Maths with Sumit Goyal By Sumit Goyal

(Ex Excise Inspector)

Ratio (अनपु ात) Sheet - 1
1. Two numbers are in the ratio of 8 : 7. If sum of 7. Three numbers are in the ratio3: 4: 5. The
these two numbers is 450, find the numbers. sum of the largest and the smallest equals to
दो सं �ाएँ 8:7 के अनुपात म� ह�। यिद इन दो सं �ाओं का योग the sum of the second number and 52. The
smallest number is
450 हो, तो सं �ाएँ बताएँ ?
rhu la[;k,a 3: 4: 5 vuqikr esa gSA ;fn lcls cM+h o
(a) 210, 240 (b) 240, 210 lcls NksVh la[;kvksa dk ;ksx nwljh la[;k o 52 ds
(c) 235, 215 (d) 215, 235 ;ksx ds cjkcj gS] rks lcls NksVh la[;k Kkr djsa \
(a) 20 (b) 27 (c) 39 (d) 52
2. Two numbers are in the ratio of 9: 11. If sum of
these two numbers is 660, find the difference 8. The ratio of the income to the expenditure
between the numbers. of a family is10: 7. If the family’s expenses
are Rs 10,500, then saving of the family is
दो सं �ाएँ 9:11 के अनुपात म� ह�। यिद इन दो सं �ाओं का योग
,d ifjokj dh vk; vkSj [kpZ dk vuqikr 10: 7 gSA
660 हो तो इन सं �ाओं का अंतर बताए? ;fn ifjokj dk [kpZ # 10500 gS] rks ifjokj dh cpr
(a) 66 (b) 56 (c) 46 (d) 76 Kkr djsa \
(a) Rs 4,500 (b) Rs 10,000
3. The ratio of two number is 3: 8 and their (c) Rs 4,000 (d) Rs 5,000
difference is 115. The smaller of the two
number is : 9. If the annual income of A, B and C are in
nks la[;kvksa dk vuqikr 3 : 8 gS vkSj mudk vUrj 115 the ratio 1: 3: 7 and the total annual income
gSA rks muesa ls NksVh la[;k Kkr djsa \ of A and C is Rs 8,00,000, then the monthly
(a) 184 (b) 194 (c) 69 (d) 59 salary of B (in Rs) is
;fn 𝐴𝐴, 𝐵𝐵 vkSj 𝐶𝐶 dh okf"kZd vk; 1: 3: 7 ds vuqikr
4. Four number are in the ratio 1 : 2 : 3 : 4. esa gSA 𝐴𝐴 vkSj 𝐶𝐶 dh dqy okf"kZd vk; 𝑅𝑅𝑅𝑅 800000
Their sum is 16. The sum of the first and gS rc 𝐵𝐵 dh ekfld vk; Kkr djs \
fourth number is equal to : (a) Rs 20,000 (b) Rs 25,000
Pkkj la[;k,¡ 1 : 2 : 3 : 4 ds vuqikr esa gSA mudk ;ksx (c) Rs 30,000 (d) Rs 15,000
16 gS] rks igyh vkSj pkSFkh la[;k dk ;ksx D;k gksxk \
(a) 5 (b) 8 (c) 10 (d) 80 10. The monthly salary of A, B and C is in the
ratio of 2 : 3 : 5. If C’s salary is Rs 12000
5. The ratio of two number is 10: 7 and their more than that of A, find annual salary of
difference is 105. The sum of these numbers B?
is 𝐴𝐴, 𝐵𝐵 rFkk 𝐶𝐶 ds ekfld osru 2: 3: 5 ds vuqikr esa
nks la[;kvksa dk vuqikr 10: 7 gS vkSj mudk vUrj gSA ;fn 𝐶𝐶 dk ekfld osru 𝐴𝐴 ds ekfld osru ls #
105 gS rks la[;kvksa dk ;ksx Kkr djsaA
12000 vf/kd gks] rks 𝐵𝐵 dk okf"kZd osru gksxk &
(a) 595 (b) 805 (c) 1190 (d) 1610
(a) Rs 1, 20,000 (b) Rs 1, 44,000
(c) Rs 1, 80,000 (d) Rs 2, 40,000
6. Marks of two candidates P and Q are in the
ratio 2 : 5 if the marks of P are 120, marks
11. The price of a refrigerator and a television
of Q are
set are in the ratio 5: 3. If the refrigerator
𝑃𝑃 vkSj 𝑄𝑄 ds vadksa dk vuqikr 2: 5 gSA ;fn 𝑃𝑃 ds
costs Rs 5500 more than the television set,
vad 120 gS] rks 𝑄𝑄 ds vad Kkr djsa \ then the price of the refrigerator is :
(a) 120 (b) 240 (c) 300 (d) 360
 Maths with Sumit Goyal By Sumit Goyal
(Ex Excise Inspector)
Ratio (अनपु ात) Sheet - 1
fÝt vkSj Vh-oh- dh dher dk vuqikr 5: 3 gSA ;fn Chakor in the ratio 3 : 6 : 2. How much share
fÝt dh dher Vh-oh- ls 5500 vf/kd gS] rks fÝt (in Rs) Chakor gets?
dh dher D;k gksxh \ 277200 ds ykHk dks 3: 6: 2 ds vuqikr esa rhu
(a) Rs 27500 (b) Rs 8250 fgLlsnkjksa vCnqYykg] Hkkuqnkl vkSj pdksj esa ckaVk tkuk
(c) Rs 13750 (d) Rs 16500 gSA pdksj dks fdruk fgLlk (# esa) izkIr gqvk\
(a) Rs 50400 (b) Rs 151200
12. Rs 738 is divided among A, B, C so that (c) Rs 75600 (d) Rs 25200
their shares are in the ratio of 2 : 3 : 4, B’s
share is 17. Sanjay’s test marks in two subjects, English
# 738 dks 𝐴𝐴, 𝐵𝐵 vkSj 𝐶𝐶 esa 2 ∶ 3 ∶ 4 ds vuqikr and Hindi are in the ratio7 ∶ 11. If he got 20
esa foHkkftr fd;k x;kA 𝐵𝐵 }kjk izkIr fgLlk Kkr djsa\ marks more in Hindi than in English, what
(a) Rs 328 (b) Rs 246 are his marks in English?
(c) Rs 264 (d) Rs 164 nks fo"k;ksa vaxzsth vkSj fgUnh ds ijh{kk esa lat; ds vadksa
dk vuqikr 7: 11 gSA ;fn vaxszth dh rqyuk esa mls
13. If Rs 126.50 is divided among A, B and C fgUnh esa 20 vad vf/kd feyrs gS] rks vaxzsth esa mls
in the ratio of 2: 5: 4, the share of B exceeds fdrus vad feys \
that of A by (a) 35 (b) 55 (c) 45 (d) 64
# 126.50 dks 𝐴𝐴, 𝐵𝐵 vkSj 𝐶𝐶 esa 2: 5: 4 ds vuqikr
18. A person distributes some amount of money
esa foHkkftr fd;k x;k A rks 𝐵𝐵 dk fgLlk] 𝐴𝐴 ls
fdruk vf/kd gS \ between his two sons A and B in the ratio of the
(a) Rs 36.50 (b) Rs 35.50 13:19. If B gets 4200 Rs. more than that of A,
(c) Rs 34.50 (d) Rs 33.50 then how many rupees the man has?
