c) 7 (d) 8 1 5

si
7 (a) (b)
45. If 0.xy = , find x² + y² =? 2 7
11

;fn 0.xy =
7
11
an by
, rc x² + y² =? (c)
3
4
(d)
6
7

n
(a) 36 (b) 44 50. Find the smallest among
(c) 45 (d) 55
ja fuEufyf[kr esa ls dkSu&lk fHkUu lcls NksVk gS\
R s
CONCEPT-04
2 8 10 16
of fraction/fHkUuksa dh) rqyuk
, , &
a th

(Comparison 3 9 27 9
Cross Multiplication Method 2 8
(a) (b)
46. Which fraction among the following is the 3 9
ty a

least?
10 16
fuEufyf[kr esa ls dkSu&lk fHkUu lcls NksVk gS\ (c) (d)
di M

27 9
5 7 8 9
, , , Proper Fractions
11 12 13 17
SSC CGL MAINS (08/08/2022) Numerator of the fraction is less then
denominator or we can say value of the
8 5 fraction is less than 1.
(a) (b)
13 11 va'k dk eku gj ls NksVk gks vFkok fHkUu dk eku 1 ls
9 7 de gksA
(c) (d)
17 12 1 2 4 7 12
, , , , etc.
47. Find the greatest of the following fractions. 2 3 5 11 23
fuEufyf•r fHkUuksa esa ls lcls cM+h fHkUu Kkr dhft,A To compare/rqyuk ds fy,%
A

8 15 4 13 Step 1: Take the difference of Nr and Dr of each

, , ,
11 19 5 21 of the fractions. /izR;sd fHkUu ds va'k rFkk gj dk
CRPF HCM 23/02/2023 (Shift - 01) varj Kkr djsaA
Step 2: Difference must be same. If the given
13 15 difference is not same, make them same by
(a) (b)
21 19 taking LCM of each difference./varj leku gksuk
4 8 pkfg,A ;fn varj leku ugh gSa rks izR;sd varj dk y-l-i-
(c) (d)
5 11 ysdj mls leku dj ysaA

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Step 3: Fraction with smaller Nr will be least Step 2: Difference must be same. If the given
and fraction with greater Nr will be greatest./ difference is not same, make them same by
bl izdkj izkIr U;wure va'k okyh fHkUu lcls NksVh taking LCM of each difference./varj leku gksuk
rFkk
vf/dre va'k okyh fHkUu lcls cM+h gksxhA pkfg,A ;fn varj leku ugh gSa rks izR;sd varj dk y-l-i-
ysdj mls leku dj ysaA
Ex: Compare/rqyuk djsaA
Step 3: Fraction with smaller N r will be
4 6 13 11 greatest and fraction with greater Nr will be
, , ,
5 7 14 12 smallest./bl izdkj izkIr U;wure va'k okyh fHkUu
lcls
Ex: The greatest value among the fractions
cM+h rFkk vf/dre va'k okyh fHkUu lcls NksVh gksxhA
Ex: Compare/rqyuk djsaA
lcls cM+k vkSj lcls NksVk fHkUu Kkr djsaA
23 37
2 1 5 3 ,
, , , 18 32
7 3 6 4 Ex: Find smallest and greatest fraction
51. What is difference between the largest and the lcls NksVk vkSj lcls cM+k fHkUu Kkr djsaA
5 7 8 11 16 20 25 35
smallest fractions among , , and ? , , ,

r
9 11 15 17 15 19 24 34
Ex: Find smallest and greatest fraction

si
esa ls lcls cM+s vkSj lcls NksVs lcls NksVk vkSj lcls cM+k fHkUu Kkr djsaA
5 7 8 11
, , vkSj
9 11 15 17
an by
fHkUu dk varj D;k gS\
15 8 11 7
, , ,
16 3 12 8

n
CRPF HCM 24/02/2023 (Shift - 02)
Base Method
29 8
(a) (b) (i) When denominator is equal.
255 ja 99
R s
tc gj cjkcj gksA
1 17
a th

(c) (d) 2 14 9 25
45 165 , , ,
17 17 17 17
52. What is the difference of the largest and
smallest of the given fractions? Fraction with greater numerator will be
ty a

greatest
nh xbZ fHkÂksa esa ls lcls cM+h vkSj lcls NksVh fHkUu dk varj and vice-versa.
D;k gS\ cM+s va'k okyk fHkUu lcls cM+k gksxk vkSj blds foi
di M

Hkh lgh gksxkA

5 5 3 6 (ii) When Numerator is equal.
, , ,
11 7 8 11 tc va'k cjkcj gksA
SSC CHSL 13/03/2023 (Shift-01) 9 9 9 9
, , ,
17 19 4 7 10 13
(a) (b)
56 56 Fraction with smaller denominator will be
1 23 greatest and vice-versa.
(c)
7
(d)
56 NksVs gj okyk fHkUu lcls cM+k gksxk vkSj bldk foij
Improper Fractions lgh gksxkA
Numerator is greater than denominator or value (iii) If we increase N r and decrease D r , then
of the fraction is greater than 1. resultant fraction will be greater.
A

va'k dk eku gj ls cM+k gks vFkok fHkUu dk eku 1 ls vf/ ;fn ge N dks c<+krs gSaDvkSj dks ?kVkrs gSa] rks ifj.kkeh
r r

d gksA fHkUUk vf/d gksxkA

3 5
3 13 6 27 e.g. (i) <
, , , etc. 7 6
2 4 5 17
101 103
To compare//rqyuk ds fy,% (ii) <
236 234
Step 1: Take the differecne of Nr and Dr of each
339 347
of the fractions./izR;sd fHkUu ds va'k rFkk gj dk varj (iii) <
237 231
Kkr djsaA

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(iv) If we decrease Nr and increase Dr then resultant

247 228
fraction will be smaller. (iii) &
437 387
;fn ge Nr dks ?kVk,¡ vkSj
Dr dks c<+k,¡ rks ifj.kkeh
fHkUu NksVk gks tk,xkA – 19 < 10%
7 6
e.g. (i) >
11 13
247 228
101 99 Sol:
(ii) > 437 387
236 247
334 329
(iii) > – 50 > 10%
229 235
(v) If we increase N r and D r together or we
Here % decrease in Dr dominates.
decrease Nr and Dr together than the resultant
fraction can be increase or decrease or will  Resultan fractions will be greater.
have no change that can be determined by 247 228
using percentage change.  
437 387

r
;fn ge Nr vkSjDr dks ,d lkFk c<+krs gSa ;kNge r
vkSj
743 691

si
D dks ,d lkFk ?kVkrs gSa rks ifj.kkeh fHkUu c<+ ;k ?kV
r
(iv) &
829 789
ldrk gS ;k blesa dksbZ ifjorZu ugha gksxk ftls çfr'kr
an by
ifjorZu dk mi;ksx djds fu/kZfjr fd;k tk ldrk gSA
– 52 > 5%

n
123 137
e.g. (i) &
237 267
+14 ja
 11% Sol: 743 691
R s
829 789
a th

123 137
Sol: – 40 < 5%
237 267
ty a

743 691
 
+30  13% 829 789
di M

Here % increase in Dr dominates.

