TNPSC 2023 -24

GROUP IV & VAO

ê˜è£˜ ä.ã.âv Üè£ìI

èEî‹ ¬è«ò´
«ïó‹ ñŸÁ‹ «õ¬ô
Time and Work

Anna Nagar West, Chennai - 600012

Phone: 9962600037, 9962600038
www.sarkariasacademy.com
 TNPSC èí‚°
«ïó‹ ñŸÁ‹ «õ¬ô
TIME AND WORK
3. A can do a some work in 12 days. B can do
same work in 20 days. First three days A, B
1. A can do some work 12 days. Then B can do work together after A left. Remaining work
same work 20 days. How many days it will done by B.
take work together? A å¼ «õ¬ô¬ò 12 èO™ º®Šð£˜.
A â¡ðõ˜ å¼ «õ¬ô¬ò 12 èO½‹. B Ü‰î «õ¬ô¬ò 20 èO™ º®Šð£˜.
B â¡ðõ˜ Ü«î «õ¬ô¬ò 20 èO½‹ A »‹ B »‹ «ê˜‰î Üš«õ¬ô¬ò Í¡Á
ªêŒî£™ Þ¼õ¼‹ «ê˜‰¶ Üš«õ¬ô¬ò ï£†èœ ªêŒî Hø° A Üš«õ¬ô¬ò
âˆî¬ù èO™ º®Šð˜ -? M†´ Mô°Aø£˜. âQ™ e÷
«õ¬ô¬ò B âˆî¬ù èO™ º®Šð£˜.
1 1
A+ B = + ( part )
12 2  1 1 
TNPSC group- IV & VAO │ (èEî‹ ¬è«ò´)

3(A+B)=3  +  part
20 + 12 32  12 20 
= =
240 240  5+3   8 
=3   =3  
4 2  60   60 
= = ( part )
340 15 4 2
= = (part)
15 1 10 5
Number of days = = 7 days
2 2 2
Remaining work=1- (1=Full work)
1 5
= days
part 3
= (part)
5
1
= part
days ( ∴ Remaining work done by B) =
Remaining work
=
2. A can do some work 30 days. B and C can do B's work
some work 20 days, 60 days. How many days
it will take work together ? 3
= 5 = 3 x 20
å¼ «õ¬ô¬ò A â¡ðõ˜ 30 èO½‹, 1 5
20
B â¡ðõ˜ 20 èO½‹ C â¡ðõ˜ 60
èO½‹ º®Šð£˜ âQ™ Íõ¼‹ B = 12 days
«ê˜‰¶ Üš«õ¬ô¬ò âˆî¬ù èO™
º®Šð£˜? 4 A&¾‹ B ¾‹ «ê˜‰¶ å¼ «õ¬ô¬ò 12
A=30 days, B=20 days, C=60 days èO™ º®‚Aø£˜. B ¾‹ C¾‹ «ê˜‰¶
15 èO½‹, C¾‹ A¾‹ «ê˜‰¶ 20
1 1 1 èO½‹ º®Šð£˜. Í¡Á «ð¼‹
A+B+C= + + (part)
30 20 60 «ê˜‰¶ Üš«õ¬ô¬ò ªêŒî£™ âˆî¬ù
2+3+1 6 èO™ º®Šð˜?
= =
60 60 A+ B + C = ?
1 A + B = 12, B + C =15, C+A = 20
A+B+C= (part)
10
1 1 1
2( A + B + C ) = + +
Number of days=10 days 12 15 20

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 TNPSC èí‚°

5 + 4 + 3 12 2 −1 1
= = =B = ( part )
60 60 20 20
1
2( A + B + C ) =( part ) B's days = 20 days
5
1
A + B + C= Suppose C’s days = ?
5x2
1 1
A + B + C = ( parts ) A+ B +C =
10 10
1
No. of days = 10 days A+ B =
12
1 1
5. A + B = 12 days C
= −
10 12
B + C = 15 days
12 − 10 2 1
C + A = 20 days C
= = =
120 120 60
A = ? days
C's days = 60 days
1 1 1

ê˜è£˜ ä.ã.âv Üè£ìI

2( A + B + C ) = + +
12 15 20 6. If 12 men and 16 boys can do a piece of work
5 + 4 + 3 12 1 in 5 days. 13 men and 24 boys can do it in 4
= = = days. The ratio of the daily work done by a
60 60 5
man to that of a boy is
1 1 12 ñQî˜èÀ‹, 16 ñ£íõ˜èÀ‹ «ê˜‰¶,
A+B+C= = (part)
5x2 10 å¼ «õ¬ô¬ò 䉶 èO™ º®Šð£˜èœ.
1 13 ñQî˜èÀ‹ 24 ñ£íõ˜èÀ‹ «ê˜‰¶
B+C= Üš«õ¬ô¬ò 4 èO™ º®Šð£˜èœ.
15
Fùº‹ ñQ, ñ£íõ¼‹ ªêŒ»‹
1
A+ B +C = «õ¬ôJ¡ MAî ÃÁ-?
10
12 M + 16 B = 5 days
1 1
− A =−  −  13 M + 24 B = 4 days
 10 15 
M:B=?
3− 2 1
=A = ( part ) 60M + 80B = 52M + 96B
30 30
60M - 52M = 96B - 80B
A's days = 30 days 8M = 16B
M 16 2
Suppose B’s days = ? = =
B 8 1
A+ B + C =
M : B = 2 :1
1
A+ B +C =
10 7. If 12 men and 16 boys can do a piece of work
1 in 5 days. 13 men and 24 boys can do it in 4
C+ A=
20 days. Find the number of days taken by 12
1 1 men and 16 boys ?
B
= −
10 20 12 ñQî˜èÀ‹, 16 ñ£íõ˜èÀ‹ «ê˜‰î

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å¼ «õ¬ô¬ò 5 èO™ º®Šð£˜èœ. A = Rs. 6000
13 ñQî˜èÀ‹ 24 ñ£íõ˜èÀ‹ «ê˜‰î B's Efficiency
B’s share = Total Amount x
Üš«õ¬ô¬ò 4 èO™ º®Šð£˜èœ Total efficiency
âQ™ 12 ñQî˜èÀ‹, 16 ñ£íõ˜èÀ‹ 4
«ê˜‰î âˆî¬ù èO™ Üš«õ¬ô¬ò =13000 x
13
º®Šð˜ ?
12 M + 16 B = 5 days B = Rs. 4000
13 M + 24 B = 4 days
C's Efficiency
12 M + 16 B = ? C’s share = Total Amount x
Total efficiency
60M + 80 B = 52M + 96B
3
60M - 52M = 96B - 80B =13000 x
13
8M = 16B
C = Rs. 3000
TNPSC group- IV & VAO │ (èEî‹ ¬è«ò´)

16 B
M=
8
M = 2B 9.A = 20 days, B = 30 days.
Take 60M + 80B A + B = 1000 (Earned)
= 60(2B) + 80 B A’s Share = ?
= 120 B + 80B A B
Total Boys = 200 B days 20 30
12M + 16B = 12(2B) + 16B 2 : 3 (days)
= 24 B + 16B Efficiency A = 3, B = 2
Given boys = 40 B 3 : 2 (efficiency)
A's Efficiency
Total Boys 200 A’s share = Total Amount x
Number of days= = = 5 days 200 3 Total efficiency
Given Boys 40 =1000 x
5
A = Rs. 600
8.A = 10 days, B = 15 days, C = 20 days
B's Efficiency
A + B + C = Rs. 13,000 (earned). find the B’s share = Total Amount x
Total efficiency
shares of A, B, C = ?
A B C 200
2
days 10 15 20 =1000 x
5
2 : 3 : 4 ..... (days)
B = Rs. 400
Efficiency A = 3 x 4 = 12
B=2x4=8
10. 4 men (or) 6 boys can finish a piece of work
C=2x3=6 in 20 days. In how many days can 6 men and
12 : 8 : 6 11 boys finish it ?
6 : 4 : 3 (Efficiency) 4 Ý‡èœ (Ü) 6 ¬ðò¡èœ å¼ «õ¬ô¬ò
A's Efficiency 20 èO™ º®Šð˜. Üš«õ¬ô¬ò 6
A’s share = Total Amount x
Total efficiency Ý‡èœ ñŸÁ‹ 11 ¬ðò¡èœ âˆî¬ù
èO™ º®Šð˜ ?
6
=13000 x 4M = 6B = 20 days
13