एक ��� ने अपने दो पुत्रो A तथा B के बीच 13 : 19 अनुपात
14. The sides of a triangle are in the ratio of
म� अपने धन को बाँटा। यिद B को A से 4200 �. अ�धक �मले
7: 9: 12. The difference between the length
of largest and smallest sides is 15cm. the हो, तो उस ��� के पास कु ल िकतना धन था?
length of the largest sides would be : (a) 22400 (b) 24200
,d f=Hkqt dh Hkqtk,a 7: 9: 12 ds vuqikr esa gSA lcls (c) 268200(d) None of these
cM+h vkSj lcls NksVh Hkqtkvksa dh yackbZ ds chp varj
15𝑐𝑐𝑐𝑐 gSA lcls cM+h Hkqtk dh yackbZ fdruh gksxh \ 19. A Profit of Rs 960 is divided between A and
(a) 36cm (b) 12cm (c) 60cm (d) 24cm 1 1
B in the ratio : . The difference of their
3 5
15. Rs 3200 is divided among A, B and C in the profit is:
1 1
ratio of 3: 5: 8 respectively. What is the # 960 ds ykHk dks 𝐴𝐴 vkSj 𝐵𝐵 esa : ds vuqikr esa
3 5
difference (in rs) between the share of B and ck¡Vk x;k gSA muds ykHkksa dk vUrj D;k gksxk\
C? (a) Rs 120 (b) Rs 160
3200 # dks 𝐴𝐴, 𝐵𝐵 rFkk 𝐶𝐶 ds chp Øe’k% vuqikr (c) Rs 180 (d) Rs 240
3: 5: 8 es ck¡Vk tkrk gSA 𝐵𝐵 vkSj 𝐶𝐶 ds fgLls esa
fdruk varj (# esa) gS \ 20. According to the will, the wealth of 11,
(a) 400 (b) 600 (c) 800 (d) 900 50,000 was to be divided between the son
2 5
and the daughter in the ratio : . How much
3 4
16. Profit of Rs. 277200 has to be divided
share did the son get (in Rs lakehs)?
among three Abdullah, Bhanudas and
 Maths with Sumit Goyal By Sumit Goyal
(Ex Excise Inspector)
Ratio (अनपु ात) Sheet - 1
olh;r ds vuqlkj 11,50,000 # dh laifÙk dk
2 5
caVokjk iq= vkSj iq=h ds chp : ds vuqikr esa gksxkA 26. Three numbers are in the ratio 2 : 3 : 4. If
3 4 the sum of their squares is 1856, then the
iq= dks fdruk fgLlk feyxk \ (yk[k # esa)
number are
(a) 5 (b) 6 (c) 7 (d) 4
rhu la[;k 2 ∶ 3 ∶ 4 ds vuqikr esa gS ;fn buds oxZ
dk ;ksx 1856 gS] rks la[;k,¡ gSa \
21. The sum of two number is 40 and their
(a) 8, 12 and 16 (b) 16, 24 and 32
difference is 4. The ratio of the number is:
nks la[;kvksa dk ;ksx 40 gSA mudk vUrj 4 gS rks mudk (c) 12, 18 and 24 (d) None of the above
vuqikr Kkr djsA
(a) 21 : 19 (b) 22 : 9 27. If A and B are in the ratio 4 ∶ 5 and the
(c) 11 : 9 (d) 11 : 18 difference of their squares is 81, what is the
value of A ?
22. The sum of two numbers is equal to 25 and ;fn 𝐴𝐴 rFkk 𝐵𝐵 4: 5 ds vuqikr esa gS vkSj muds oxksZ
their difference in 20. The ratio of the two dk varj 81 gS] rks 𝐴𝐴 dk eku Kkr djsa \
numbers is (a) 36 (b) 445 (c) 15 (d) 12
nks la[;kvksa dk ;ksx 25 gS vkSj mudk varj 20 gS]
rks nks la[;kvksa dk vuqikr gS \ 28. Three numbers are in the ratio5: 6: 7. If the
(a) 9 : 1 (b) 7 : 9 (c) 3 : 5 (d) 2 : 7 product of the number is 5670, then the
greatest number is
23. The sum of two numbers is 55 and their rhu la[;kvksa dk vuqikr 5: 6: 7 gSA ;fn la[;kvksa
difference is 9. What is the ratio of the two dk xq.kuQy 5670 gS rks cM+h la[;k D;k gS \
(a) 15 (b) 18 (c) 21 (d) 28
numbers?
दो सं �ाओं का योग 55 है तथा इनका अंतर 9 है। इन सं �ाओं 29. The product of two positive integers is 1575
का अनुपात बताए? and their ratio is9:7. The smaller integer is
(a) 32:23 (b) 23:32 दो धना�क पूणा�को का गुणनफल 1575 है और उनका अनुपात
(c) 31:13 (d) 32:13 9:7 है तो छोटी पूणा�क �ात करो।
(a) 35 (b) 25 (c) 45 (d) 70
24. The sum of two numbers is 64 and their
difference is 8. What is the ratio of the two 30. If the sum of two quantities is equal to three
numbers? times of their difference, then the ratio of
दो सं �ओं का योग 64 है तथा इनका अंतर 8 है। इन सं �ाओं the two quantities is
का अनुपात बताए? ;fn nks la[;kvksa dk ;ksx muds vUrj dk frxquk gS]
rks la[;kvksa dk vuqikr Kkr djsa \
(a) 9:5 (b) 9: 8 (a) 1 : 3 (b) 3 : 1 (c) 2 : 1 (d) 2 : 3
(c) 9:7 (d) 9:11
31. Two numbers are in the ratio 3 : 4 and their
25. Three numbers are in the ratio of 3: 2: 5 and LCM is 180. The first number is
the sum of their squares is 1862. The दो सं �ाएं 3:4 के अनुपात म� ह� और उनका लघु�म समापव�र्
smallest of these numbers is
180 है तो पहली सं �ा �ात कर�।
rhu la[;kvksa dk vuqikr 3: 2: 5 gS vkSj muds oxksZa
dk ;ksx 1862 gS] rks lcls NksVh Kkr djsa (a) 15 (b) 60 (c) 36 (d) 45
(a) 24 (b) 21 (c) 14 (d) 35
 Maths with Sumit Goyal By Sumit Goyal
(Ex Excise Inspector)
Ratio (अनपु ात) Sheet - 1
32. Two numbers are in the ratio3:5and their LCM 37. The bus fare between two cities is increased in
is 225. The smaller number is the ratio 5:11. find the increase in the fare, if the
यिद दो सं �ाएं 3:5 के अनुपात म� ह� और उनका लघु�म original fare is Rs.275.
समापव�र् 225 है तो छोटी सं �ा �ात कर�। दो शहरों के बीच बस का भाडा 5:11 के अनुपात म� बढ़ाया गया है
(a) 45 (b) 60 (c) 75 (d) 90 भाडे म� �ई वृ�द्ध का पता लगाए, यिद मूल भाडा 275 �. है।
(a) Rs. 605 (b) Rs. 121
33. A person distributes his pens among four (c) Rs. 330 (d) Rs.242
1 1 1 1
friends A, B, C, D in the ratio : : : . What
3 4 5 6
is the minimum number of pens that the 38. The bus fare between two cities is increased in
person should have ? the ratio 17:20. Find the increase in the fare, if
एक ��� ने कु छ कलम� अपने दो�ों A, B, C और D म� the original fare is Rs.425
1 1 1 1 दो शहरों के बीच बस का भाड़ा 17:20 के अनुपात म� बढ़ाया गया
: : : के अनुपात म� बाँटी तो उसके पास कम से कम िकतनी
3 4 5 6 है। भाड़े म� �ई वृ�द्ध का पता लगाएं , यिद मूल भाड़ा 425 �. है।
सं �ा म� कलम� ह�?
(a) Rs.500 (b) Rs.100
(a) 57 (b) 65 (c) 75 (d) 45
(c) Rs.200 (d) Rs.75
39. A person bought some rice and wheat for Rs
34. The bus fare between two cities is increased in
380. The ratio of weight of rice and wheat
the ratio 29:31. What is the increment in the is 4 : 3 and the price of equal amount of rice
fare, if the original fare is Rs. 725 and wheat is in the ratio 5 : 6. The rice was
दो शहरो के बीच बस का भाड़ा 29 : 31 के अनुपात म� बढ़ाया गया bought of worth.