CONCEPT-05
 Resultant fraction will be smaller.
(Ladder fractions)
123 137
  1
237 267 53. 1 =?
1
1
4
423 492 1
(ii) & 5
322 389
21 17
(a) (b)
+69 < 20% 17 13
23 23
(c) (d)
14 15
A

423 492 1
Sol: 54. The value of 1 +
322 389 1
1+
1
1+
1
+ 67 > 20% 1+
2
1+
Here % increase in Dr dominates. 3
 Resultant fraction will be smaller. 21 17
(a) (b)
13 2
423 492 34 8
  (c) (d)
322 389 21 5

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55. Find the value of x in the following equation: 59. What will the value after simplifying this
continued fraction?
fuEufyf•r lehdj.k esa x dk eku Kkr dhft,%
bl fujarj fHkUu dks ljy cukus ds ckn eku D;k gksxk\
  1
 
  1
1 6 x 2+
1   1 = 1
 1  11 2 3+
1 1
 1 2+
 1  4
 5 NTPC CBT-1, 03/02/2021 (Shift-02)
NTPC CBT-2 17/06/2022 (Shift-3) 43 43
(a) (b)
(a) 2 (b) 1 5 19
5 19
1 2 (c) (d)
(c) (d) 19 43
2 3 1 9
60. If A  = , then the value of A is:
1 10
1 5 1
1

r
56. If = , then what is the value of x? 2
1 8 3
1+

si
1 1 9
1+ ;fn A  , gS] rksA dk eku gS%
1 =
1+ 1 10
an by x 1
2
1
3

n
1 5 SSC CPO 03/10/2023 (Shift-3)
;fn 1
= , gks] rks
x dk eku D;k gS\
8
1+ 3 2
ja 1 (a) (b)
R s
1+ 10 5
1
1+
a th

x 1 1
(c) (d)
10 5
(a) 1 (b) 2
(c) 3 (d) 4 1
61. Simplify: 15 +
ty a

1
1 6+
57. Find the value of 1 – 1
1 8+
di M

1– 10
1
1– CRPF HCM 01/03/2023 (Shift - 02)
2
1–
3 81 71
(a) 15 (b) 15
496 186
2 1
(a) (b) 
3 3 81 31
(c) 15 (d) 15
1 2 472 374
(c) (d) 
3 3
1
62. 2+ =?
1 1
58. 1 =? 2–
1 1
A

1– 3–
1 1
1 4–
1 4
1–
1
1 CRPF HCM 28/02/2023 (Shift - 01)
3
41 15
1 11 (a) (b) 2
(a) (b) 67 41
2 7
41 15
3 9 (c) 2 (d)
(c) (d) 67 41
4 4

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63. Find the value of the following 1 17

68.  find a + b + c + d =?
fuEufyf[kr dk eku Kkr dhft,A a
1 60
1
5 b
4– 1
1 c
1+ d
1
3+
1 (a) 11 (b) 12
2+
4
(c) 13 (d) 14
1 1
(a) (b) 1 30
4 8 69.  find a + b + c + d = ?
1 43
2 3 a
(c) (d) 1
4 7 2b 
1
3c 
64. The value of/dk eku fdruk gksxk\ d
(a) 10 (b) 11
1 1
3 3

r
7 2  1 (c) 7 (d) None
is :
1 1 1
3 3 3

si
4 7 1 70. If a, b, c, d are integers such that
2
1
an by 2
2
a
1
1

29
154
, then a + b + c + d = ?

n
ICAR Mains, 10/07/2023 (Shift-2) 1
b
(a) 213.50 (b) 209.25 1
c
(c) 225.15 ja (d) 232.35 d
R s
65. 5 =?
a th

3 (a) 12 (b) 13
3
5
7 (c) 14 (d) 15
1
5
45 1
ty a

9 13 71. If  , where a, b and c are

(a) (b) 53 1
13 9 a
1
di M

b
11 19 2
(c) (d) c–
2 5 5
Positive integers, then what is the value of
(4a + b + 3c)?
1
66. 2 =? SSC CGL TIER - II 15/11/2020
1
3
1 (a) 5 (b) 4
4
1
5 (c) 6 (d) 7

7 4
(a) (b) 72. If 1 29 , where x, y and y are
4 7 
1 79
x
A

11 12 2
(c) (d) y
14 5 1
z
4
1 13
67.  find a – b + c=? natural numbers, then the value
1 29
a (2x + 3y – z) is:
1
b
c SSC CGL TIER - II 16/11/2020
(a) 1 (b) 2 (a) 1 (b) 4
(c) 0 (d) 3 (c) 0 (d) 2

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CONCEPT-06 79.
1

1

1
+.....+
1
1 2  3 2  3  4 3  4  5 98  99  100
(Continuous Fraction Series/lrr fHkUukRed Js.kh
)
4949 1980
 1 1  1  1 1  1 
(a) (b)
73.  19800 49490
1 – 
 1 –  1 – 
 1 – 
  .... 
1 – 
1 – 


 3  4  5  6  99   100  
9898 1980
(c) (d)
2 1 19800 47490
(a) (b)
99 25 80. Which of the following statement is true?