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 TNPSC èí‚°
6M + 11B = ? days 3
Re mainingWork = 5
80M = 120B 9
100
120 3 100
M= B = x
80 5 9
3 20
M= B = days
2 3
3  3
6M+11B=6   B+11B
2 2
= 6 days
3
=9B+11B
=20B
12. A + B = 12 days
Total Boys A alone = 20 days
No.of days=
Given Boys B alone = ? days
120
= 1 1
20 A +B= ,A=
12 20

ê˜è£˜ ä.ã.âv Üè£ìI

=6 days 1 1
B= −
12 20
11. A alone = 25 days 5−3 2
=B =
B alone = 20 days 60 60
A started the work and was joined by B after 1
B= ( part )
10 days. The lasted for ? 30
B's days = 30 days
A = 25 days
B = 20 days
13. A can do a certain job in 12 days. B is 60%
A «õ¬ô¬ò ªî£ìƒA 10 ï£†èœ èNˆ¶
more efficient than A. How many days B
B «ê˜Aø£˜ âQ™ Ü‰î «õ¬ô º®»‹
alone take to do the same job ?
ï£†èœ -?
2 12 èO™ A â¡ðõ˜ å¼ «õ¬ô¬ò
 1  º®‚Aø£˜. B â¡ðõ˜ A ä Mì 60%
10 A = 10   Part
 25  Fø¬ñò£ùõ˜ âQ™ B îQò£è Ü«î
5 «õ¬ô¬ò âˆî¬ù èO™ º®Šð£˜
?
2 A’s efficiency x A’s day’s = B’s efficiency x
= (part)
5 B’s days
2 3
RemainingWork =1 − = ( part )
5 5 ........
100 x 12 = 160 x B’s days
Remaining part
R emainingWork done by A+B = 5
100 x 12
3
(A+B) part B’s days = B is 60% more than A
160 8 2
1 1 4+5 9
A+ B = + = =
25 20 100 100 15
=
2

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1
= 7 days 1 1 3+ 2
2 P+Q= + =
20 30 60
Days (èœ) 5 1
= = (part)
60 12
14. A works 3 times as fast as B and is able to take Re mainingwork
( P + Q )days =
a task in 24 days less than B. Find the time in ( P + Q ) work
which can complete a work together? 3
A â¡ðõ˜ B äŠ «ð£™ 3 ñ샰 = 4
1
Fø¬ñò£ùõ˜. B ä Mì 24 ï£†èœ 12
º¡ð£è º®‚Aø£˜ âQ™ Þ¼õ¼‹
3 3
«ê˜‰¶ âˆî¬ù èO™ º®Šð˜ -? = x 12
4
(P+Q) days = 9 days
A B
TNPSC group- IV & VAO │ (èEî‹ ¬è«ò´)

Alternative Days (å¡Á M†ì èœ)

Fø¬ñ 3x 1x
16. A and B can do a piece of work in 12 days and
ï£†èœ days 1x 3x
9 days Respectively. They work on alternative
3x - 1x = 24 days starting with A on the first duty. In how
2x = 24 many days they will be completed ?
x = 12 A ñŸÁ‹ B å¼ «õ¬ô¬ò º¬ø«ò
A= x 12 ñŸÁ‹ 9 èO™ º®Šð˜. A ™
A = 12days ªî£ìƒA A ñŸÁ‹ B å¡ÁM†ì å¡Á
èO™ «õ¬ô ªêŒA¡øù˜ âQ™
B = 3x
«õ¬ô¬ò º®‚è Ý°‹ ï£†èœ -?
= 3(12)
B = 36 days
A = 12 days. B = 9 days
1 1 3+ 4 7
1 1 A+ B = + = =
A+ B = + 12 9 36 36
12 36
3+1 4 1
= = = ( part ) 7 x 5 < 36
36 36 9
7
5(A+B) = 5 x
A + B = 9 days 36
35
(10days ) = ( part )
15. P = 20 days, Q = 30 day. They started the work 36
together and Q left after some days of work
35 1
and P finished the remaining in 5 days. How Re mainingwork =−
1 =
36 36
many days form the start did Q leave ?
Remaining work
Remaining Work done by A = A work
 1  1
5P 5=
=   ( part )
 20  4 1
4 = 36
1
1 3 12
1− =
Remining work = 4 4 1
= x12
36

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 TNPSC èí‚°

=
1
days 5 50
3 = x x5
50 5
1
Total days = 10 days. = 5 days.
3

17. If 12 men can build a wall 96 m long in 6 days. 20. å¼ «õ¬ô¬ò 210 Ý†èœ ï£À‚° 12
What length of a similar wall can be built by ñE«ïó‹ iî‹ 18 ï£†èœ ªêŒAø£˜.
15 men in 3 days. Ü«î «õ¬ô¬ò ÷£¡Á‚° 14 ñE
12 Ý†èœ 6 èO™ 96e c÷ºœ÷ «ïó‹ iî‹ 20 èO™ º®‚è âˆî¬ù
²õ¬ó 膮 º®ˆî£™ 15 Ý†èœ 3 Ý†èœ «î¬õ ?
èO™ âšõ÷¾ c÷ ²õŸ¬ø 膮
º®Šð˜? Men hrs days
Men Days Distance 210 12 18
Ý†èœ ï£†èœ c÷‹ ? 14 20
12 6 96
15 3 ?
6 9
12 18 3
x x 210 21
15 3 14 7 20 2
=6x9x3
4
= x x 96 8 = 15 x 4 = 60
12 63
= 162

ê˜è£˜ ä.ã.âv Üè£ìI

= 60 m

18. If the wages of 15 labour 6 days are Rs. 7200. Execrise Sums :
Find the wages of 23 labourers for 5 days. 1. A ñŸÁ‹ B å¼ «õ¬ô¬ò 10 èO½‹,
15 ªî£Nô£÷˜èÀ‚° 6 èÀ‚è£ù B ñŸÁ‹ C Ü«î «õ¬ô¬ò 15
ÃL Ï. 7200 âQ™ 23 ªî£Nô£÷˜èÀ‚° èO½‹, C ñŸÁ‹ A Ü«î «õ¬ô¬ò
5 èÀ‚è£ù ÃL âšõ÷¾ ? 18 èO½‹ º®Šð˜ âQ™, B îQ«ò
Üš«õ¬ô¬ò âšõ÷¾ èO™
labours Days wages º®Šð£˜?
ªî£Nô£÷˜èœ ï£†èœ ÃL A and B can do a piece of work in 10 days; B
15 6 7200 and C in 15 days; C and A in 18 days. In how
23 5 ? many days can B alone do it ?
(A) 30 days (B) 20 days
400 (C) 12 days (D) 18 days
1200
23 5 Solution:
= x x 7200
15 6 1
3 A+ B = ........ (1)
10
= 23 x 400 1
B+C = ........ (2)
= Rs. 9200 15
1
C +A = ........ (3)
18
19. Ý†èœ «õ¬ô èœ
5 5 5 eqn (1) + (2) + (3)
50 50 ?
1 1 1
A+ B + B + C + C +A =  + + 
 10 15 18 

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 TNPSC èí‚°
1 3+ 2 1
= +
1 1 1 4 36 x
2A + 2B + 2C =  + + 
 10 15 18  1 5 1
= +
1 1 1 4 36 x
2 (A + B + C) =  + + 
 10 15 18  1 1 5
= −
1 1 1 1 x 4 36
A+ B + C = x + + 
2  10 15 18  9−5 4