ह�। भाड़े म� �ई वृ�द्ध का पता लगाएं , यिद मूल भाड़ा 725 �. है। ,d O;fDr 𝑅𝑅𝑅𝑅 380 esa dqN pkoy o xsgw¡ [kjhnrk gSA
(a) Rs.50 (b) Rs.775 pkoy o xsgw¡ ds otu dk vuqikr 4: 3 gS vkSj mudh
dher dk vuqikr 5: 6 gS rks pkoy dks fdrus esa
(c) Rs. 155 (d) Rs. 310 [kjhnk x;k \
35. The bus fare between two cities is increased in (a) Rs 380 (b) Rs 300
the ratio 25:29. Find the increase in the fare, if (c) Rs 200 (d) Rs 180
the original fare is Rs.625
दो शहरों के बीच बस का भाड़ा 25:29 के अनुपात म� बढ़ाया गया 40. The ratio of fares of the first and second class
है। भाड़े म� �ई वृ�द्ध का पता लगाएं , यिद मूल भाड़ा 625 �. है। train between two stations is 3 : 1 and that of
(a) Rs.725 (b) Rs. 145 the numbers of passengers travelling between
(c) Rs. 290 (d) Rs. 100 the two stations by first and second classes is 1
: 50. If on a particular day Rs 1325 are collected
36. The bus fare between two cities is increased in from passengers travelling between the two
the ratio 5: 7. What is the increase in the fare, if stations Then the amount collected from the
the original fare is Rs.625? second class passengers is
दो शहरों के बीच बस का भाड़ा 5:7 के अनुपात म� बढ़ाया गया है। दो �ेशनों के बीच एक ट�ेन म� पहली श्रेणी और दू सरी श्रेणी के
भाड़े म� �ई वृ�द्ध का पता लगाएं , यिद मूल भाड़ा 625 � है। िकरायों का अनुपात 3:1 है और पहली श्रेणी और दू सरी श्रेणी म�
(a) Rs.875 (b)Rs. 175 सफर कर रहे या�त्रयों क� सं �ा का अनुपात 1:50 है। यिद एक
(c)Rs. 350 (d) Rs. 250
 Maths with Sumit Goyal By Sumit Goyal
(Ex Excise Inspector)
Ratio (अनपु ात) Sheet - 1
�वशेष िदन �. 1325 का कु ल िकराया वसूला गया तो दू सरी श्रेणी (a) 3 : 2 : 1 (b) 1 : 2 : 6
से वसूल िकया गया कु ल िकराया �ात कर�। (c) 1 : 3 : 6 (d) 2 : 4 : 6
(a) Rs. 1250 (b) Rs. 1000
47. If 𝑎𝑎: 𝑏𝑏 ∷ 2: 3 , 𝑏𝑏: 𝑐𝑐 ∷ 4: 3 , 𝑐𝑐: 𝑑𝑑 ∷ 5: 2 ,
(c) Rs. 850 (d) Rs.750
𝑑𝑑: 𝑒𝑒 ∷ 3: 4 Find 𝑎𝑎: 𝑏𝑏: 𝑐𝑐: 𝑑𝑑: 𝑒𝑒.
(a) 120 : 180 : 135 : 54 : 72
41. If 𝑎𝑎 ∶ 𝑏𝑏 = 2 ∶ 3 and 𝑏𝑏 ∶ 𝑐𝑐 = 5 ∶ 6, then 𝑎𝑎 ∶ (b) 180 : 120 : 135 : 20 : 19
𝑏𝑏 ∶ 𝑐𝑐 is equal to : (c) 72 : 180 : 135 : 120 : 16
;fn 𝑎𝑎 ∶ 𝑏𝑏 = 2 ∶ 3 vkSj 𝑏𝑏 ∶ 𝑐𝑐 = 5 ∶ 6 gS] rks 𝑎𝑎 ∶ (d) 180 : 135 : 54 : 72 : 120
𝑏𝑏 ∶ 𝑐𝑐 cjkcj gS %
(a) 4 : 6 : 5 (b) 6 : 9 : 16 48. If 𝐴𝐴: 𝐵𝐵 = 1: 2 , 𝐵𝐵: 𝐶𝐶 = 3: 4 , 𝐶𝐶: 𝐷𝐷 = 6: 9 ,
𝐷𝐷: 𝐸𝐸 = 12: 16 then 𝐴𝐴: 𝐵𝐵: 𝐶𝐶: 𝐷𝐷 is equal to
(c) 6 : 9 : 12 (d) 10 : 15 : 18
;fn 𝐴𝐴: 𝐵𝐵 = 1: 2 , 𝐵𝐵: 𝐶𝐶 = 3: 4 , 𝐶𝐶: 𝐷𝐷 = 6: 9 ,
𝐷𝐷: 𝐸𝐸 = 12: 16 gks] rks 𝐴𝐴: 𝐵𝐵: 𝐶𝐶: 𝐷𝐷: 𝐸𝐸 fdlds
42. If 𝑎𝑎: 𝑏𝑏 ∷ 2: 3, 𝑏𝑏: 𝑐𝑐 ∷ 4: 5. Find 𝑎𝑎: 𝑏𝑏; 𝑐𝑐
(a) 8 : 12 : 15 (b) 4 : 3 : 5 cjkcj gksxk \
(c) 4 : 6 : 9 (d) 2 : 4 : 7 (a) 1 : 3 : 6 : 12 : 16 (b) 2 : 4 : 6 : 9 : 16
(c) 3 : 4 : 8 : 12 : 16 (d) 3: 6: 8: 12 : 16
43. If 𝑎𝑎: 𝑏𝑏 = 7: 9 and 𝑏𝑏: 𝑐𝑐 = 5: 7, then what is
𝑎𝑎: 𝑐𝑐 ? 49. If the ratio of A and B is 4:7 the ratio of B
;fn 𝑎𝑎: 𝑏𝑏 = 7: 9 vkSj 𝑏𝑏: 𝑐𝑐 = 5: 7] rks 𝑎𝑎: 𝑐𝑐 D;k and C is 5:6 the ratio of C and D is 4:3 and
gksxk \ the ratio of E:D is 7:13. Find the ratio of A
(a) 5 : 9 (b) 3 : 5 (c) 7 : 21 (d) 7 : 15 : B : C : D : E.
;fn 𝐴𝐴 vkSj 𝐵𝐵 dk vuqikr 4: 7 gS] 𝐵𝐵 vkSj 𝐶𝐶 dk
44. If A and B are in the ratio 3: 4 and B and C vuqikr 5: 6 gS] 𝐶𝐶 vkSj 𝐷𝐷 dk vuqikr 4: 3 gS vkSj
in the ratio 12: 13. Then A and C will be in 𝐸𝐸: 𝐷𝐷 dk vuqikr 7: 13 gSA 𝐴𝐴: 𝐵𝐵: 𝐶𝐶: 𝐷𝐷: 𝐸𝐸 dk
the ratio vuqikr Kkr djsaA
;fn 𝐴𝐴 vkSj 𝐵𝐵 3: 4 vuqikr esa gks vkSj 𝐵𝐵 o (a) 910 : 520 : 1092 :819 : 420
𝐶𝐶 12: 13 ds vuqikr esa gks rks 𝐴𝐴 vkSj 𝐶𝐶 dk vuqikr (b) 420 : 520 : 1092 :819 : 420
Kkr djsa \ (c) 819 : 910 : 1092 :520 : 420
(a) 3: 13 (b) 9: 13 (c) 36: 13 (d) 13: 9 (d) 520 : 910 : 1092 :819 : 441

45. If 𝑎𝑎: 𝑏𝑏 ∷ 2: 3, 𝑏𝑏: 𝑐𝑐 ∷ 4: 1 , 𝑐𝑐: 𝑑𝑑 ∷ 2: 5 find 50. If 𝐴𝐴: 𝐵𝐵 = 3: 4 and 𝐵𝐵: 𝐶𝐶 = 6: 5 , then
𝑎𝑎: 𝑏𝑏: 𝑐𝑐: 𝑑𝑑. 𝐴𝐴: (𝐴𝐴 + 𝐶𝐶) is equal to
(a) 14 : 8 : 9 : 7 (b) 17 : 24 : 7 : 14 rhu la[;k 𝐴𝐴: 𝐵𝐵 = 3: 4 vkSj 𝐵𝐵: 𝐶𝐶 = 6: 5] gS rks
(c) 16 : 24 : 6 : 15 (d) 19 : 25 : 8 : 17
𝐴𝐴: (𝐴𝐴 + 𝐶𝐶) cjkcj gksxk \
(a) 9: 10 (b) 10: 9 (c) 9: 19 (d) 19: 9
1 1
46. If 𝑥𝑥 = 𝑦𝑦 and 𝑦𝑦 = 𝑧𝑧, then 𝑥𝑥: 𝑦𝑦: 𝑧𝑧, is equal
3 2
51. The ratio of A and B is 2: 3 and the ratio of
to?
1 1 B and C is 4: 5.Then find 𝐴𝐴2 : 𝐵𝐵2 : 𝐵𝐵𝐵𝐵.