1 1 1 1 1 1 5
(c) (d) I.    ......... 
50 100 2 6 12 110 6
74. The sum of 1 1 1 1 7
II.    ......... 
1 1 1 1 3 15 35 143 13
+ + + ..... +
2 6 12 n  n +1 is: SSC CHSL 13/03/2023 (Shift-04)
(a) Only I
1 1 1 1 (b) Both I and II

r
+ +
2 6 12
+ ..... +
n  n +1 dk ;ksx gS& (c) Only II
(d) Neither I nor II

si
NTPC CBT-1, 02/03/2021 (Shift-03) 1 1 1 1
81. If x = + + ......+ , y =
 n  1
(a) 
n 

an by (b)
n 1
2n 1
12.13 13.14 14.15
1 1 1
23.24
x

n
+ + .......+ then is
n n  1 n 36.37 37.38 38.39 71.72 y
(c) (d)
2 n 1 equal to:
ja
R s
1 1 1 1 1 1
75.    .......  (a) (b)
11  12 12  13 13  14 80  81 3 24
a th

69 70 1
(a) (b) (c) (d) 3
890 891 72
1 1 1
ty a

71 72   ...... 
(c) (d) 82.
790 891 1 3  5 3  5 7 9  11  13
di M

1 1 1 1 35 35
76.    .......  (a) (b)
1  4 4  7 7  10 97  100 429 439
33 34 25 25
(a) (b) (c) (d)
100 99 329 329
1 1 1
35 37 83.   ...... 
(c) (d) 123 4 23 4 5 6789
99 100
83 84
1 1 1 1 (a) (b)
77.   +....+ 1512 1513
3  7 7  11 11  15 899  903
83 84
21 18 (c) (d)
(a) (b) 1415 1413
509 409
A

1 1
25 29 84.  +.................+
(c) (d) 1 3  5 7 3  5 7  9
301 31
1
1 1 1 1
78.    .......  11  13  15  17
4  9 9  14 14  19 99  104
20 22
7 9 (a) (b)
(a) (b) 1991 1989
104 100
25 27
5 8 (c) (d)
(c) (d) 1990 1991
104 105

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1 1 1 1 1 1 1
85.   + ....+ 91.    ..... 
4  11  18 11  18  25 18  25  32 22 – 1 4 2 – 1 62 – 1 202 – 1
1 9 10
67  74  81 (a) (b)
19 19
425 425
(a) (b) 11 10
263736 253737 (c) (d)
19 21
424 425
(c) (d) 1 1 1 1
253737 253736 92. 2 2
 2 2
 2 2
 .... 
7 –3 13 – 3 19 – 3 49 – 32
2

1 1
86. + + ..........+ 1 3
1 2  3 4  5 23456 (a) (b)
26 52
1
10  11  12  13  14 1 3
(c) (d)
13 26
10009 10009
(a) (b) CONCEPT-07
960960 960970

r
10019 10018 b
Types of numbers/izdkj dh la[;k,a)

si
(c) (d) (a
960961 960961 c
5 7
an by 9 11 13 (a) If denominator of a number same as multiplier
87. + + + + +
22.32 32.42 4 2.52 52.62 62.72
;fn fdlh la[;k dk gj mlds xq.kt ds leku gks rks

n
15 17 19
2 2 + 2 2 + is equal to. 95
7 .8 8 .9 9 .102
2
93. The value of 99  99 is
99
1 ja 6
R s
(a) (b) (a) 9798 (b) 9997
100 25
(c) 9898 (d) 9896
a th

101
(c) (d) 1 98
100 94. 999  99 is equal to:
99
4 6 8 10 12 (a) 98999 (b) 99899
  
ty a

88. +
3  7 7  13 13  21 21  31 31  43
(c) 99989 (d) 99998
39 40
di M

(a) (b) 994

128 129 95. 999  999
999
41 42 (a) 908999 (b) 999099
(c) (d)
130 135 (c) 998995 (d) 989095
1 1 1 1 1 (b) If difference between numerator and denomi-
89.    + +
1 3  5 1 4 3  5  7 4  7 579 nator is 1.
1 ;fn va'k vkSj gj ds chp dk varj 1 gks rks
+.....+ upto 20 terms
7  10
1 791
6179 6070 96. + 999 × 99
(a) (b) 8 792
15275 14973 (a) 89000 (b) 88900
(c) 95900 (d) 99000
A

7191 5183
(c) (d)
15174 16423 1 494
97. Find the value of  999  99
1 1 1 5 495
90. a1  , a2  , a3  t h e n , (a) 90000 (b) 99000
25 58 8  11
a1 + a2 + .... + a100 + ? (c) 90900 (d) 99990
25 30 1  692 
(a) (b) 98.   999   99 is equal to:
151 157 7  693 
1 9 (a) 1 (b) 99000
(c) (d)
4 55 (c) 99800 (d) 99900

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(c) Series Type/Js.kh izdkj • Sum of the cubes of first 'n' natural numbers.

1 2 4 izFken izkÑfrd la[;kvksa ds ?kuksa dk ;ksxiQy

99. 999 + 999 + ........... + 999
5 5 5 2
 (n + 1) 
(a) 3798 (b) 3998 13 + 23 + 33 +...........+n3 =  n 
 2 
(c) 3899 (d) 9939
• Sum of even integers/le iw.kkZadksa dk ;ksxiQy
100. Find the value of
2 + 4 + 6........... + 2n = n (n + 1)
1 2 3 4 • Sum of odd integers/fo"ke iw.kkZadksa dk ;ksxiQy
777  777  777  777
5 5 5 5
1 + 3 + 5 +............(2n – 1) = n2
1 2 3 4
777  777  777  777 dk eku Kkr dhft,A 101. What is sum of odd numbers from 1 to 50?
5 5 5 5
1 ls 50 rd fo"ke la[;kvksa dk ;ksx D;k gS\
NTPC CBT-1, 03/03/2021 (Shift-01)
(a) 625 (b) 650
(a) 3110 (b) 3018
(c) 667 (d) 670

r
(c) 3000 (d) 3108
102. What is sum of first 50 odd numbers?

si
CONCEPT-08 çFke 50 fo"ke la[;kvksa dk ;ksx D;k gS\
Some Standard Formulae for Addition
an by (a) 2500 (b) 2600
tksM+ ds fy, dqN lkekU; lw=k (c) 2700 (d) 2800

n
• Sum of first 'n' natural numbers 103. 72 + 8² + ....+ 12² =?
izFken izkÑfrd la[;k dk ;ksxiQYk (a) 459 (b) 559
ja
R s
n(n +1) (c) 567 (d) 570
1 + 2 + 3 +.........+ n =
2 104. Find the value of 212 + 222 + 232 ........ + 30²
a th

• Sum of the squares of first 'n' natural numbers. 212 + 222 + 232 ........ + 30² dk eku Kkr dhft,A
izFken izkÑfrd la[;kvksa ds oxksaZ dk ;ksxiQy (a) 6855 (b) 6585
n(n +1)(2n +1) (c) 5865 (d) 8565
ty a

12 + 22 + 32 +..........+ n2 =
6 105. 9³ + 10³ +.....+ 14³ + 15³
Sum of square of n odd/even number/n fo"ke@le
di M

• (a) 12104
n(n +1)(n + 2) (b) 12105
la[;kvksa ds oxksaZ =dk ;ksx where n is last (c) 13104
6
odd/even number/tgk¡n vafre fo"ke@le la[;k gSA (d) 14104
A