1  18 + 12 + 10  36 = 369
= x 
2  180  1 1
=
2
x 9
1 40
x x = 9 days
2 9 18 0
1
A+ B + C =
TNPSC group- IV & VAO │ (èEî‹ ¬è«ò´)

9
B alone do the work 3. A»‹ B»‹ «ê˜‰¶ å¼ «õ¬ô¬ò 30
1 èO™ ªêŒõ˜. B ñ†´‹ Üš«õ¬ô¬ò
A+ B + C = 40 ï£O™ ªêŒõ£˜ âQ™, A ñ†´‹
9
1 1 Üš«õ¬ô¬ò âˆî¬ù ï£O™ ªêŒõ£˜?
18 + C = (from eqn 3)
9 A and B can together do a piece of work in 30
1 1 1
C = 9 − 18 = 2 − 1 = days. B alone can do it in 40 days. A alone can
18 18 do it in
= 18 days
(A) 100 days (B) 140 days
(C) 120 days (D) 180 days
2. A, B, C Íõ¼‹ «ê˜‰¶ å¼ «õ¬ô¬ò 4
Solution:
èO™ º®Šð˜. A îQ«ò 12 èO½‹
B îQ«ò 18 èO½‹ Üš«õ¬ô¬ò 1 1
º®ˆî£™ C îQ«ò Üš«õ¬ô¬ò A+ B = , B=
30 40
âšõ÷¾ èO™ º®Šð£˜? Find A = ?
A, B and C together can finish a piece of work A=A+ B - B
in 4 days. A alone can do in 12 days and B
alone in 18 days. How many days will be taken 1 1
= -
by C to do it alone? 30 40
(A) 10 days (B) 12 days 40 − 30
=
(C) 9 days (D) 18 days 1200
Solution: 10 1
1 = =
A + B + C = 1200 120
4
1 B = 120 days
A=
12
1
B=
18 4. å¼ ñQî¡ å¼ «õ¬ô¬ò îQ«ò
C=? 5 èO½‹ ñèÂì¡ «ê˜‰¶ Ü«î
C Üš«õ¬ô¬ò ªêŒò Ý°‹ ï£†èœ «õ¬ô¬ò 3 èO½‹ º®‚Aø£˜ âQ™
A+ B + C = A+ B + C ñè¡ ñ†´‹ Üš«õ¬ô¬ò âˆî¬ù
1 1 1 1 èO™ º®Šð£˜?
= + +
4 12 18 x A man can do a piece of work in 5 days, but
with his son he can do it in 3 days. In what time

8
 TNPSC èí‚°
can the son do it alone?
A) 6 ½ days B) 7 days 1 1
A= −
C) 7 ½ days D) 8 days 6 15
Solution: 5−2
=
30
1 1
A= ,A+ B = 3
5 3 =
3010
1 = 10 days
A + B =
3 A = 10 days
1 1
+ B =
53 A ñŸÁ‹ B Þ¼õ¼‹ «ê˜‰¶ å¼
6.

ñè¡ «õ¬ô ñ†´‹ = ?
1 1 «õ¬ô¬ò 6 èO™ º®Šð˜. B ñ†´‹
B = - îQò£è Üš«õ¬ô¬ò 10 èO™
3 5
º®ˆî£™, Ü«î «õ¬ô¬ò A ñ†´‹
5−3
= îQò£è ªêŒ¶ º®‚è â´ˆ¶‚ªè£œÀ‹
15
èœ
2 1 1
=
= = If A and B, working together, can finish a work
15 15 7
1
in 6 days and B alone can complete the work in
2 2

ê˜è£˜ ä.ã.âv Üè£ìI

10 days, then A working alone, can complete
7.5 the work in
2 15
14 A) 14 days B) 18 days
___
C) 12 days D) 15 days
1

Solution:

1 1
1 A+ B = B = A= ?
= 7 6 10
2
1 A=A+ B - B
ñè¡ «õ¬ô¬ò º®‚è 7 èœ
2
Ý°‹. 1 1
= −
6 10
5. A&»‹ B-&»‹ «ê˜‰¶ å¼ «õ¬ô¬ò 6 10 − 6
=
èO™ º®Šð˜. B ñ†´‹ îQò£è 60
Üš«õ¬ô¬ò 15 èO™ º®ˆî£™, 4
A îQò£è Üš«õ¬ô¬ò º®‚è =
60 15
â´ˆ¶‚ªè£œÀ‹ ï£†èœ âšõ÷¾?
A and B together can do a work in 6 days. B A = 15 days
can do the same work in15 days. In how many 7. å¼ «õ¬ô¬ò óñ£ 18 èO™ ªêŒ¶
days can A do the same work? º®Šð£˜. Ü«î «õ¬ô¬ò ó£î£ 15
A) 10 days B) 9 days èO™ ªêŒ¶ º®Šð£˜. 10 èœ
C) 7 days D) 20 days ó£î£ «õ¬ô ªêŒ¶M†´ MôA M†ì£˜.
e÷ «õ¬ô¬ò óñ£ âˆî¬ù
Solution:
èO™ ªêŒ¶º®Šð£˜?
1 1 Rama can finish a work in 18 days and Radha
A+ B = ,B= A= ? can finish a work in 15 days. Radha worked
6 15
for 10 days and left the job. In how many days
A=A+ B - B Rama can finish the remaining work?

9
 TNPSC èí‚°
A) 4 B) 10 x = 5 days
C) 8 D) 6
Solution: 9. å¼ «õ¬ô¬ò º¿¬ñò£è îQˆîQ«ò
ªêŒ¶ º®‚è A, B, C ÝA«ò£¼‚° 12
1 1
A= , B= èœ, 6 ï£†èœ ñŸÁ‹ 3 èœ
18 15 â¡è. A, B Þ¼õ¼‹ «õ¬ô¬ò ªêŒò
1 2 Ýó‹Hˆ¶ ñÁ C‹ Üõ˜è«÷£´
B’s 10 day’s work = x 102 = «õ¬ô¬ò ªêŒî£™, Ü‰î «õ¬ô¬ò
153 3
º¿¬ñò£è ªêŒ¶ º®‚èˆ «î¬õò£ù
2 1
Remaining work = 1 - = èœ
3 3
A can do a work in 12 days; B in 6 days and C
1 in 3 days. A and B start working together and
Work done by A in = 6
18 x
3 after a day, C joins them. The total number of
= 6 days
days required to complete the work is
TNPSC group- IV & VAO │ (èEî‹ ¬è«ò´)

A = 6 days
2 2
(A) 2 days (B) 1 days
8. A â¡ðõ˜ å¼ «õ¬ôJ¡ 2 ð°F¬ò 7 7
3
10 èO™ ªêŒ¶ º®Šð£˜. Ü«î 1 1
(C) 2 days (D) 1 days
1 7 7
«õ¬ôJ¡ - ð°F¬ò A ªêŒ¶ º®‚è
3 1 1 1
A= ,B= ,C=
Ý°‹ èO¡ â‡E‚¬è 12 6 3
2
A can complete part of a work in 10 days. x = fraction of the job they do in 1 day
1 3
A can comple part of the same work in A+ B = x
3
(A) 3 days (B) 4 days
1 1 3 1
(C) 5 days (D) 6 days x
= + = =
12 6 12 4 4
Solution:
1
x=
2 4
= 10 days
3 3x
A+ B + C =
1 t
A ð°F¬ò ªêŒ¶ º®‚è Ý°‹
3 1 3
èO¡ â‡E‚¬è x â¡è 3x
A+ B + C = 4= 4
1 t t
=x
3 3
1 1 1 4
2 1 + + =
12 6 3 t
3 =3
10 x 1+ 2 + 4 3
=
12 4t
Cross multiple 3x 12
3
9
7= 7=
4t t
2 10
x= 7t = 9
3 3
5
10 3
x= x =5 t=
3 2 7 9 16
Total working days + t = + =
7 7 7
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 TNPSC èí‚°
2
7 16 3
(1) x (3) → 12M + 18 W =
__
14 8
2 4
2 (2) x (4) → 12M + 28W =
= 2 days (-) 10
7