;fn 𝑥𝑥 = 𝑦𝑦 vkSj 𝑦𝑦 = 𝑧𝑧 rc 𝑥𝑥: 𝑦𝑦: 𝑧𝑧 fdlds 𝐴𝐴 vkSj 𝐵𝐵 dk vuqikr 2: 3 gS rFkk 𝐵𝐵 vkSj 𝐶𝐶 dk
3 2
cjkcj gksxk \ vuqikr 4: 5 gSA rks 𝐴𝐴2 : 𝐵𝐵2 : 𝐵𝐵𝐵𝐵 dk eku D;k gksxk\
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Ratio (अनपु ात) Sheet - 1
(a) 15 : 20 : 25 (b) 8 : 24 : 32
(c) 16 : 36 : 45 (d) 9 : 18 : 27 𝐴𝐴 𝐵𝐵 𝐶𝐶
58. If 𝐴𝐴: 𝐵𝐵: 𝐶𝐶 = 2: 3: 4 , then ratio : : is
𝐵𝐵 𝐶𝐶 𝐴𝐴
52. If 𝑎𝑎: 𝑏𝑏: 𝑐𝑐 = 3: 4: 7, then the ratio (𝑎𝑎 + 𝑏𝑏 + equal to
𝐴𝐴 𝐵𝐵 𝐶𝐶
𝑐𝑐): 𝑐𝑐 is equal to ;fn 𝐴𝐴: 𝐵𝐵: 𝐶𝐶 = 2: 3: 4 gks] rks : : dk vuqikr
𝐵𝐵 𝐶𝐶 𝐴𝐴
;fn 𝑎𝑎: 𝑏𝑏: 𝑐𝑐 = 3: 4: 7 gks rc (𝑎𝑎 + 𝑏𝑏 + 𝑐𝑐): 𝑐𝑐 Kkr djsa \
Kkr djsa \
(a) 8 : 9 : 16 (b) 8 : 9 : 12
(a) 2 : 1 (b) 14 : 3 (c) 7 : 2 (d) 1 : 2
(c) 8 : 9 : 24 (d) 4 : 9 : 12
53. If 𝐴𝐴: 𝐵𝐵 = 2: 3 and 𝐵𝐵: 𝐶𝐶 = 3: 7 , then 𝐴𝐴 +
𝐵𝐵: 𝐵𝐵 + 𝐶𝐶: 𝐶𝐶 + 𝐴𝐴 is. 59. If 𝑎𝑎: 𝑏𝑏: 𝑐𝑐 = 7: 3: 5 , then (𝑎𝑎 + 𝑏𝑏 +
;fn 𝐴𝐴: 𝐵𝐵 = 2: 3 vkSj 𝐵𝐵: 𝐶𝐶 = 3: 7 ] rks 𝐴𝐴 + 𝑐𝑐): (2𝑎𝑎 + 2𝑏𝑏 + 𝑐𝑐) is equal to
𝐵𝐵: 𝐵𝐵 + 𝐶𝐶: 𝐶𝐶 + 𝐴𝐴 D;k gksxk \ ;fn a 𝑎𝑎: 𝑏𝑏: 𝑐𝑐 = 7: 3: 5 gks] rks (𝑎𝑎 + 𝑏𝑏 +
(a) 4 : 10 : 9 (b) 5 : 10 : 9 𝑐𝑐): (2𝑎𝑎 + 2𝑏𝑏 + 𝑐𝑐) fdlds cjkcj gS \
(c) 5 : 8 : 9 (d) 4 : 8 : 9 (a) 1: 2 (b) 2: 3 (c) 3: 5 (d) 5: 4
1 1 1 1
54. If 𝐴𝐴: 𝐵𝐵 = : , 𝐵𝐵: 𝐶𝐶 = : , then (𝐴𝐴 +
2 3 5 3 60. If 6𝐴𝐴 = 4𝐵𝐵 = 9𝐶𝐶; what is A : B : C ?
𝐵𝐵): (𝐵𝐵 + 𝐶𝐶) is equal to : ;fn 6𝐴𝐴 = 4𝐵𝐵 = 9𝐶𝐶; rks 𝐴𝐴 ∶ 𝐵𝐵 ∶ 𝐶𝐶 \
1 1 1 1
;fn 𝐴𝐴: 𝐵𝐵 = : , 𝐵𝐵: 𝐶𝐶 = : , rFkk (𝐴𝐴 + (a) 6 ∶ 4 ∶ 9 (b) 9 ∶ 4 ∶ 6
2 3 5 3
𝐵𝐵): (𝐵𝐵 + 𝐶𝐶) ds cjkcj gS \ (c) 4 ∶ 9 ∶ 6 (d) 6 ∶ 9 ∶ 4
(a) 9 ∶ 10 (b) 6 ∶ 15
(c) 5 ∶ 8 (d) 15 ∶ 16 61. If two times of A is equal to three times of
B and also equal to four times of C, then A
2 1 2 5 7 3
55. If 𝑎𝑎: 𝑏𝑏 = : , 𝑏𝑏; 𝑐𝑐 = : and 𝑑𝑑: 𝑐𝑐 = : : B : C is
9 3 7 14 10 5
then find 𝑎𝑎: 𝑏𝑏: 𝑐𝑐: 𝑑𝑑. ;fn 𝐴𝐴 dk nksxquk] 𝐵𝐵 ds frxqus o 𝐶𝐶 ds pkj xqus ds
(a) 4 : 6 : 7 : 9 : 8 cjkcj gS rks 𝐴𝐴: 𝐵𝐵: 𝐶𝐶 dk vuqikr Kkr djsa \
(b) 16 : 24 : 30 : 35 (a) 2 : 3 : 4 (b) 3 : 4 : 2
(c) 8 : 12 : 15 : 7 (c) 4 : 6 : 3 (d) 6 : 4 : 3
(d) 30 : 35 : 24 : 16
62. If 4a = 6b = 5c then a :b:c will be equal to:
56. If 𝐴𝐴: 𝐵𝐵 = 3: 4, 𝐵𝐵: 𝐶𝐶 = 5: 7 and 𝐶𝐶: 𝐷𝐷 = 8: 9 यिद 4a = 6b = 5c हो तो a: b: c बराबर है:
then 𝐴𝐴: 𝐷𝐷 is equal to (a) 15:10:12 (b) 12:10:15
;fn 𝐴𝐴: 𝐵𝐵 = 3: 4 , 𝐵𝐵: 𝐶𝐶 = 5: 7 vkSj 𝐶𝐶: 𝐷𝐷 = (c) 5:6:4 (d) None of these
8: 9 gS] rc 𝐴𝐴: 𝐷𝐷 fdlds cjkcj gS \
(a) 3 : 7 (b) 7 : 3 (c) 21 : 10 (d) 10 : 21 63. If 6A = 11B = 7C; find A: B : C
यिद 6A= 11B = 7C है; तो A : B : C का पता लगाएं ।
57. If 𝑎𝑎: 𝑏𝑏 = 5: 7 and 𝑐𝑐: 𝑑𝑑 = 2𝑎𝑎: 3𝑏𝑏 then (a) 66:42:77 (b) 77:42: 66
𝑎𝑎𝑎𝑎: 𝑏𝑏𝑏𝑏 is : (c) 42:77: 66 (d) 7:11:6
;fn 𝑎𝑎: 𝑏𝑏 = 5: 7 vkSj 𝑐𝑐: 𝑑𝑑 = 2𝑎𝑎: 3𝑏𝑏 rc
3 7 4
𝑎𝑎𝑎𝑎: 𝑏𝑏𝑏𝑏 D;k gksxh \ 64. If 𝑝𝑝 = 𝑄𝑄 = 𝑅𝑅, then what is the ratio of
5 9 5
(a) 20:38 (b) 50:147 (c) 10:21 (d) 50:151 P, Q and R respectively?
 Maths with Sumit Goyal By Sumit Goyal
(Ex Excise Inspector)
Ratio (अनपु ात) Sheet - 1
3 7 4
;fn 𝑃𝑃 = 𝑄𝑄 = 𝑅𝑅 rks Øe’k% 𝑃𝑃, 𝑄𝑄 rFkk 𝑅𝑅 73. If x:y=3 : 1, then (x 3 – y 3 ): (x 3 + y 3 ) = ?
5 9 5
dk vuqikr D;k gS \ यिद x :y=3:1, हो तो (x 3 – y 3 ): (x 3 + y 3 )�ा होगा?
(a) 35 : 36 : 15 (a) 13:14 (b) 14:13 (c) 10:11 (d) 11:10
(b) 140 : 108 : 105
(c) 135 : 140 : 105
74. If (a+b) : (a-b) = 9:1 then (𝑎𝑎2 + 𝑏𝑏 2 ) will be
(d) 70 : 45 : 63
equal to:
2
65. If of A = 75% of B = 0.6 of C, then A : B : C is यिद (a+b): (a-b)=9:1 तो (𝑎𝑎2 + 𝑏𝑏2 ) िकसके बराबर
3
2 है?