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ANSWER KEY
1.(d) 2.(c) 3.(a) 4.(a) 5.(d) 6.(d) 7.(d) 8.(a) 9.(a) 10.(d)

11.(a) 12.(a) 13.(b) 14.(a) 15.(a) 16.(c) 17.(c) 18.(d) 19.(b) 20.(d)

21.(a) 22.(a) 23.(c) 24.(b) 25.(d) 26.(a) 27.(a) 28.(b) 29.(c) 30.(b)

31.(c) 32.(c) 33.(c) 34.(a) 35.(d) 36.(c) 37.(d) 38.(c) 39.(c) 40.(d)

41.(a) 42.(c) 43.(c) 44.(a) 45.(c) 46.(b) 47.(c) 48.(a) 49.(d) 50.(c)

51.(a) 52.(b) 53.(c) 54.(c) 55.(a) 56.(b) 57.(c) 58.(d) 59.(d) 60.(d)

61.(a) 62.(c) 63.(b) 64.(b) 65.(d) 66.(b) 67.(a) 68.(c) 69.(c) 70.(c)

r
si
71.(a) 72.(d) 73.(c) 74.(d) 75.(b) 76.(a) 77.(c) 78.(c) 79.(a) 80.(d)

81.(d) an by
82.(a) 83.(a) 84.(b) 85.(a) 86.(a) 87.(b) 88.(b) 89.(b) 90.(a)

n
91.(d) 92.(a) 93.(d) 94.(a) 95.(c) 96.(d) 97.(b) 98.(b) 99.(b) 100.(a)

101.(a) 102.(a) ja103.(b) 104.(b) 105.(c)

R s
a th
ty a
di M
A

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SIMPLIFICATION/ljyhdj.k
(Practice Sheet With Solution)
1. What value should come in the place of 6. Simplify the following
question mark in the following equation? fuEufyf[kr dks gy dhft,A
fuEufyf[kr lehdj.k ds iz'uokpd fpÉ ds LFkku ij 3

dkSu&lk eku vkuk pkfg,\ 814 + [(20 ÷ 5 of 3 × 6)+{(8 ÷ 24 of 3)× 4} – 10

–2
(0.006 ÷ 0.01 ) + (0.008 ÷ ?)–(0.003 ÷ 0.03)
= 0.6
 1 5
÷ 5] – 
 32 
UPSI 1/12/2021 (Shift-01)
(a) 0.08 (b) 0.001 SSC CPO 09/11/2022 (Shift-01)

r
(c) 0.8 (d) 0.008 1 1
(a) 24 (b) 21

si
2. Find the value approximate to two decimals. 4 9
nks n'keyo rd vuqekfur eku Kkr dhft,A 4 4
an by
(44.6+346.33+3346.333+ 33346.3333) ÷ 50 = ?
UPSI 13/11/2021 (Shift-02)
(c) 27
5
(d) 29
9

n
7. Solve the following equation.
(a) 742.67 (b) 740.67
fuEufyf[kr lehdj.k dks gy dht,A
(c) 743.67 ja (d) 741.67
R s
3. What is the value of 123 × (162 – 142 – 40) ÷ 2 – 94 = ?
SSC CPO 09/11/2022 (Shift-03)
a th

7 5 14  10 10 (a) 17280 (b) 6561

× + ?
7– 5 14 – 10 5 (c) 10719 (d) 986
8. If 65% of 350 – ?% of 250 + 40% of 120 = 158,
7 5 14  10 10
dk eku D;k gS\
ty a

× + then find the value of ?

7– 5 14 – 10 5
;fn 350 dk 65% – 250 dk ?% + 120 dk 40%
SSC CGL MAINS (08/08/2022) = 158 gks] rks
? dk eku Kkr djsaA
di M

(a) 2 +1 (b) 2 2 +2 SSC CGL 19/07/2023 (Shift-03)

(c) 2+ 2 (d) 2 2 +1 (a) 57 (b) 63
4. What value should come in the place of (c) 47 (d) 54
question mark (?) in the following equation? 9. Simplify: [0.08 – {3.5 – 4.9 – (12.5 – 7.8 – 4.6)})
fuEufyf•r lehdj.k esa ç'u fpÉ (\) ds LFkku ij D;k [0.08 – {3.5 – 4.9 – (12.5 – 7.8 – 4.6)}) dk eku
eku vkuk pkfg,\ Kkr dhft,A
(0.006 ÷ ?) + (0.004 ÷ 0.04) + (0.03 ÷ 0.3) SSC CGL 20/07/2023 (Shift-04)
= 0.3 (a) 1.58
UPSI 14/11/2021 (Shift-03) (b) 0.08
A

(a) 0.006 (b) 0.6 (c) 2.58

(c) 0.001 (d) 0.06 (d) 12.58
5. If (48 ÷ 72 × 3) – [15 ÷ 8 × (40 – 32) – 10] + 2P 0.04
= 6 ÷ 2, then find the value of P 10 Find the value of of
0.05
;fn (48 ÷ 72 × 3) – [15 ÷ 8 × (40 – 32) – 10] +
2P = 6 ÷ 2, rksPdk eku Kkr dhft,  1 1 1 1
 3 – 2   of 1
3 2 2 4
SSC CPO 03/10/2023 (Shift-3)
1 1 1
(a) 2 (b) 4  of
3 5 9
(c) 1 (d) 3

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15. Simplify/ljy dhft,A

 1 1 1 1
 3 – 2   of 1 3
–2744× 3 –216
0.04 3 2 2 4
of 1 1 1 dk eku Kkr dhft,A 64
0.05  of 3
3 5 9 729
SSC CPO 03/10/2023 (Shift-01) SSC CPO 09/11/2022 (Shift-01)
(a) 5 (b) 0.4 (a) 164 (b) 512
(c) 3 (d) 0.03 (c) 189 (d) 156
11. The square root of is:/dk oxZewy gS% 16. Simplify/ljy dhft,A
 1   1   1   1   36  3 76  19 
          456 – 76 +152  + of ÷ 
4 9 25   49   121  4 18  72 × 24 
SSC CPO 04/10/2023 (Shift-01) SSC CPO 10/11/2022 (Shift-02)
(a) 443 (b) 256
11 1
(a) (b) (c) 356 (d) 401
12.60 1260
17. Simplify/ljy dhft,A

r
11 1260
(c) (d) 3 76  19 
1260 11 456 – 76 +152  +

si
of ÷ 
12. The value of 4 18  72 × 24 

1
2  3  1 
5  4  4 2
an by
  3  1 
 1 1 1  
1  3  1   
2 3 3 
(a) 17
SSC CPO 10/11/2022 (Shift-03)
(b) 21

n
(c) 19 (d) 12
18. Simplify/ljy dhft,A
2  3  1   1 1 1  
1   3  1 
5  4  4 2 ja 1  3  1   
2 3 3  dk eku  5  3  5 3  
R s
 –  –  –    of 8.8 –1.2
fdruk gksxkA 8 8 8 8 
a th