10. 56 Ý‡èœ å¼ «õ¬ô¬ò 42 èO™ 3 4

10W = -
º®‚A¡øù˜. Ü«î «õ¬ô¬ò 14 8 10
èO™ º®Šð «î¬õŠð´‹ 15 − 16
݇èO¡ â‡E‚¬è =
40
If 56 men can do a piece of work in 42 days, 1
number of men do the same work in 14 days − low = −
40
is = 40 days
(A) 156 (B) 168 1 0 ª ð ‡ è œ 4 0 ï £ † è O ™ ª ê Œ ¶
(C) 119 (D) 148 º®Šð˜.
Solution:
Case of inverse variation 12. A-»‹, B-»‹ å¼ «õ¬ô¬ò ªêŒ¶ º®‚è
Men : days Ï𣌠600-‚° 効‚ ªè£‡ì£˜èœ. A

ê˜è£˜ ä.ã.âv Üè£ìI

56  42 ñ†´‹ Üš«õ¬ô¬ò 6 èO½‹,
B ñ†´‹ Üš«õ¬ô¬ò 8 èO½‹
x  14
º®Šð£˜èœ. C â¡ðõ¼ì¡ A, B «ê˜ˆ¶
28 4
Üš«õ¬ô¬ò 3 èO™ º®ˆî£™. ‘C’
56 x 42 ªðÁ‹ õ¼ñ£ù‹ â¡ù?
x=
14 7
A & B undertake to do a piece of work for Rs.
x = 4 x 42= 168 600, A alone can do it in 6 days while B alone
can do it in 8 days. With the help of C, they

finish it in 3 days. Find the share of ‘C’
11. 4 ݇èœ, 6 ªð‡èœ «ê˜‰¶ å¼
(A) Rs. 75 (B) Rs. 100
«õ¬ô¬ò 8 èO™ º®Šð˜. Ü«î
(C) Rs. 150 (D) Rs. 50
«õ¬ô¬ò 3 ݇èœ, 7 ªð‡èœ «ê˜‰¶
10 èO™ º®Šð˜. 10 ªð‡èœ «ê˜‰¶ Solution:
«õ¬ô ªêŒî£™ Üš«õ¬ô¬ò âˆî¬ù
1 1 1
èO™ ªêŒ¶ º®Šð˜? A= B = A+ B + C =
6 8 3
4 men and 6 women finish a job in 8 days, A+ B + C =A+ B + C
while 3 men and 7 women finish it in 10 days.
In how many days will 10 women finish it? 1 1 1 1
+ + =
(A) 32 (B) 24 6 8 C 3
(C) 36 (D) 40 4+3 1 1
+ =
Solution: 24 C 3
Men(݇èœ) = M and Women(ªð‡èœ) 7 1 1
+ =
=W 24 C 3
1 1 7
1 = −
4M + 6W = ....... (1) C 3 24
8
1 8−7
1 =
3M + 7W = .......... (2) C 24
10
11
 TNPSC èí‚°
20 more days. A alone can finish the work in
1 1 A) 48 days B) 50 days
= C = 24
C 24 C) 54 days D) 60 days
3 75 Solution:
C ªðÁ‹ õ¼ñ£ù‹ = x 600
24 8 A»‹ B»‹ 30 èO™ å¼ «õ¬ô¬ò
C = Rs.75
º®‚è º®»‹
13. A ñŸÁ‹ B â¡ðõ˜èœ å¼ «õ¬ô¬ò 8
1
èO½‹, B ñŸÁ‹ C â¡ðõ˜èœ, 12 A + B =
30
èO½‹, C ñŸÁ‹ A â¡ðõ˜èœ 24
èO½‹ Üš«õ¬ô¬ò º®‚A¡øù˜. 1 2
A + B x ªñ£ˆî ï£†èœ = x20 =
A, B ñŸÁ‹ C â¡ðõ˜èœ Üš«õ¬ô¬ò 30 3
«ê˜‰¶ ªêŒî£™, Üõ˜èœ Üš«õ¬ô¬ò 2 1
º®‚èˆ «î¬õŠð´‹ èœ. left in 1 day = 1 - =
3 3
A and B can do a work in 8 days, B and C in A ñ†´‹ e÷ «õ¬ô¬ò 20
TNPSC group- IV & VAO │ (èEî‹ ¬è«ò´)

12 days, C and A in 24 days. If A, B and C èO™ ªêŒ¶ º®ˆî£˜.

work together, then the number of days, they
will complete the work is 1 3
âQ™ 20= ÷ 20
= x 60
(A) 6 (B) 7 3 1
A ñ†´‹ º¿õ¶‹ ªêŒ¶ º®‚è 60
(C) 8 (D) 4 ï£†èœ Ý°‹.
Solution:
15. 7 ñQî˜èœ å¼ «õ¬ô¬ò 12 èO™
1 1 1
A+ B = B+C= C +A= º®Šð˜. Üõ˜èœ «õ¬ô¬ò Ýó‹Hˆ¶
8 12 24
5 èÀ‚° Hø° Þó‡´ ñQî˜èœ
1 1 1 «õ¬ô¬ò M†´„ ªê¡ÁM†ìù˜.
A+ B + B + C + C +A= + +
8 12 24 ޡ‹ âˆî¬ù èO™ eî‹
3 + 2 +1 àœ÷õ˜èœ Ü‰î «õ¬ô¬ò º®Šð˜?
2A + 2B + 2C =
24 Seven men can complete a work in 12 days.
They started the work and after 5 days, two
1 3 + 2 +1 1 6 1
A+ B + C = x = x = men left. In how many days will the work be
2 24 2 244 8
completed by the remaining men?
1
= (A) 5.8 days (B) 6.8 days
8 (C) 9.8 days (D) 8 days
«õ¬ô¬ò º®‚èˆ «î¬õŠð´‹ èœ
= 8 Solution:
Men = 7, Days = 12
14. A- »‹ B- »‹ «ê˜‰¶ å¼ «õ¬ô¬ò 30 Work done = 7 x 12 = 84
èO™ º®‚è º®»‹. Þ¼õ¼‹ ܉î 2 men left after 5 days = 7 x 5 = 35
«õ¬ô¬ò 20 ï£†èœ «ê˜‰¶ ªêŒîù˜. remaining = 84 - 35 = 49
Hø° B Ýùõ˜ «õ¬ô‚° õóM™¬ô.
remaining men = 7 - 2 = 5 men
A- ñ†´‹ e÷ Ü‰î «õ¬ô¬ò 9.8
20 ï£†èœ ªêŒ¶ º®ˆî£˜ âQ™ A- 49
ñ†´‹ º¿õ¶‹ Ü‰î «õ¬ô¬ò ªêŒò remaining work = 5
âˆî¬ù ï£†èœ Ý°‹? 9.8 days
A and B can together finish a work in 30 days.
They worked at it for 20 days and then B left. 16. 1 0 ª ð ‡ è œ å ¼ « õ ¬ ô ¬ ò 7
The ramaining work was done by A alone in èO™ º®Šð£˜èœ. 10 °ö‰¬îèœ