यिद A का =B का 75% = C का 0.6, तब A : B:C �ात
3 (a) 41 (b) 40 (c) 42 (d) 38
कर�।
(a) 2:3:3 (b) 3:4:5
75. If (x + y):(x - y) = 11 : 1, find value of (5x+3y)
(c) 4:5:6 (d) 9:8:10
(x - 2y).
यिद (x +y):(x -y)= 11:1, तो (5x+3y)/(x -2y) का मान
𝑥𝑥 3 −𝑦𝑦 3
66. If (;fn) 𝑥𝑥: 𝑦𝑦 ∷ 5: 2, then (rc) 3 3 =? �ात करो।
𝑥𝑥 +𝑦𝑦
117 114 129 168 (a) 45/4 (b) 4/45 (c)-45/4 (d)-4/45
(a) (b) (c) (d)
133 132 144 135

𝑥𝑥 2 −𝑥𝑥𝑥𝑥+𝑦𝑦 2 76. If x:y=3:5 then (10x + 3y) : (5x+2y)= ?

67. If (;fn) 𝑥𝑥: 𝑦𝑦 ∷ 5: 2, then (rc) =?
𝑥𝑥 2 +𝑥𝑥𝑥𝑥+𝑦𝑦 2 यिद x :y=3:5 हो, तो (10x +3y) : (5x +2y)= ?
68 19 17 15
(a)
35
(b)
39
(c)
86
(d)
23
(a) 9:4 (b) 5:9 (c) 9:5 (d) 4:9

𝑥𝑥𝑥𝑥−𝑥𝑥 2 77. If a:b=3:2, then(5a+2b): (3a+4b) is equal

68. If (;fn) 𝑥𝑥: 𝑦𝑦 ∷ 5: 2, then (rc) =?
𝑥𝑥 2 +𝑦𝑦 2 to:
17 19 −15 19
(a)
29
(b)
39
(c)
29
(d)
29
;fn 𝑎𝑎: 𝑏𝑏 = 3: 2, rks (5𝑎𝑎 + 2𝑏𝑏): (3𝑎𝑎 + 4𝑏𝑏)
dk eku D;k gksxk \
𝑥𝑥 2 +𝑦𝑦 (a) 16:15 (b) 8:7 (c) 19:17 (d) 17:14
69. If (;fn) 𝑥𝑥: 𝑦𝑦 ∷ 5: 2, then (rc) =?
𝑥𝑥+𝑦𝑦 2
(a) 5 (b) 4 (c) 2 78. If (5𝑎𝑎 − 3𝑏𝑏) ∶ (4𝑎𝑎 − 2𝑏𝑏) = 2: 3, then
(d) can’t be determined 𝑎𝑎: 𝑏𝑏 is equal to:
;fn (5𝑎𝑎 − 3𝑏𝑏): (4𝑎𝑎 − 2𝑏𝑏) = 2: 3, rks 𝑎𝑎: 𝑏𝑏
70. If (;fn) (4𝑥𝑥 2 − 3𝑦𝑦 2 ): (2𝑥𝑥 2 + 5𝑦𝑦 2 ) ∷ dk eku D;k gksxk \
12: 19 then (rc) 𝑥𝑥: 𝑦𝑦 =? (a) 3:4 (b) 2:3 (c) 5:8 (d) 5:7
(a) 1: 2 (b) 4: 3 (c) 4: 5 (d) 3: 2
79. There are three numbers A, B, C such that
𝑥𝑥 3 2𝑥𝑥+3𝑦𝑦
71. If (;fn) = , then (rc) =? twice A is equal to thrice B and four times
𝑦𝑦 4 3𝑥𝑥−2𝑦𝑦
B is equal to five times C. then the ratio
(a) -9 (b) 0 (c) 18 (d) 1
between A and C is
𝑎𝑎 3 𝑎𝑎2 +𝑏𝑏2 rhu la[;k 𝐴𝐴, 𝐵𝐵, 𝐶𝐶 bl izdkj gS fd 𝐴𝐴 dk nksxquk 𝐵𝐵
72. If (;fn) = , then (rc) =?
𝑏𝑏 2 𝑎𝑎2 −𝑏𝑏2 ds rhu xqus ds cjkcj gS vkSj 𝐵𝐵 dk pkj xquk 𝐶𝐶 ds
13 5 14 15
(a)
5
(b)
13
(c)
5
(d)
7 ik¡p xqus ds cjkcj gS] rks 𝐴𝐴 vkSj 𝐶𝐶 ds chp dk vuqikr
Kkr djsa \
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(Ex Excise Inspector)
Ratio (अनपु ात) Sheet - 1
(a) 3 : 4 (b) 8 : 15 (c) 15 : 8 (d) 4 : 3 ;fn fØdsV eSp dh ,d ikjh esa rhu f[kykfM+;ksa }kjk
dqy 361 ju cuk, x,A ;fn 𝐴𝐴 vkSj 𝐵𝐵 }kjk cuk,
80. A man divided his property so that his son’s x, juksa dk vuqikr o 𝐵𝐵 vkSj 𝐶𝐶 ds }kjk cuk, x,
share to his wife’s and wife’s share to his juksa dk vuqikr 3: 2 gks] rks 𝐴𝐴 }kjk cuk, x, ju
daughters are both as in the ratio 3: 1. If the Kkr djsa \
daughters get Rs. 10000 less than son, the (a) 171 (b) 181 (c) 185 (d) 161
value (in rupees) of the whole property is :
,d vkneh us viuh lEifÙk dks viuh iRuh] cPps vkSj
iq=h esa bl izdkj ckVk fd iq= vkSj iRuh ds fgLls dk 84. In a school, the ratio of boys to girls is 4 ∶ 3
vuqikr rFkk iRuh vkSj iq=h ds fgLls dk vuqikrk 3: 1 and the ratio of girls, to teachers is 8 ∶ 1.
gSA ;fn iq=h dks iq= ls 10000# de feyrs gSa rks The ratio of students to teachers is :
dqy lEifÙk fdruh # Fkh \ ,d Ldwy esa yM+ds vkSj yM+fd;ksa dk vuqikr% 4 ∶ 3
(a) Rs. 16250 (b) Rs. 16000 gS vkSj yM+fd;ksa o v/;kidksa dk vuqikr 8 ∶ 1 gS] rks
(c) Rs. 18200 (d) Rs. 17000 Nks=ksa o v/;kidksa dk vuqikr Kkr djsa \
(a) 56: 3 (b) 55: 1 (c) 49: 3 (d) 56: 1
81. The sum of three number is 116. The ratio
of second to the third is 9: 16 and the first
85. Rs. 2420 were divided among A, B, C, so
to third is 1: 4 the second number is.