SSC CPO 04/10/2023 (Shift-01)

1 1  3 3
4 ÷2.5 × 2 ÷ of 60 +  – 
(a) 1 (b) 3 6 6  4 8
(c) 2 (d) 0 SSC CPO 11/11/2022 (Shift-01)
ty a

13. Simplify/ljy dhft,A 22 23

(a) 5 (b) 3
 1 7  3 2 1 43 67
di M

 2 ÷1  ÷  9 ÷11 of  44 4
2 8 8 3 8 (c) 4 (d) 4
85 5
SSC CHSL 09/08/2023 Shift-04
19. Find the value of/dk eku Kkr djsaA
33 11
(a) (b) 8 7  1 1 2 1
135 135 6 ÷ of 1 +5  + ÷7
15 9 10 5 5 5
28 57 SSC CPO 11/11/2022 (Shift-02)
(c) (d)
135 135
25 5
14. Simplify/ljy dhft,A (a) (b)
16 14
 1 1 4 3  1 1 25 5
 4 3  3 3  1 5  3 4  1 2  1 3  
A

(c) (d)
18 18
2 5 2 20. What is the positive value of the following
   
3 6 3 expression?
SSC CHSL, 10/08/2023 (Shift-2)
fuEufyf[kr O;atd dk /ukRed eku D;k gksxk\

3 3  25 × 4 ÷ 4 of 
(a) 11 (b) 10  
8 8 36 ÷ 15 of 2 of  29 – 8 – 11 ÷
 
3 5   9 × 5 ÷ 5 of 3 
(c) 14 (d) 16
8 8 SSC CPO 11/11/2022 (Shift-02)

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25. Simplify the following expression.
5 1
(a) 1 (b) 1 fuEu O;atd dk eku Kkr dhft,A
6 5
 72 
67
 48   36 
12  5   71    [(51  4  13)  (13  12  7)]
4 3  16   11
(c) 2 (d) 2  
5 5 232

21. Simplify/ljy dhft,A SSC CGL 19/07/2023 (Shift-02)

–31 31
 16+ 28 of 7÷22    (a) (b)
 2 3   233 233
 25 +8÷2 –   2 2 1  
  – 18 ÷12 of    41 31
  8  (c) (d)
232 232
SSC CPO 11/11/2022 (Shift-03)
(a) 626 (b) 529 x 24
26. If 1+ = , then the value of x is:
(c) 721 (d) 579 529 23

r
22. Find the value of/dk eku Kkr djsaA x 24
;fn 1+ = gS] rks
x dk eku Kkr dhft,A

si
3 529 23
40 – of 32
4 SSC CPO 11/11/2022 (Shift-02)
3
37 – of (34 – 6)
4
an by (a) 15 (b) 27

n
(c) 47 (d) 30
SSC CPO 23/11/2020 (Shift-1) 27. Simplify the given expression.
(a) 1 ja (b) 0 y + 2x – [(y – (y – x + y) – (x + y) + y] – 2y.
R s
fn, x, O;atd dk eku Kkr dhft,A
1 1
a th

(c) – (d) y + 2x – [(y – (y – x + y) – (x + y) + y] – 2y.

2 2
SSC CGL TIER I 17/07/2023 (Shift-01)
23. Find the value of/dk eku Kkr djsaA (a) – y (b) – 2x
ty a

 1 3 1  1 7 9  (c) Y (d) 2x
 5 ÷ of  ÷  5 – 7 ÷ 9  28. What is the value of the given expression ?
4 7 2 9 8 20 
di M

1 4 a  4 –5 × 4 a  2
11 
× –  5 ÷ 2 of  15 × 4 a –22 × 4 a
21 2
fn, x, O;atd dk eku D;k gS\
SSC CPO 23/11/2020 (Shift-2)
4 a  4 –5 × 4 a  2
35
(a) 0 (b) 15 × 4 a –22 × 4 a
24
SSC CGL (PRE) 24/07/2023 (Shift-1)
15
(c) –2 (d) (a) 16 (b) 64
28
24. Find the value of/dk eku Kkr djsaA (c) 20 (d) 24

4 –2 –7 5
A

 1  1 3 1 29. Arrangement of the fractions , , , in

 5 ÷ 2 of  +  5 ÷ of  3 9 8 12
2 4 7 2
ascending order is
 1 7 9  11
÷  5 – 7 ÷ 9 × 4 –2 –7 5
9 8 20  21 fHkUuksa
, , , dks vkjksgh Øe esa O;ofLFkr djuk gS
3 9 8 12
SSC CPO 24/11/2020 (Shift-1)
7 2 5 4 7 2 4 5
(a) – ,– , , (b) – ,– , ,
35 15 8 9 12 3 8 9 3 12
(a) (b)
24 28 2 7 5 4 2 7 4 5
(c) – ,– , , (d) – ,– , ,
(c) –2 (d) 8 9 8 12 3 9 8 3 12

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11 7 3
30. Sum of thre fractions is 2 . On dividing the (a) (b)
24 9 7
7
largest fraction by the smallest fraction is 5 7
6 (c) (d)
9 10
1
obtained which is greater than the middle 34. A fraction having denominator 30 and lying
3
fraction. The smallest fraction is 5 7
between and is
8 11
11
rhu fHkUuksa dk2;ksx gSA lcls cM+h fHkUu dks lcls
24 5 7
,d fHkUu ftldk gj 30 gS vkSj tks vkSj ds chp gS
7 8 11
NksVh fHkUu ls foHkkftr djus çkIr
ij gksrk gS tks fd
6 18 19
1 (a) (b)
eè; fHkUu ls vf/d gSA lcls NksVh fHkUu gSA 30 30
3
20 21
5 3 (c) (d)

r
(a) (b) 30 30
8 4

si
35. The greatest number among 0.7  0.16 ,
5 3
(c) (d)
6 7 0.6
31.
an by
Which of the largest of the following fraction?
fuEufyf•r esa ls dkSu lk fHkUu lcls cM+k gS\
1.02 –
24
, 1.2 × 0.83 and 1.44

n
0.6
8 3 0.7  0.16 , 1.02 – 24 , 1.2 × 0.83 vkS j
(a) (b)
11 ja 5
esa ls lcls cM+h la[;k
R s
1.44
11 2
(c) (d) (a) 0.7  0.16 (b)
a th