12
 TNPSC èí‚°
Ü«î «õ¬ô¬ò 14 èO™ ªêŒ¶ 3 ݇èœ, 8 CÁõ˜èœ «ê˜‰¶, Ü«î
º®Šð£˜èœ. 5 ªð‡èœ ñŸÁ‹ 10 «õ¬ô¬ò,11 èO™ ªêŒ¶ º®Šð˜
°ö‰¬îèœ «ê˜‰¶ Üš«õ¬ô¬ò âQ™,Ü«î «ð£™ Í¡Á ñ샰
âˆî¬ù èO™ ªêŒ¶ º®Šð£˜èœ? «õ¬ô¬ò, 8 ݇èœ, 6 CÁõ˜èœ
10 women can complete a work in 7 days and «ê˜‰¶ âˆî¬ù èO™ ªêŒ¶ º®Šð˜?
10 children take 14 days to complete the same 2 men and 7 boys can do a piece of work in
work. How many days will 5 women and 10 14 days, 3 men and 8 boys can do the same in
children take to complete the work. 11 days. in how many days, 3 times the work
(A) 3 (B) 5 can be completed by 8 men and 6 boys ?
(C) 7 (D) None of these (A) 21 days (B) 18 days
Solution: (C) 24 days (D) 36 days
10 women → 7 days Solution:
10 Children → 14 days Consider M is Men B
5 W + 10 C = ? 1
2M+7b= ..........(1)
1
14
5 10 1 1 2 1
+ = + = = 1
70 14 14 0 14 14 147 7 3M + 8 b = ........(2)
11

ê˜è£˜ ä.ã.âv Üè£ìI

7 èO™ ªêŒ¶ º®Šð˜ 3
eqn (1) x 3 → 6m + 21b =
14
17. A, B ñŸÁ‹ C â¡ðõ˜èœ å¼ «õ¬ô¬ò 2
eqn (2) x 2 → 6m + 16b =
º®‚è º¬ø«ò 24, 6, 12 ï£†èœ â´ˆ¶‚ 11
ªè£œõ˜ âQ™, Ü«î «õ¬ô¬ò Üõ˜èœ (-) (-)

ܬùõ¼‹ ެ퉶 ªêŒ¶ º®‚è
âˆî¬ù ï£†èœ «î¬õŠð´‹ ?-
3 2
A, B and C can complete a piece of work in 5b = -
24, 6 and 12 days respectively. If they work 14 11
together, in how many days they will complete 33 − 28
5b =
the same work ? 154
(A) 1/24 day (B) 7/24 day 5 1
b= x
(C) 24/7 days (D) 24/11 days 154 5
Sol.: 1
b=
154
1 1 1
A= ,B= ,C= 1
24 6 12 2m + 7b =
14
1 1 1
A+ B + C = + + 1 1
24 6 12 2 m + 7x =
154 22 14
1+ 4 + 2 7
= = 1 1
24 24 2m = −
14 22
24
= days 11 − 7
7 2m=
154
18. 2 ݇èœ. 7 CÁõ˜èœ «ê˜‰¶ å¼ 4
2m = =
«õ¬ôJ¬ù 14 èO™ º®Šð˜; 154

13
 TNPSC èí‚°
Solution:
2
4 1
m= = x 1 1
154 77 2 A= ,B=
10 15
1 A ñŸÁ‹ B ↴‹ ªî£¬è = 1500
m=
77
15 + 10 25
1 3 1 A+ B = =
8m + 6b = 8 x +6 x 150 150
77 154 77 ªñ£ˆî ðƒ° = 25
8 3 11 1
= + = = ª è
77 77 77 7 7 1 ðƒ° =
ªñ£ˆî ðƒ°
= 7 days 60
1500
3 times the work can be completed by 8 men = = 60
and 6 boys = 3 x 7 = 21 days 2515 ðƒ° = 15 x 60 = 900
TNPSC group- IV & VAO │ (èEî‹ ¬è«ò´)

21 days 10 ðƒ° = 10 x 60 = 600

Another method
(2m + 7b) x 14 = (3m + 8b) x 11 20. 6 ݇èœ, 8 CÁõ˜èœ ެ퉶 å¼
28 m + 98 b = 33 m + 88 b «õ¬ô¬ò„ ªêŒò, 10 ï£†èœ «î¬õŠð´‹,
ñŸÁ‹ 26 ݇èœ, 48 CÁõ˜èœ ެ퉶
33 m - 28 m = 98 b - 88 b
Ü«î «õ¬ô¬ò 2 èO™ ªêŒõ˜
5 m = 10 b âQ™, 15 ݇èœ, 20 CÁõ˜èœ «ê˜‰¶
m = 2b Ü«î «õ¬ô¬ò„ ªêŒò âˆî¬ù èœ
So, 2m + 7b in 14 days «î¬õŠð´‹ ?
2(2b) + 7b = 11b in 14 days If 6 men and 8 boys can do a piece of work in
we want 10 days while 26 men and 48 boys can do the
8m + 6b = 8(2b) + 6b same work in 2 days, then what is the time
taken by 15 men and 20 boys to complete the
= 16b + 6b
same type of work ?
= 22 b
(A) 4 days (B) 5 days
22 b can do in 7 days (C) 6 days (D) 7 days
for 3 times the work Solution:
7 x 3 = 21 days Consider
M→ ݇èœ, b → CÁõ˜èœ
19. A å¼ «õ¬ô¬ò 10 èO½‹ B ܬî 1
6 M+8b= .........(1)
15 èO½‹ ªêŒ¶ º®Šð˜. Þ¼õ¼‹ 10
«ê˜‰¶ Üš«õ¬ô¬ò„ ªêŒ¶ Ï. 1,500&ä 1
26 M + 48 b = ........(2)
߆®ù£™, ܈ªî£¬è¬ò âšõ£Á HKˆ¶‚ 2
ªè£œõ˜ ?
15 M + 20 b = ? .........(3)
A can do a work in 10 days and B can do the 6
eqn 1 x 6 → 36 M + 48 b =
same work in 15 days. They earn Rs. 1,500 10
together. How will they share this amount ? 1
eqn (2) → 26 M + 48 b =
(A) Rs. 850 and Rs. 650 (-) (-) 2

(B) Rs. 900 and Rs. 600
(C) Rs. 950 and Rs. 550 6 1
(D) Rs. 1,000 and Rs. 500 10M = -
10 2

14
 TNPSC èí‚°
B =A+ B -A
12 − 10
10 M =
20 1 1
= −
2 1 20 24
M= x
20 10 12 − 10 2 1
= = =
1 240 240120 120
M= = 120 days
100
M is sub in eqn (1) 22. A ñŸÁ‹ B «ê˜‰¶ å¼ «õ¬ô¬ò 15
èO™ ªêŒ¶ º®Šð˜. Þ«î «õ¬ô¬ò
1 îQò£è B , 45 èO™ ªêŒ¶ º®Šð£˜
6M + 8b =
10 âQ™
3 1 1 A) B ¬ ò M ì A Þ ¼ ñ ì ƒ ° ï ™ ô
6 x
+ 8b = «õ¬ô‚è£ó˜
100 50 10
B) A ¬ ò M ì B Þ ¼ ñ ì ƒ ° ï ™ ô
1 3
8=
b − «õ¬ô‚è£ó˜
10 50
C) B ¬ ò M ì A º ‹ ñ ì ƒ ° ï ™ ô
5−3 «õ¬ô‚è£ó˜

8b =
50 ß) A ¬ò Mì B º‹ñ샰 ï™ô
2 1 «õ¬ô‚è£ó˜

ê˜è£˜ ä.ã.âv Üè£ìI

b= x A and B together can complete a work in 15
50 8 4
days. B alone can complete the same work in
1 45 days. Then
b =
200 A) A is twice as good workman as B
1 1 B) B is twice as good workman as A
eqn (3) → 15 M + 20 b = 15 x +20 x
100 200 C) A is thrice as good workman as B
D) B is thrice as good workman as A
1 1
= 315 x + 20 x Solution:
20 100 200 10
3 1 3+ 2 5 1 1 1
+ = = = A+ B = , B=
20 10 20 20 4 4 15 45
1 1
= 4 days A= −
15 45