that 𝐴𝐴 ∶ 𝐵𝐵 = 5 ∶ 4 and 𝐵𝐵 ∶ 𝐶𝐶 = 9 ∶ 10 then
rhu la[;kvksa dk ;ksx 116 gSA nwljh vkSj rhljh C gets
la[;k dk vuqikr 9: 16 gS vkSj igyh vkSj rhljh 2420 # dh jkf’k 𝐴𝐴, 𝐵𝐵, 𝐶𝐶 esa bl izdkj forfjr dh
la[;k dk vuqikr 1: 4 gS] rks nwljh la[;k gS \ xbZ fd 𝐴𝐴 ∶ 𝐵𝐵 = 5 : 4 vkSj B : C = 9 ∶ 10 rks
(a) 30 (b) 32 (c) 34 (d) 36 crkb, 𝐶𝐶 dks fdruh jkf’k feyk \
(a) 680 (b) 800 (c) 900 (d) 950
82. Of the three numbers, the ratio of the first
and the second is 8: 9 and that of the second 86. A sum is divided among A, B, C and D such
and third is 3: 4 of the product of the first that the ratio of the shares of A and B is 2 ∶
and third number is 2400. Then the second 3, that of B and C is 1 ∶ 2 and that of C and
number is : D is 3 ∶ 4 . If the difference between the
rhu la[;kvksa esa igyh vkSj nwljh la[;kvksa dk vuqikr
shares of A and D is Rs 648, then the sum
8: 9 gS vkSj nwljh o rhljh dk vuqikr 3: 4 gSA ;fn of their shares is :
igyh vkSj rhljh dk xq.kuQy 2400 gS] rks nwljh ,d jkf’k dks 𝐴𝐴, 𝐵𝐵, 𝐶𝐶 vkSj 𝐷𝐷 esa bl izdkj ckaVk tkrk
la[;k Kkr djsa \ gS fd 𝐴𝐴 vkSj 𝐵𝐵 ds Hkkx dk vuqikr 2 ∶ 3, 𝐵𝐵 vkSj
(a) 45 (b) 40 (c) 24 (d) 10
𝐶𝐶 ds Hkkx dk vuqikr 1 ∶ 2 rFkk 𝐶𝐶 vkSj 𝐷𝐷 ds Hkkx
dk vuqikr 3 ∶ 4 gksrk gSA ;fn 𝐴𝐴 vkSj 𝐷𝐷 ds fgLlksa
83. In an innings of a cricket match, total of 361
esa # 648 dk varj gS] rks fgLls dh jkf’k dk ;ksx
runs. If the ratio of the number of runs
D;k gksxkA
scored by A to that scored by B and also
number of runs scored by B to that scored (a) Rs 2,484 (b) Rs 2,160
by C be 3: 2, the number of runs scored by (c) Rs 1,944 (d) Rs 2,052
A was
 Maths with Sumit Goyal By Sumit Goyal
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Ratio (अनपु ात) Sheet - 1
87. The sum of three numbers is 252. If the first (a) 138, 69 (b) 183, 24
number is thrice the second and third (c) 108, 99 (d) 137, 70
number is two third of the first, then the
second number is : 91. Rs. 9900 distributed among A, B and C such
rhu la[;kvksa dk ;ksx 252 gSA ;fn igyh la[;k] 2
nwljh la[;k frxquh gS vkSj rhljh la[;k] igyh la[;k that share of B is times of share of A and C
7
3
dh nks&frgkbZ gS rks nwljh la[;k D;k gksxh \ together and share of C is times of share of A
8
(a) 41 (b) 21 (c) 42 (d) 84 and B together. Find the share of A.
9900 �. को A, B और C म� इस प्रकार बाँटा जाता है िक B का
88. Rs 3400 is divided among A, B, C and D in 2
िह�ा A और C के िह�े का भाग तथा C का िह�ा A और
such a way that the ratio of A’s and B’s 7
3
share, B’s and C’s share and C’s and D’s B के िह�े का भाग है। A का िह�ा बताए?
8
share are 2 ∶ 3, 4 ∶ 3 and 2 ∶ 3 respectively. (a) 4000 (b) 5000
Find the total share of B and D ? (c) 6000 (d) 5500
# 3400 dks 𝐴𝐴, 𝐵𝐵, 𝐶𝐶, 𝐷𝐷 esa bl izdkj foHkkftr
fd;k tkrk gS fd 𝐴𝐴 vkSj 𝐵𝐵 ds Hkkxksa] 𝐵𝐵 vkSj 𝐶𝐶 ds 92. Rs.19400 distributed among A,B,C and D such
Hkkxksa] 𝐶𝐶 vkSj 𝐷𝐷 ds Hkkxksa esa Øe’k 2 ∶ 3, 4 ∶ 3 rFkk that when A get Rs. 1 then B get 80 paise. When
2 ∶ 3 ds vuqikr jgsa] rks 𝐵𝐵 vkSj 𝐷𝐷 ds Hkkxksa dk ;ksx B get Rs. 2 then C get 20 paisa and when C get
gSA Rs.1 then D get 75 paise. Find the share of A.
(a) Rs 2040 (b) Rs 1680 19400 �. क� रा�श को A,B,C और D के बीच इस प्रकार से
(c) Rs 2000 (d) Rs 1720 बाँटा जाता है िक जब A को 1 �. �मलता है तो B को 80 पैसा
तथा जब B को 2 �. �मलता है तो C को 20 पैसा, और जब C
89. A sum of Rs x is divided among A, B and को 1 �. �मलता है तो D को 75 पैसा �मलता है। A का िह�ा
C such that the ratio of the shares of A and बताए?
B is 6:7 and that of B and C is 3:2. If the
(a) 10,000 (b) 5,000
difference the shares of A and C is Rs540,
(c) 12,000 (d) 7,000
then the value of x is:
#𝑥𝑥 dks 𝐴𝐴, 𝐵𝐵 vkSj 𝐶𝐶 ds chp foHkkftr fd;k tkrk gS
93. If (𝑎𝑎 + 𝑏𝑏): (𝑏𝑏 + 𝑐𝑐): (𝑐𝑐 + 𝑎𝑎) ∷ 4: 7: 9 &
tSls fd 𝐴𝐴 vkSj 𝐵𝐵 ds 'ks;jksa dk vuqikr 6: 7 gS vkSj
𝑎𝑎 + 𝑏𝑏 + 𝑐𝑐 = 30 then find c.
𝐵𝐵 vkSj 𝐶𝐶 dk vuqikr 3: 2 gSA ;fn 𝐴𝐴 vkSj 𝐶𝐶 ds ;fn (𝑎𝑎 + 𝑏𝑏) ∶ (𝑏𝑏 + 𝑐𝑐) ∶ (𝑐𝑐 + 𝑎𝑎) = 4 : 7 : 9
'ks;j dk varj #540 gS] rks 𝑥𝑥 dk eku gS% vkSj 𝑎𝑎 + 𝑏𝑏 + 𝑐𝑐 = 30 rks 𝑐𝑐 dk eku D;k gksxk\
(a) 7155 (b) 7290 (c) 7020 (d) 7425 (a) 16 (b) 17 (c) 15 (d) 18

90. Divide 207 into two parts in such a way that 94. If (𝑎𝑎 + 𝑏𝑏) ∶ (𝑏𝑏 + 𝑐𝑐) ∶ (𝑐𝑐 + 𝑎𝑎) = 5 : 7 : 6
eighth part of the first and fifth part of the and 2a -3b + 4c = 66 then value of c will be
?
second are in the ratio 5 : 4. Find both parts?
;fn (𝑎𝑎 + 𝑏𝑏) ∶ (𝑏𝑏 + 𝑐𝑐) ∶ (𝑐𝑐 + 𝑎𝑎) = 5 : 7 : 6
1
207 को दो भागों म� इस प्रकार बाँटा जाता है िक पहले भाग का vkSj 2a -3b + 4c = 66 rks 𝑐𝑐 dk eku D;k gksxk\
8
1 132
भाग तथा दू सरे भाग का भाग का अनुपात 5:4 हो जाता है। वे (a) 12 (b) 18 (c) 24 (d)
7
5
दोनों भाग बताए?
 Maths with Sumit Goyal By Sumit Goyal
(Ex Excise Inspector)
Ratio (अनपु ात) Sheet - 1
95. If (𝑎𝑎 + 𝑏𝑏): (𝑏𝑏 + 𝑐𝑐): (𝑐𝑐 + 𝑎𝑎) ∷ (6 ∶ 7 ∶ ;fn (𝑥𝑥 − 𝑦𝑦 + 𝑧𝑧): (𝑦𝑦 − 𝑧𝑧 + 2𝑤𝑤): (2𝑥𝑥 + 𝑧𝑧 −
8)& (𝑎𝑎 + 𝑏𝑏 + 𝑐𝑐) = 14 them find 𝑐𝑐 ? 𝑤𝑤) = 2 ∶ 3 ∶ 5, rks (3𝑥𝑥 + 3𝑧𝑧 − 2𝑤𝑤): 𝑤𝑤 dk
;fn (𝑎𝑎 + 𝑏𝑏) ∶ (𝑏𝑏 + 𝑐𝑐) ∶ (𝑐𝑐 + 𝑎𝑎) = 6 : 7 : 8 eku D;k gksxk \
vkSj 𝑎𝑎 + 𝑏𝑏 + 𝑐𝑐 = 14 rks 𝑐𝑐 dk eku D;k gksxk\ (a) 7:1 (b) 4:3 (c) 9:1 (d) 8:1
(a) 4 (b) 6 (c) 8 (d) 7
𝑎𝑎 𝑐𝑐 3 13𝑎𝑎−111𝑐𝑐
101. If (;fn) = = , then (rc) =?
𝑏𝑏 𝑑𝑑 2 13𝑏𝑏−111𝑑𝑑
96. If (𝑎𝑎 + 𝑏𝑏) ∶ (𝑏𝑏 + 𝑐𝑐) ∶ (𝑐𝑐 + 𝑎𝑎) = 7 ∶ 3 1 5 3
6 ∶ 5 and 𝑎𝑎 + 𝑏𝑏 + 𝑐𝑐 = 27, then what (a) (b) (c) (d)
2 2 2 5
1 1 1
will be the value of : : ?