17 3 1.44
32. Which of the following fractions does not lie 0.6
(c) 1.2 × 83 (d) 1.02 
5 8 24
between and ?
ty a

6 15
4 9
5 8 36. The least number among , , and (0.8)2 is
fuEufyf•r esa ls dkSu lk fHkUuvkSj ds chp ugha 9 49 0.45
di M

6 15
gS\ 4 9
, , vkSj(0.8)2 esa lcls NksVh la[;k gS
2 3 9 49 0.45
(a) (b)
3 4
4 9
4 6 (a) (b)
(c) (d) 9 49
5 7
(c) 0.45 (d) (0.8)2s
9
33. A fraction becomes
11
, if 2 is added to both 37. Find the value of/dk eku Kkr dhft,A
the numerator and the denominator. If 3 is 1 × 2 + 2 × 3 + 3 × 4 + 4 × 5 + ..... ..... ... + 10 × 11
added to both the numerator and the (a) 4329 (b) 5826
A

5 (c) 4290 (d) 3815

denominator it becomes . What is the
6 38. If 5 3 + 75 = 17.32 then the value of
fraction?
14 3 + 108 is:
9
,d fHkUu gks tkrh gS] ;fn mlds va'k vkSj gj nksuksa ;fn 5 3 + 75 = 17.32 gS] rks14 3 + 108 dk
11
eku Kkr djsaA
esa 2 tksM+ fn;k tk,A ;fn va'k vkSj gj nksuksa esa 3 tksM+
SSC CGL 20/04/2022 (Shift-03)
5
fn;k tk, rks ;g gks tkrk gS fHkUu D;k gS\ (a) 32.46 (b) 35.64
6 (c) 34.64 (d) 33.86

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39. Find the value of/dk eku Kkr dhft,A 45. Simplify/ljy dhft,A

1 1 1 1 1 1 1 1 1 2 3 4 5 6
       999 + 999 + 999 + 999 + 999 + 999
2 6 12 20 30 42 56 72 7 7 7 7 7 7

7 3 (a) 5997 (b) 5979

(a) (b)
9 4 (c) 5994 (d) 2997

6 8  999 
(c) (d) 46.  999  7  is equal to/fdlds cjkcj gS%
5 9 1000 
40. Find the value of/dk eku Kkr dhft,A
7 7
1 1 1 1 1 (a) 6993 (b) 7000
    1000 1000
20 30 42 72 90
7 993
1 3 (c) 6633 (d) 6999
(a) (b) 1000 1000
10 5
Find the value of/dk eku Kkr dhft,A

r
47.
3 7
(c) (d)
995

si
20 20
999 × 999
41. Find the value of/dk eku Kkr dhft,A 999

1

1

1

1

1
an by

1

1

1
(a) 990809
(c) 999824
(b) 998996
(d) 998999

n
20 30 42 56 72 90 110 132
1 1 998
(a) (b) 48. 999 × 999 is equal to/fdlds cjkcj gSA
8 ja 7 999
R s
(a) 998999 (b) 999899
1 1
a th

(c) (d) (c) 989999 (d) 999989

6 10
42. Find the value of/dk eku Kkr dhft,A 49. Simplify/ljy dhft,A

1 1 1 1 1
ty a

    1
15 35 63 99 143 2
1
2
di M

5 4 1
(a) (b) 2
39 39 1
2
5
2 7
(c) (d)
39 39 137 157
43. The simplified value of/dk ljyhÑr eku gSA (a) (b)
85 65
 1  1  1  1  1  138 183
1 –  1 –  1 –  ....... 1 –  1 –  (c) (d)
3 4 5 99 100  72 95
2 1 50. Simplify/ljy dhft,A
(a) (b)
99 25
1
A

2
1 1 1
(c) (d) 1
50 100 1
3
1
44. The value of/dk eku gS 2
5
 1  1  1  1 
1   1   1   ....... 1   136 127
2 3 4 120  (a) (b)
49 36
(a) 30 (b) 40.5
153 189
(c) (d)
(c) 60.5 (d) 121 64 81

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51. Simplify/ljy dhft,A (a) 1 (b) 4

2 (c) 3 (d) 2
2
3 5 1
5
4 56. If A 
3
and B 
a tahen the value
1 1
3 3–
5 2 1
1– 2–
25 141 3 5
(a) (b) 7
11 69
of A + B
138 125
(c) (d)
60 65 5 1
52. Simplify/ljy dhft,A ;fn A  3 rFkkB  1 rksA + B dk
3 3–
9 2 1
3 1– 2–
3 3 5
2 7
7
1 eku D;k gS\
8
297 531 7 7

r
(a) (b) (a) (b)
54 65 3 6

si
413 217 13 8
(c) (d) (c) (d)
91 98 12 5
53.
1 1
an by
On simplification, the expression
57. If A = 1 
1
and B 
1
, then what

n
4 –2 1 2
7 7 1 1 3
1 1 1 1 1
3 1 2 1 2
2 7 ja 1 is equal to
9 2
R s
2 is the value of 19 (A + B)?
1
5–
5 1
a th

1
1 1 ;fn A  1  1 rFkkB  rks19 (A +
4 –2 1 2
7 7 1 1 3
1 1
1 1 1 9 2
3 1 2 2
ty a

ljyhdj.k djus ij O;atd 2 7

2
1 ds B) dk eku D;k gS\
1
5– (a) 34 (b) 200
di M

5 (c) 30 (d) 25
cjkcj gS
1
28 24
(a) (b) 58. If A  1 then what will be the value
65 53 3
1
56 14 1
(c) (d) 1
53 65 2
4
54. The value of/dk eku gSA of 24A?
a 1
1– ;fn A  rks 24A dk Ekku D;k gS\
1 1
1 3
a 1
1 1
1– a 1
A

2
(a) a (b) 1 – a 4
(c) 1 (d) 0 13
(a)
55. The value of/dk eku gSA 4
1 1
13
4 –2 (b)
7 4 1 40
1 1 1 13
3 1 2 (c)
2 7 1 12
2
1 13
5–
5 (d)
2