3 −1 2
21. A»‹ B»‹ «ê˜‰¶ å¼ «õ¬ô¬ò 20 A= =
45 45
èO™ ªêŒ¶ º®Šð˜. A ñ†´‹
Ü‰î «õ¬ô¬ò 24 èO™ º®ˆî£™ 23. å¼ Ý‡ ñŸÁ‹ å¼ ªð‡ Þ¼õ¼‹
B ñ†´‹ Ü‰î «õ¬ô¬ò º®‚èˆ «ê˜‰¶ å¼ «õ¬ô¬ò ªêŒAø£˜èœ.
«î¬õŠð´õ¶ ݇ å¼ «õ¬ô¬ò 4 èO™ ªêŒ¶
If A and B together complete a work in º®Šð£˜. å¼ ªð‡ Ü«î «õ¬ô¬ò 12
20days. If A alone completes the work in 24 èO™ ªêŒ¶ º®Šð£˜. Üš«õ¬ô¬ò
days, then B alone completes the work in Þ¼õ¼‹ «ê˜‰¶ âˆî¬ù èO™
A) 14 days B) 44 days º®Šð£˜èœ ?
C) 120 days D) 48 days A man and woman are engaged in a work. A
Solution: man can do a piece of work in 4 days and the
woman can do in 12 days. Find how many
1 1 days will they take to finish it together?
A+ B ,A=
20 24 A) 6 days B) 5 days

15
 TNPSC èí‚°
C) 4 days D) 3 days together ?
Solution: 5
(A) 6 days (B) 5 11 days
1 1 (C) 7 days (D) 8 days
A= ,B=
4 12 Solution:
1 1
A+ B = + 1
4 12 A= ,B=
10 12
3 +1 4 1

= = = 1 1
12 12 3 3 A+ B = +
10 12
= 3 days 11
12 + 10 22 11
= = =
120 120 60 60
24. A å¼ «õ¬ô¬ò 20 èO½‹, B
TNPSC group- IV & VAO │ (èEî‹ ¬è«ò´)

ܬî 25 èO½‹ ªêŒ¶ º®Šð˜. 5

Þ¼õ¼‹ «ê˜‰¶ Üš«õ¬ô¬ò„ ªêŒ¶ 11 60
Ï. 3,600 & ä ߆®ù£™ ܈ªî£¬èJ™ 55
____
A&¡ ðƒ°
5
A can do a piece of work in 20 days and B can
do it in 25 days. Both of them finished the 5
work and earned Rs. 3,600. Then A’s share is =5 days
11
A) Rs. 1,600 B) Rs. 2,000
C) Rs. 3,000 D) Rs. 3,100 26. A, B, C ÍõK¡ å¼ ï£¬÷ò õ¼ñ£ù‹
Solution: Ï.300. A ñŸÁ‹ CJ¡ õ¼ñ£ù‹ Ï.188,
B ñŸÁ‹ CJ¡ õ¼ñ£ù‹ Ï.152 âQ™
1 1 CJ¡ å¼ ï£¬÷ò õ¼ñ£ù‹
A= ,B=
20 25 A, B and C together earn Rs. 300 per day.
A ñŸÁ‹ B ߆´‹ ªî£¬è = 3600 while A and C together earn Rs. 188 and B and
C together earn Rs. 152. The daily earning of
1 1
A+ B = C is
20 25
A) Rs. 68 B) Rs. 150
25 + 20 45 C) Rs. 112 D) Rs. 40
= =
500 500
ªñ£ˆî ðƒ° = 45 Solution:
A + B + C = 300
400 80
3600 A + C = 188
ªñ£ˆî ðƒ° = = = 80
45 5 B + C = 152
A - J¡ ðƒ° = 25 x 80 = 2000 A + B + C + C = 188 + 152
300 + C = 340
25. A â¡ðõ˜ å¼ «õ¬ô¬ò 10 èO™ C = 340 - 300
ªêŒAø£˜. Ü«î «õ¬ô¬ò B â¡ðõ˜ 12 C = 40
èO™ ªêŒAø£˜. Þ¼õ¼‹ «ê˜‰¶
Ü«î «õ¬ô¬ò ªêŒî£™ âˆî¬ù 27. å ¼ « õ ¬ ô ¬ ò 1 2 Ý ‡ è À ‹ , 1 6
èO™ º®Šð˜ ? ªð‡èÀ‹, 5 èO½‹, Ü«î
A can do a piece of work in 10 days and B «õ¬ô¬ò 13 ݇èÀ‹ 24 ªð‡èÀ‹
can do the same work in 12 days. How long 4 èO™ ªêŒ¶ º®‚Aø£˜èœ âQ™
will they take to finish the work, if both work

16
 TNPSC èí‚°
å¼ ï£O™ ªêŒò‚ îò ݇èÀ‚°‹ º®‚A¡øù˜. Ü«î «õ¬ô¬ò 110 «ð˜
ªð‡èÀ‚°ñ£ù MAî‹ âˆî¬ù èO™ º®Šð˜?
If 12 men and 16 women can do a piece of 140 men can finish a piece of work in 11 days.
work in 5 days. 13 men and 24 women can do How many days will 110 men take to finish
it in 4 days. Then the ratio of the daily work the same work ?
done by a man to that of a women is A) 15 days B) 12 days
A) 3 : 1 B) 2 : 3 C) 13 days D) 14 days
C) 2 : 1 D) 4 : 5 Solution:
Solution: 140 men 11 days
M → Men W → Women 140 : 11
110 : ?
1
12M + 16 W = ......... (1) Both are cross multiple
5
1 14 0 x 11
13 M + 24 W = ..........( 2) x=
4 11 0
x = 14 days
3
eqn (1) x 3 → 36 M + 48 W =
5
2 1 1

ê˜è£˜ ä.ã.âv Üè£ìI

eqn 2 x 2 → 26 M + 48 W = = 29. A â¡ðõ˜ å¼ «õ¬ôJ¡ ð°F¬ò
4 2 4
(-) (-) (-)
20 èO™ ªêŒ¶ º®Šð£˜. Ü«î
10 M = 3 − 1
5 2 3
«õ¬ôJ¡ ð°F¬ò A ªêŒ¶ º®‚è
4
6−5 1 1 1 Ý°‹ èO¡ â‡E‚¬è
M = = x =
10 10 10 100 A can complete 1/4 part of a work in 20 days.
1 A can complete remaining 3/4 part of the work
M = in
100
M is sub in eqn (1) A) 10 B) 20
C) 30 D) 60
1
12 M + 16 W = Solution:
5
1 1 1
12 x +16W = of work can be done in = 20 days
100 5 4
12 1 4
+ 16W = = 20 x = 80 days
100 5 1
1 12 20 − 12 8 8 1 3 3
16W = − = = = x work can be done = 80 20 x
5 100 100 100 100 16 2 4 4
= 20 x 3 = 60 days
1
W= =
200
30. å¼ «õ¬ô¬ò A â¡ðõ˜ 12 èO½‹
1 1 1 1
M:W= : = : B â ¡ ð õ ˜ A- ¬ ò ‚ è £ † ® ½ ‹ 6 0 %
100 200 100 2 00 ÜFèñ£è ªêŒ¶ º®Šð£˜ âQ™ B ñ†´‹
= 2 :1
Üš«õ¬ô¬ò ªêŒ¶ º®ŠðîŸè£ù
èœ
28. 140 «ð˜ å¼ «õ¬ô¬ò 11 èO™
A can do certain job in 12 days. B is 60% more