𝑎𝑎 𝑏𝑏 𝑐𝑐 𝑎𝑎 𝑐𝑐 𝑒𝑒 9 2𝑎𝑎+3𝑐𝑐+5𝑒𝑒
;fn (𝑎𝑎 + 𝑏𝑏) ∶ (𝑏𝑏 + 𝑐𝑐) ∶ (𝑐𝑐 + 𝑎𝑎) = 7 ∶ 102. If = = = then =?
𝑏𝑏 𝑑𝑑 𝑓𝑓 5 2𝑏𝑏+3𝑑𝑑+5𝑓𝑓
1 1 1
6 ∶ 5 vkSj 𝑎𝑎 + 𝑏𝑏 + 𝑐𝑐 = 27, rks : : dk (a)
3
(b)
2
(c)
9
(d)
3
𝑎𝑎 𝑏𝑏 𝑐𝑐
4 5 5 7
eku D;k gksxk \
(a) 4 : 3 : 6 (b) 3 : 4 : 2 𝑎𝑎 𝑐𝑐 𝑒𝑒 𝑚𝑚𝑚𝑚+𝑛𝑛𝑛𝑛+𝑝𝑝𝑝𝑝
(c) 3 : 2 : 4 (d) 3 : 6 : 4 103. If (;fn) = = =2, then (rc) =
𝑏𝑏 𝑑𝑑 𝑓𝑓 𝑚𝑚𝑚𝑚+𝑛𝑛𝑛𝑛+𝑝𝑝𝑝𝑝

𝑝𝑝+𝑞𝑞+𝑟𝑟
?
97. If (;fn) 𝑄𝑄 = & (𝑄𝑄 − 𝑝𝑝): (𝑄𝑄 − (a) 1 (b) 2 (c) 3 (d) 4
2
𝑞𝑞): (𝑄𝑄 − 𝑟𝑟) ∷ 17: 5: 8, then (rc) 𝑝𝑝: 𝑞𝑞: 𝑟𝑟 =?
(a) 16 : 19 : 21 (b) 7 : 8 : 5 𝑎𝑎 𝑐𝑐 𝑒𝑒
104. If (;fn) = = =3 , then (rc)
(c) 14 : 19 : 21 (d) 13 : 25 : 22 𝑏𝑏 𝑑𝑑 𝑓𝑓
𝑚𝑚𝑎𝑎2 +𝑛𝑛𝑐𝑐 2 +𝑝𝑝𝑒𝑒 2
=?
𝑚𝑚𝑏𝑏2 +𝑛𝑛𝑑𝑑 2 +𝑝𝑝𝑓𝑓2
98. If a triangle 𝐴𝐴𝐴𝐴𝐴𝐴, (𝑠𝑠 − 𝑎𝑎): (𝑠𝑠 − 𝑏𝑏): (𝑠𝑠 −
(a) 3 (b) 9 (c) 1 (d) 18
𝑐𝑐) ∷ 11: 8: 7 where is semi perimeter.
𝑎𝑎, 𝑏𝑏, 𝑐𝑐 are sides. Find the ratio of 𝑎𝑎: 𝑏𝑏: 𝑐𝑐.
𝑎𝑎 𝑐𝑐 𝑒𝑒
f=Hkqt 𝐴𝐴𝐴𝐴𝐴𝐴 esa (𝑠𝑠 − 𝑎𝑎): (𝑠𝑠 − 𝑏𝑏): (𝑠𝑠 − 𝑐𝑐) ∷ 105. If (;fn) 𝑏𝑏 = 𝑑𝑑 = 𝑓𝑓 = 4 , then (rc)
11: 8: 7 tgk¡ 𝑠𝑠 v)Zifjeki gS rFkk Hkqtk,a 𝑎𝑎, 𝑏𝑏, 𝑐𝑐 𝑚𝑚2 𝑎𝑎+22 𝑐𝑐+𝑝𝑝2 𝑒𝑒
gSA rks 𝑎𝑎, 𝑏𝑏, 𝑐𝑐 \ =?
𝑚𝑚2 𝑏𝑏+𝑛𝑛2 𝑑𝑑+𝑝𝑝2 𝑓𝑓
(a) 7 : 8 : 11 (b) 14 : 17 : 19 (a) 1 (b) 4 (c) 8 (d) 16
(c) 15 : 18 : 19 (d) 9 : 13 : 21
106. If 𝑝𝑝 ∶ 𝑞𝑞 = 𝑟𝑟 ∶ 𝑠𝑠 = 𝑡𝑡 ∶ 𝑢𝑢 = 2 ∶ 3 , then
99. If (𝑥𝑥 − 2𝑦𝑦 + 8𝑧𝑧) ∶ (𝑦𝑦 − 3𝑧𝑧 + 4𝑤𝑤) ∶ (𝑚𝑚𝑚𝑚 + 𝑛𝑛𝑛𝑛 + 𝑜𝑜𝑜𝑜) ∶ (𝑚𝑚𝑚𝑚 + 𝑛𝑛𝑛𝑛 + 𝑜𝑜𝑜𝑜) is
(4𝑥𝑥 + 5𝑧𝑧 − 7𝑤𝑤) = 3 ∶ 4 ∶ 7 then find
6𝑥𝑥+2𝑦𝑦−17𝑤𝑤 equal to :
=? ;fn 𝑝𝑝 ∶ 𝑞𝑞 = 𝑟𝑟 ∶ 𝑠𝑠 = 𝑡𝑡 ∶ 𝑢𝑢 = 2 ∶ 3 gks rks
𝑤𝑤
;fn (𝑥𝑥 − 2𝑦𝑦 + 8𝑧𝑧) ∶ (𝑦𝑦 − 3𝑧𝑧 + 4𝑤𝑤) ∶ (𝑚𝑚𝑚𝑚 + 𝑛𝑛𝑛𝑛 + 𝑜𝑜𝑜𝑜) ∶ (𝑚𝑚𝑚𝑚 + 𝑛𝑛𝑛𝑛 + 𝑜𝑜𝑜𝑜) fdlds
(4𝑥𝑥 + 5𝑧𝑧 − 7𝑤𝑤) = 3∶ 4∶ 7 rks cjkcj gksxk \
6𝑥𝑥+2𝑦𝑦−17𝑤𝑤
dk eku D;k gksxk \ (a) 1 ∶ 3 (b) 1 ∶ 2 (c) 2 ∶ 3 (d) 3 ∶ 2
𝑤𝑤
(a) 5 (b) 6 (c) 7 (d) 8
107. If 𝑎𝑎 ∶ 𝑏𝑏 = 𝑐𝑐 ∶ 𝑑𝑑 = 𝑒𝑒 ∶ 𝑓𝑓 = 1 ∶ 2, then
100. If (𝑥𝑥 − 𝑦𝑦 + 𝑧𝑧): (𝑦𝑦 − 𝑧𝑧 + 2𝑤𝑤): (2𝑥𝑥 + 𝑧𝑧 − (𝑝𝑝𝑝𝑝 + 𝑞𝑞𝑞𝑞 + 𝑟𝑟𝑟𝑟): (𝑝𝑝𝑝𝑝 + 𝑞𝑞𝑞𝑞 + 𝑟𝑟𝑟𝑟) is equal
𝑤𝑤)=2 ∶ 3 ∶ 5, then (3𝑥𝑥 + 3𝑧𝑧 − 2𝑤𝑤): 𝑤𝑤=? to:
 Maths with Sumit Goyal By Sumit Goyal
(Ex Excise Inspector)
Ratio (अनपु ात) Sheet - 1
9 11 7 7
;fn 𝑎𝑎 ∶ 𝑏𝑏 = 𝑐𝑐 ∶ 𝑑𝑑 = 𝑒𝑒 ∶ 𝑓𝑓 = 1 ∶ 2 gks rks (a) (b) (c) (d)
5 7 11 4
(𝑝𝑝𝑝𝑝 + 𝑞𝑞𝑞𝑞 + 𝑟𝑟𝑟𝑟): (𝑝𝑝𝑝𝑝 + 𝑞𝑞𝑏𝑏 + 𝑟𝑟𝑟𝑟) cjkcj gksxk
\ 4 √6 𝑥𝑥+2√2
(a) 𝑝𝑝 ∶ (𝑞𝑞 + 𝑟𝑟) (b) (𝑝𝑝 + 𝑞𝑞) ∶ 𝑟𝑟 115. For 𝑥𝑥 = , what is the value of +
√2+√3 𝑥𝑥−2√2
(c) 2 ∶ 3 (d) 1 ∶ 2 𝑥𝑥+2√3
=?