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59. What is the value of /Ekku D;k gS\ 65. Simplify the given expression.
1 fn, x, O;atd dks ljy dhft,A
1 (4.2)3 – 0.008
5–
1
3– ? (4.2)2  0.84  0.04
1
5– SSC CHSL, 14/08/2023 (Shift-2)
4
(a) 4 (b) –2
45 53
(a) (b) (c) 2 (d) –4
291 246 66. Simplify the expression:
48 96 fuEufyf[kr O;atd dks ljy dhft,A
(c) (d)
297 281 143  143  143  139  139  139
60. The value of/dk eku gSA 143  143  143 – 139  139  139
SSC CHSL 17/08/2023 (Shift-3)
(157  157)  (157  133)  (133  133)
(157  157  157)  (133  133  133) 1
(a) (b) 282
2

r
SSC CPO 04/10/2023 (Shift-02)
1

si
1 (c) (d) 4
(a) 24 (b) 4
290
an by 67. The value of/dk eku Kkr djsaA
1
(c) 290 (d) 6.35 × 6.35 × 6.35 + 3.65 × 3.65 × 3.65
24

n
6.35 × 6.35 + 3.65 × 3.65 – 6.35 × 3.65
61. Simplify the given expression.
SSC CPO 23/11/2020 (Shift-1)
fn, x, O;atd dks ljy dhft,A
ja (a) 0.01 (b) 10
R s
0.09  0.09  0.04  0.04  0.16  0.16  2  0.09
(c) 1 (d) 0.1
0.04  2  0.04  0.16  2  0.09  0.16
a th

68. Simplify the given expression.

0.3  0.3  0.2  0.2  0.4  0.4
SSC CHSL 02/08/2023 Shift-04 a 2 – b2 – 2bc – c2
(a) 0.38 (b) 0.24 a 2  b2  2ab – c2
ty a

(c) 0.32 (d) 0.29 fuEufyf[kr O;atd dk eku D;k gS\

4913  343
di M

62. Simplify the given expression . a 2 – b2 – 2bc – c2

289  49  119
a 2  b2  2ab – c2
4913  343
fn, x, O;atd dks ljy dhft,A SSC CPO 03/10/2023 (Shift-02)
289  49  119
a– bc
SSC CHSL 03/08/2023 (Shift-02) (a)
a bc
(a) 24 (b) 26 a bc
(c) 22 (d) 20 (b)
a– b–c
63. Simplify/ljy djsa% a b–c
3.3213  2.6813  1.2453  3  3.321  2.681  1.245
(c)
a– b–c
3.3212  2.6812  1.2452  3.321  2.681  2.681  1.245  1.245  3.321
a–b–c
SSC CHSL 04/08/2023 Shift-01 (d)
A

ab–c
(a) 6.125 (b) 8.645
69. Simplify the following expression. (3x + 5)² + (3x
(c) 7.247 (d) 10.245
– 5)²
64. Simplify the given expression.
fn, x, O;atd dks ljy dhft,A fuEufyf[kr O;atd dk ljyhdj.k djsaA
(80  80  80)  (70  70  70)  (50  50  50) – 840000 (3x + 5)² + (3x – 5)²
6400  4900  2500 – 5600 – 3500 – 4000 SSC CGL 17/07/2023 (Shift-01)
SSC CHSL 10/08/2023 (Shift-01)
(a) 500x (b) 450x
(a) 100 (b) 200
(c) 9x² + 50 (d) 2(9x2 + 25)
(c) 400 (d) 300

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256x 4  16y 4 74 The value of 1801 ×1801 is:

70. Simplify 80x 2  20y 2 16 x 2  4y 2 .
   1801 × 1801 dk eku --------- gSA
SSC CPO 09/11/2022 (Shift-02)
4
256x  16y 4 (a) 3423601 (b) 3243601
80x  20y 16x  4y  dks ljyhÑr dhft,A
2 2 2 2 (c) 2343601 (d) 3243106
75. Convert 0.18 into vulgar fraction
SSC CGL (PRE) 25/07/2023 (Shift-2)
0.18 dks vf'k"V fHkUu esa ifjofrZr djsa
1
(a) 5 (b) 17 18
20 (a) (b)
90 99
1 2 20 16
(c) (d) (c) (d)
5 5 99 90
76. Convert 0.43213 into vulgar fraction
s 2 + t2 + 2st - u 2
71. Simplify the expression , dks vf'k"V fHkUu esa ifjofrZr djsa
s 2 - t2 - 2tu - u 2 0.43213
provided (s + t + u)  0.

r
4316 4317
(a) (b)
s 2 + t2 + 2st - u 2 9999 9990

si
O;atd , dk eku dhft,] ;fn (s + t +
s 2 - t2 - 2tu - u 2 3217 2553
an by (c) (d)
u)  0. fn;k x;k gksA 9990 9999
SSC CGL PRE 25/07/2023 (Shift-4) 77. The difference of 5.76 and 2.3 is

n
s+t– u s+t+u vkSj 2.3 ds chp varj gSA
(a) (b) 5.76
s–t–u s – t+u
ja (a) 2.54 (b) 3.73
R s
s–t–u s–tu
(c) (d)
s+t– u stu (c) 3.46 (d) 3.43
a th

72. Simplify
78. 0.142857 ÷ 0.285714 is equal to/ds cjkcj gSA
1 1 1 x (a) 10 (b) 2
+ + , when p =
2 + 2p 2 + 2q 2 + 2r yz
1 1
ty a

y z (c) (d)
2 3
q= and r =
z+x x +y
di M

x z
79. 0.11  0.22 × 3 is equal to/ds cjkcj gSA
y
;fn p = y  z gS] vkSj
q= vkSjr =
x +y
gS rks (a) 3 (b) 1.9
z+x
1 1 1 (c) 1 (d) 0.3
+ +
2 + 2p 2 + 2q 2 + 2r
dks ljyhd`r dhft,A
80. The vulgar fraction of 0.39 is:
(a) 1 (b) x + y + c
0.39 dh vf'k"V fHkUu gSA
1
(c) 2 (d) 15 11
2 (a) (b)
33 39
x– y
73. Simplify the expression , where x = 2 17 13
x+ y (c) (d)
A

39 33
and y = 3.
81. The vulgar fraction of 2.3 49
x – y
;fn x = 2 vkSjy = 3 gS] rks x + y O;atd dks gy
2.3 49 dh vf'k"V fHkUu gSA
dhft,A
2326 2326
SSC CGL PRE 25/07/2023 (Shift-4) (a) (b)
999 990
(a) 2 6 – 6 (b) 6 –5
2347 2347
(c) 5 – 2 6 (d) 2 6 – 5 (c) (d)
999 990