17
 TNPSC èí‚°
efficient than A. How many days does B alone = 27 days
take to do the same job?
32. A, B Þ¼õ¼‹ å¼ «õ¬ô¬ò 18 èO™
1 1
A) 8 days B) 6 days ªêŒ¶ º®Šð˜. B, C Ü«î «õ¬ô¬ò 24
2 2
èO™ ªêŒ¶ º®Šð˜. C, A Ü«î
1 1
C) 9 days D) 7 days «õ¬ô¬ò 36 èO™ ªêŒ¶ º®Šð˜.
2 2 Íõ¼‹ «ê˜‰¶ Üš«õ¬ô¬ò âˆî¬ù
Solution:
èO™ ªêŒ¶ º®Šð˜?
1 A and B can do a piece of work in 18 days,
A is work in 1 day =
12 B and C in 24 days, C and A in 36 days. In
A â¡ðõ˜ 100% â¡è how many days can they do it all working
B = 100 + 60 = 160 together?
(A) 16 (B) 12
1
B’s work in 1 day = 160% of (C) 13 (D) 26
TNPSC group- IV & VAO │ (èEî‹ ¬è«ò´)

12
Solution:
28
16 0 1 2 1 1 1 1 1 1
x = = = =7 A+ B = ,B+C= , C +A=
5 10 0 123 15 15 7
1 2 18 24 36
2 2
1 1 1 4+3+ 2
7.5 2(A + B + C) = + + =
2 15 18 24 36 72
14
___ 9 1 1
A+ B + C = = x =
1 72 8 2 16
1
= 16%
= 7 days
2
33. 24 Ý†èœ 180 ðEè¬÷ 15 èO™
31. 7 «ð˜ å¼ «õ¬ô¬ò Fù‹ 9 ñE º®Šð˜ âQ™ 240 ðEè¬÷ 12 èO™
«ïó‹ «õ¬ô ªêŒ¶ 30 èO™ º®‚èˆ «î¬õŠð´‹ ݆èO¡
º®‚A¡øù˜. Ü«î «õ¬ô¬ò 10 «ð˜ â‡E‚¬è¬ò 裇è.
Fù‹ 7 ñE «ïó‹ ªêŒî£™, âˆî¬ù If 24 persons can do 180 jobs in 15 days, then
èO™ º®Šð˜? find the number of persons required to do 240
Seven men working 9 hours a day can do a jobs in 12 days
piece of work in 30 days. In how many days A) 38 B) 40
will 10 men working for 7 hours a day do the C) 42 D) 44
same work?
Solution:
A) 28 days B) 30 days
Ý†èœ = 24, ðE → 180, ï£†èœ →
C) 32 days D) 27 days
15
Solution:
15 èO™ = 180 ðEè¬÷ º®Šð˜
7 → men, hours → 9, days → 30
1 men working in 7 hours 180
12
1  = = 12 ðE
15
30 x 9 x 7 2 x ðEèO¡ â‡E‚¬è = ݆èO¡
=
7 â‡E‚¬è = 2 x 12 = 24
10 men working in 7 hours
ðE = 240, ï£†èœ = 12
12 èO™ = 240
30 x 9 x 7 3 0 x 9 x 7
= =
10 x 7 10 x 7

18
 TNPSC èí‚°
35. A,B,C â ¡ ø Í ¡ Á ñ Q î ˜ è œ å ¼
240 20 «õ¬ô¬ò îQˆîQ«ò 10,15, 30
1  = = 20
12 èO™ º®Šð£˜èœ. A »‹ B »‹ Í¡Á
2 x ðEèO¡ â‡E‚¬è = ݆èO¡ èÀ‚° «ê˜‰¶ «õ¬ô 𣘈¶M†´
â‡E‚¬è A MôA Mì C «ê˜‰¶ ªè£œAø£˜.
2 x 20 = 40 e÷ «õ¬ô¬ò B & »‹ C&»‹
âˆî¬ù èO™ º®Šð˜ ?
34. A, B, C â¡ø Íõ˜ å¼ «õ¬ô¬ò Three men A,B and C can complete a work
º¬ø«ò 8, 12, 16 èO™ º®Šð£˜èœ. in 10,15,30 days respectively. A and B work
A, C Þ¼õ¼‹ «ê˜‰¶ Üš«õ¬ô¬ò together for 3 days then A leaves and C joins.
2 èÀ‚° ªêŒîù˜. H¡ù˜ C In how many days can B and C finish the
Mô°Aø£˜, B «ê¼A¡ø£˜ âQ™ A, B remaning work?
ÝAò Þ¼õ¼‹ «ê˜‰¶ Üš«õ¬ô¬ò A) 5 days B) 6 days
âˆî¬ù èO™ º®Šð£˜èœ? T h r e e C) 10 days D) 7 days
men A, B and C can complete a job in 8, 12 and Solution:
16 days respectively. A and C work together 1 1 1
for 2 days then C leaves and B joins. In how A= ,B= ,C=
10 15 30
many days can A and B finish the work? A »‹ B »‹ 3 ï£†èœ «õ¬ô ªêŒAø£˜èœ
(A) 1 (B) 3
1 1

ê˜è£˜ ä.ã.âv Üè£ìI

(C) 4 (D) 5 = 3 + 
 10 15 
Solution:
 15 + 10   25  1
= 3  = 3  =
1 1 1  150   150 50  2
A= ,B= ,C = 2

8 12 16 1
e÷ «õ¬ô = 1 −
1 1 1 2
A+ B + C = + +
8 12 16 2 −1 1
= =
6 + 4 + 3 13 2 2
A+ B + C = = B ñŸÁ‹ C ªêŒ»‹ «õ¬ô ï£†èœ =
48 48
1 1 3+ 2 5 1 1 
A+ B = + = = x + 
8 12 24 24  15 30 
1 1 2 +1
A+ C = + =  2 +1 
8 16 16 = x 
 30 
3
A+ C = = 3x x
16 =
=
A ñŸÁ‹ C «ê˜‰¶ 2 èÀ‚° «õ¬ô 30 10 10
ªêŒîù˜. âQ™ x 1
=
10 2

3
A + C in 2 days = 2 x 10
5
16 8 x=
3 8−3 5
2
x = 5 èœ
Remaining work = 1 − = =
8 8 8
5 8 1 36. ‘A’ å ¼ « õ ¬ ô ¬ ò 1 0 ï £ † è O ™
Work completed = x = º®‚Aø£˜. Ü«î «õ¬ô¬ò ‘B’ 15
3 24 5 3
= 3 days èO™ º®‚Aø£˜. Þó‡´ «ð¼‹
å«ó «õ¬ô¬ò º®‚°‹ è£ô Ü÷¬õ

19
 TNPSC èí‚°
‘A’ does a work in 10days and ‘B’ does the
same work in 15days. In how many days they 1
A+ B =
together will do the same work? 10
A) 5 days B) 6 days 1
C) 8 days D) 4 days A= ,B=?
15
solution: B =A+ B -A

1 1 1 1 15 − 10 5
A= ,B= = − = = = 30
10 15 10 15 150 150 30
1 1
A+ B = + = 30 days
10 15
15 + 10 25 1
= = = 39. å¼ «õ¬ô¬ò A ñ†´‹ 60 èO½‹, B
150 150 6 6
6 ï£†èœ ñ†´‹ 20 èO½‹ ªêŒò º®»ñ£ù£™
TNPSC group- IV & VAO │ (èEî‹ ¬è«ò´)

Þ¼õ¼‹ «ê˜‰¶ Üš«õ¬ô¬ò ªêŒò

37. 100 Ý†èœ å¼ «õ¬ô¬ò 7 èO™ âšõ÷¾ ï£†èœ Ý°‹
º®‚è‚ Ã´‹ âQ™ Ü«î «õ¬ô¬ò If A can do a work in 60 days and B in 20 days.
35 èO™ º®‚è âˆî¬ùŠ «ð˜ If they work together they complete the work
«î¬õŠð´õ˜? in
If 100 persons can finish a work in 7 days, how (A) 10 days (B) 15 days
many persons can finish the same work in 35
(C) 20 days (D) 17 days
days?
(A) 20 persons (B) 50 persons Solution:
(C) 30 persons (D) 25 persons
1 1
Solution: A= ,B=
60 20
100 Ý†èœ «õ¬ô ªêŒ»‹ ï£†èœ = 7
1  = 7 x 100 1 1
A+ B = +
35 èO™ º®‚è «î¬õŠð´‹ Ý†èœ 60 20
20 + 60 80 1
20 = = =
7 x 100 1200 1200 15 15
= = 20
35 5
= 20 Ý†èœ = 15 days