𝑥𝑥−2√3
(a) 1 (b) √2 (c) √3 (d)2
108. If 𝑎𝑎 ∶ 𝑏𝑏 = 𝑐𝑐 ∶ 𝑑𝑑 = 𝑒𝑒 ∶ 𝑓𝑓 = 1 ∶ 2, then (3𝑎𝑎 +
5𝑐𝑐 + 7𝑒𝑒) ∶ (3𝑏𝑏 + 5𝑑𝑑 + 7𝑓𝑓) is
116. If (4𝑎𝑎 + 7𝑏𝑏)(4𝑐𝑐 − 7𝑑𝑑) = (4𝑎𝑎 − 7𝑏𝑏) (4𝑐𝑐 +
;fn 𝑎𝑎 ∶ 𝑏𝑏 = 𝑐𝑐 ∶ 𝑑𝑑 = 𝑒𝑒 ∶ 𝑓𝑓 = 1 ∶ 2 gS] rks
7𝑑𝑑) , then which one of the following is
(3𝑎𝑎 + 5𝑐𝑐 + 7𝑒𝑒) ∶ (3𝑏𝑏 + 5𝑑𝑑 + 7𝑓𝑓) dk eku
correct ?
Kkr djsa \
;fn (4𝑎𝑎 + 7𝑏𝑏)(4𝑐𝑐 − 7𝑑𝑑) = (4𝑎𝑎 − 7𝑏𝑏)
(a) 8 ∶ 1 (b) 2 ∶ 1 (c) 1 ∶ 4 (d) 1 ∶ 2
(4𝑐𝑐 + 7𝑑𝑑) gS rks fuEufyf[kr esa ls lgh dkSulk gS\
𝑎𝑎 𝑐𝑐 𝑎𝑎 𝑐𝑐
𝑎𝑎 𝑏𝑏 (a) = (b) =
109. If (;fn) 𝑎𝑎, 𝑏𝑏, 𝑐𝑐 > 0, then (rc) = = 𝑏𝑏 𝑑𝑑 𝑑𝑑 𝑏𝑏
𝑏𝑏+𝑐𝑐 𝑐𝑐+𝑎𝑎 𝑎𝑎 𝑑𝑑 4𝑎𝑎 𝑐𝑐
𝑐𝑐
=? (c) = (d) =
𝑏𝑏 𝑐𝑐 7𝑏𝑏 𝑑𝑑
𝑎𝑎+𝑏𝑏
1 3 7 5
(a) (b) (c) (d) 𝑎𝑎 𝑏𝑏 𝑐𝑐
2 2 5 3 117. If = = then which one of the
𝑏𝑏+𝑐𝑐
𝑐𝑐+𝑎𝑎 𝑎𝑎+𝑏𝑏
𝑎𝑎 following statements is correct?
110. If (;fn) 𝑎𝑎, 𝑏𝑏, 𝑐𝑐 > 0, then (rc) = 𝑎𝑎 𝑏𝑏 𝑐𝑐
𝑎𝑎+𝑏𝑏+𝑐𝑐
𝑏𝑏 𝑐𝑐 ;fn = = gS] rks fuEufyf[kr esa ls
𝑏𝑏+𝑐𝑐 𝑐𝑐+𝑎𝑎 𝑎𝑎+𝑏𝑏
= =?
𝑎𝑎+𝑏𝑏+𝑐𝑐 𝑎𝑎+𝑏𝑏+𝑐𝑐 dkSUk&lk dFku lgh gS \
5 1 7 2
(a) (b) (c) (d) (a) Each fraction is equal to 1 or -1
9 3 3 3
izR;sd fHkUu 1 ;k −1 ds cjkcj gS A
𝑎𝑎 1
111. If (;fn) 𝑎𝑎, 𝑏𝑏, 𝑐𝑐 > 0, then (rc) = (b) Each fraction is equal to or 1.
2
2𝑎𝑎+𝑏𝑏+𝑐𝑐
𝑏𝑏 𝑐𝑐 1
= =? izR;sd fHkUu ;k 1 ds cjkcj gS A
𝑎𝑎+2𝑏𝑏+𝑐𝑐 𝑎𝑎+𝑏𝑏+2𝑐𝑐 2
1 1
(a) 2 (b) 1 (c) -1 (d) (c) Each fraction is equal to or -1.
4 2
1
izR;sd fHkUu ;k −1 ds cjkcj gS A
𝑦𝑦 𝑦𝑦+𝑥𝑥 𝑥𝑥 2
112. If (;fn) = = =? then (rc) (d) Each fraction is equal to only.
1
𝑥𝑥−𝑧𝑧 𝑧𝑧 𝑦𝑦
2
𝑥𝑥: 𝑦𝑦: 𝑧𝑧 = ? izR;sd fHkUu dsoy
1
ds cjkcj gS A
(a) 3 : 2 : 4 (b) 4 : 3 : 2 2

(c) 4 : 2 : 3 (d) 1 : 2 : 3
118. If 6/7th of 8/5th of a number is 192, then 3/4th
𝑧𝑧 2𝑧𝑧+𝑥𝑥 2𝑥𝑥 𝑥𝑥+𝑦𝑦+𝑧𝑧 of that number is
113. If (;fn) = = then (rc) =?
𝑥𝑥−2𝑦𝑦 2𝑦𝑦 𝑧𝑧 𝑧𝑧 यिद 192 िकसी सं �ा के 8/5 का 6/7 है, तो उस सं �ा का 3/4
35 37 44 41
(a) (b) (c) (d) �ा होगा?
16 12 18 18
(a) 105 (b) 77 (c) 36 (d) 80
(𝑎𝑎+𝑏𝑏) 6 (𝑏𝑏+𝑐𝑐) 9
114. If (;fn) = and = then (rc)
𝑐𝑐 5 𝑎𝑎 2
𝑎𝑎+𝑐𝑐
=?
𝑏𝑏
 Maths with Sumit Goyal By Sumit Goyal
(Ex Excise Inspector)
Ratio (अनपु ात) Sheet - 1
119. 35% of a number is 75% of another number. of the second are in the ratio 3:4. The first part
What is the ratio between the first and the is :
second number, respectively? 94 �. को दो भागों म� इस प्रकार �वभा�जत िकया गया िक पहले
िकसी सं �ा का 35% एक अ� सं �ा के 75% के बराबर है। 1 1
का वाँ भाग और दू सरे का वाँ भाग का अनुपात 3:4 म� है, तो
5 8
प्रथम और दू सरी सं �ा का अनुपात बताए? पहला भाग �ात कर�।
(a) 35:6 (b) 15:7 (c) 23:7 (d) 32:9 (a) 30 (b) 36 (c) 28 (d) 40

120. Rs. 94 is divided into two parts in such a way

that the fifth part of the first and the eighth part

Answer Key
01=b 02=a 03=c 04=b 05=a 06=c 07=c 08=a 09=b 10=b
11=c 12=b 13=c 14=a 15=b 16=a 17=a 18=a 19=d 20=d
21=c 22=a 23=a 24=c 25=c 26=b 27=d 28=c 29=a 30=c
31=d 32=a 33=a 34=a 35=d 36=d 37=c 38=d 39=c 40=a
41=d 42=a 43=a 44=b 45=c 46=c 47=a 48=d 49=d 50=c
51=c 52=a 53=b 54=d 55=b 56=d 57=b 58=c 59=c 60=d
61=d 62=a 63=b 64=b 65=d 66=a 67=b 68=c 69=d 70=d
71=c 72=a 73=a 74=a 75=c 76=c 77=c 78=d 79=c 80=a
81=d 82=a 83=a 84=a 85=b 86=d 87=c 88=a 89=a 90=a
91=b 92=a 93=d 94=c 95=b 96=a 97=d 98=c 99=a 100=c
101=a 102=c 103=b 104=b 105=b 106=c 107=d 108=d 109=a 110=b
111=d 112=c 113=b 114=d 115=d 116=a 117=c 118=a 119=b 120=a