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82. What value should come in the place of ques- 87. A and B have together three times what B and
tion mark (?) in the following question? C have, while A, B, C together have thirty
rupees more than that of A. If B has 5 times
fuEufyf•r ç'u esa ç'u fpÉ (\) ds LFkku ij dkSu & lk
that of C, then A has
eku vkuk pkfg,\
A vkSj B ds ikl dqy feykdj B vkSj C ls rhu xquk
0.537 – 0.335  0.234 = ? vf/d gS] tcfd A] B] C ds ikl dqy feykdj A ls
UPSI 14/11/2021 (Shift-02) rhl #i;s vf/d gSaA ;fn B ds ikl C ls 5 xquk vf/d
(a)
422
(b)
412 gS] rks
A ds ikl gSaA
990 990 (a) Rs 60 (b) Rs 65
442 432
(c) (d) (c) Rs 75 (d) Rs 45
990 990
83. Natu and Buchku each have certain number of 88. 252 m of pant cloth and 141 m of shirt cloth
orange. Natu says to Buchku. "If you give me are available in a cloth store. To stitch one
10 of your oranges. I will have twice the 1 3
number of oranges left with you" Buchku pant and one shirt, 2 m and 1 m of cloth
2 4
replies, "If you give me 10 of your oranges. I

r
will have the same number of oranges as left are needed respectively. Then the approximate
with you". What is the number of oranges with number of pants and shirts that can be made

si
Natu and Buchku, respectively? out of it are
ukVw vkSj cqpdw çR;sd ds ikl fuf'pr la[;k esa larjs gSaA ukVw]
an by ,d diM+s dh nqdku esa 252 ehVj iSaV dk diM+k vkSj 14
cqpdw ls dgrk gS- ;fn vki eq>s vius 10 larjs ns nsa rks esjs ehVj 'kVZ dk diM+k miyC/ gSA ,d iSaV vkSj ,d 'kV
ikl vkids ikl cps gq, larjksa ls nksxqus larjsa gksaxs cqpdw mÙkj

n
1 3
nsrk gS] ;fn vki eq>s vius 10 larjs ns nsaxs rks esjs ikl flyus ds fy, Øe'k%2 2 ehVj vkSj1 4 ehVj diM+sa dh
vkids ikl cps gq, larjksa ds leku la[;k gksxhA ukVw vkSj
ja vko';drk gksrh gSA fiQj blls cukbZ tk ldus okyh iSaV
R s
cqpdw ds ikl Øe'k% larjksa dh la[;k fdruh gS\
vkSj 'kVZ dh vuqekfur la[;k gS
(a) 50, 20 (b) 70, 50
a th

(c) 20, 50 (d) 50, 70 (a) (80, 100) (b) (100, 80)
84. In an exam the sum of the scores of A and B (c) (10, 90) (d) (90, 80)
is 120, that of B and C is 130 and that of C
89. There are 50 boxes and 50 persons. Person 1
ty a

and A is 140. Then the score of C is:

keeps 1 marble in every box. Person 2 keeps
,d ijh{kk esaA vkSjB ds vadksa dk ;ksx 120 BgS]
vkSj 2 murpbles in every 2nd box person 3 keeps
C ds vadksa dk ;ksx 130 gS vkSj
C vkSj A ds vadksa dk
di M

3 marbles in every third box. This process goes

;ksx 140 gSA Crks
dk vad gS% on till person 50 keeps 50 marbles in the 50th
(a) 65 (b) 75 box. Find the total number of marbles kept in
(c) 70 (d) 60 the 50th box.
85. A number is doubled and 9 is added. If the ogk¡ 50 cDls vkSj 50 O;fÙkQ gSaA O;fÙkQ 1 çR;sd fM
resultant is trebled, it becomes 75. What is 1 ekcZy j•rk gSA O;fÙkQ 2 çR;sd nwljs ckWDl esa 2 ek
that number?
j•rk gS] O;fÙkQ 3 çR;sd rhljs ckWDl esa 3 ekcZYl j•rk
,d la[;k dks nksxquk fd;k tkrk gS vkSj 9 tksM+k tkrk gSA
gSA ;g çfØ;k rc rd pyrh jgrh gS tc rd fd 50
;fn ifj.kke dks frxquk dj fn;k tk,] rks ;g 75 gks O;fÙkQ 50osa fMCcs esa 50 ekcZy u j• ysA 50osa fM
tkrk gSA og la[;k D;k gS\ j•s x, dapksa dh dqy la[;k Kkr dhft,A
(a) 6 (b) 35
A

(a) 43 (b) 78
(c) 8 (d) None of these
86. The sum of two number is 8 and their product (c) 6 (d) 93
is 15. the sum of their reciprocals 90. The sum of a two digit number and the number
nks la[;kvksa dk ;ksx 8 gS vkSj mudk xq.kuiQy 15 gSA
obtained by reversing its digits is a square
muds O;qRØeksa dk ;ksx number. How many such numbers are there?
8 15 nks vadksa dh la[;k vkSj mlds vadksa dks myVus ij çkIr la[;
(a) (b) dk ;ksx ,d oxZ la[;k gksrh gSA ,slh fdruh la[;k,¡ gSa\
15 8
15 (a) 5 (b) 6
(c) 23 (d)
8 (c) 7 (d) 8

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Answer Key
1.(a) 2.(d) 3.(a) 4.(d) 5.(d) 6.(d) 7.(c) 8.(c) 9.(a) 10.(c)

11.(c) 12.(a) 13.(c) 14.(d) 15.(c) 16.(a) 17.(c) 18.(c) 19.(c) 20.(b)

21.(d) 22.(a) 23.(c) 24.(d) 25.(d) 26.(c) 27.(d) 28.(a) 29.(a) 30.(b)

31.(b) 32.(d) 33.(a) 34.(b) 35.(b) 36.(b) 37.(c) 38.(c) 39.(d) 40.(c)

41.(c) 42.(a) 43.(c) 44.(c) 45.(a) 46.(d) 47.(b) 48.(a) 49.(b) 50.(a)

51.(c) 52.(a) 53.(c) 54.(d) 55.(a) 56.(b) 57.(a) 58.(d) 59.(b) 60.(d)

r
61.(d) 62.(a) 63.(c) 64.(b) 65.(a) 66.(c) 67.(d) 68.(d) 69.(d) 70.(c)

si
71.(a) 72.(a) 73.(d) 74.(b) 75.(a) 76.(b) 77.(d) 78.(c) 79.(c) 80.(d)

81.(b)
an by
82.(d) 83.(b) 84.(b) 85.(c) 86.(a) 87.(b) 88.(b) 89.(d) 90.(d)

n
ja
R s
a th
ty a
di M
A

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