38. Þó‡´ CÁõ˜èœ «ê˜‰¶ ªêŒ»‹ «ð£¶ 40. A, B Þ¼õ¼‹ å¼ «õ¬ô¬ò 6 èO™
å¼ «õ¬ô¬ò 10 èO™ º®Šð˜. ªêŒ¶ º®Šð˜. B, C Þ¼õ¼‹ Ü«î
ºî™ CÁõ¡ Üš«õ¬ô¬òˆ îQ«ò 15 «õ¬ô¬ò 10 èO™ ªêŒ¶ º®Šð˜.
èO™ º®ˆî£™, Þó‡ì£‹ CÁõ¡ C, A Þ¼õ¼‹ 7½ èO™ ªêŒ¶
îQ«ò Üš«õ¬ô¬ò âˆî¬ù èO™ º®Šð˜. Íõ¼‹ «ê˜‰¶ Üš«õ¬ô¬ò
ªêŒ¶ º®Šð£˜? âˆî¬ù èO™ ªêŒ¶ º®Šð˜?
Two boys can finish a work in 10 days when A, B together do a job in 6 days, B, C together
they work together. The first boy can do it do the same job in 10 days, C, A together do
alone in 15 days. Find in how many days will the same job in 7½ days. If all three work
the second boy do it all by himself ? together in how many days will they complete
the job ?
(A) 24 days (B) 30 days
(A) 5 days (B) 4 ½ days
(C) 32 days (D) 40 days (C) 4 days (D) 3 days
Solution: Solution:
1 1 1
A+ B = , B + C = , C +A=
6 10 1
7
2
20
 TNPSC èí‚°
1 1 2
A+ B + B + C + C +A= + + 2 3− 2 1
6 10 15 Remaing work = 1 − = =
3 3 3
5+3+ 4
2A + 2B + 2C = 1 1
30 work is done by A in = = 618 x = 6
3 3
5+3+ 4 6 days
2 (A + B + C) =
30
43. X å¼ «õ¬ô¬ò 18 èO½‹, Y
1  12  1
6
1  5+3+ 4 
=   =   = ܬî 24 èO½‹ ªêŒ¶ º®Šð˜.
2  30  2  30 5  5
= 5 days Þ¼õ¼‹ «ê˜‰¶ Üš«õ¬ô¬ò„ ªêŒ¶
Ï. 42,000 ߆®ù£™ Y -‚° A¬ì‚°‹
41. 18 ñQî˜èœ å¼ «õ¬ô¬ò 20 èO™ ªî£¬è âšõ÷¾?
º®Šð˜. Ü«î «õ¬ô¬ò 24 ñQî˜èœ X can do a piece of work in 18 days and Y can
º®‚è «î¬õò£ù ï£†èœ do it 24 days. How much Y get if they finish
If 18 men can do a work in 20 days, then 24 the work and earn Rs. 42,000
men can do this work in A) Rs. 24,000 B) Rs. 18,000
(A) 20 days (B) 25 days C) Rs. 20,000 D) Rs. 22,000
(C) 21 days (D) 15 days 1 1
=x = , y
Solution: 18 24

ê˜è£˜ ä.ã.âv Üè£ìI

18 ñQî˜èœ «õ¬ô¬ò º®‚°‹ ï£†èœ x+ y =Rs.42000
= 20
y=?
1 ñQî¡ «õ¬ô¬ò º®‚°‹ ï£†èœ =
20 x 18 = 360 1 1
x+ y = +
24 ñQî˜èœ «õ¬ô¬ò º®‚°‹ ï£†èœ 18 24
15 4+3
360 =
= = = 15 72
24
= 15 ï£†èœ ªñ£ˆî ðƒ° = 7
6000

42. A â¡ðõ˜ å¼ «õ¬ô¬ò 18 èO½‹ 1 ðƒ° = 42000

B â¡ðõ˜ Ü«î «õ¬ô¬ò 15 èO½‹ 7
ªêŒõ˜. B Ü‰î «õ¬ô¬ò 10 ï£†èœ ðƒ° 3x
Y A¬ì‚°‹ = = 6000 18000
ªêŒ¶M†´ Mô°Aø£˜ âQ™, A ñ†´‹
e÷ «õ¬ô¬ò âˆî¬ù èO™
ªêŒ¶ º®Šð£˜-? 44. 20 ªð‡èœ 16 èO™ å¼ «õ¬ô¬ò
º®Šð˜ Ü«î «õ¬ô¬ò 16 ݇èœ
A can finish a work in 18 days and B can do
15 èO™ º®Šð˜ âQ™ ݇èœ,
the same work in 15 days. B worked for 10
ªð‡èœ «õ¬ôˆFø¡ MAî‹ ò£¶?
days and left the job. In how many days, A
alone can finish the remaining work? 20 women can do a work in 16 days. 16 men
1
can do the same work in 15 days what is the
A) 5 days B) 5 days ratio between the capacity of the men and the
2 women?
C) 6 days D) 8 days
Solution: A) 5 : 4 B) 4 : 5
C) 3 : 4 D) 4 : 3
1 1 20 Women can complete th work in 16 days
A= ,B=
18 15 1 Women = = 20 x 16 = 320
1 2 2
B’s 10 day’s work = x 10 =
15 3 3
21
 TNPSC èí‚°
1 30 èœ
1 Women one day Work = 320
16 Men can complete the work in 15 days 46. å¼ Ý‡ å¼ «õ¬ô¬ò îQò£è 3
1 Men = 16 x 15 = 240 èO™ º®Šð£˜. Ü«î «õ¬ô¬ò å¼
ªð‡ îQò£è 9 èO™ º®Šð£˜.
1
Ü«î «õ¬ô¬ò Þ¼õ¼‹ ެ퉶
1 Men one day Work = 240 âˆî¬ù èO™ º®Šð£˜èœ?
A man can do a work in 3 days alone and a
320 240 women can do the same work in 9 days alone.
If both are work together in how many days
4:3 they finished the same work.
45. å¼ «õ¬ô¬ò A â¡ðõ˜ 80 èO™ (A) 92 days (B) 6 days
ªêŒ¶ º®Šð£˜. Üõ˜ 10 ï£†èœ «õ¬ô 71
ªêŒî H¡ eF «õ¬ô¬ò B â¡ðõ˜ (C) 2 1 days (D) 3 1 days
TNPSC group- IV & VAO │ (èEî‹ ¬è«ò´)

4 2
ñ†´‹ 42 èO™ ªêŒ¶ º®ˆî£˜. Solution:
A»‹ B»‹ «ê˜‰¶ «õ¬ô ªêŒî£™
Üš«õ¬ô¬ò Üõ˜èœ âšõ÷¾ 1
M= .
è£ôˆF™ ªêŒ¶ º®Šð˜? 3
1
A can do piece of work in 80 days. He works W→
at it for 10 days and then B alone finishes the 9
remaining work in 42 days. In how much time 1 1
M +W = +
will A and B working together finish the work? 3 9
A) 28 days B) 30 days 4

C) 29 days D) 31 days 9 + 3 12
= =
27 27
Solution: 9

1 1
A→ M+W= =
80 9
4
10 ï£†èœ «õ¬ô ªêŒî H¡ = 10 = 1 1 èœ
80 8 =2
4
1 7 47. å¼ «õ¬ô¬ò A»‹ B»‹ «ê˜‰¶
e÷ «õ¬ô =1 − =
8 8 6 èO½‹, B»‹ C»‹ «ê˜‰¶ 12
èO½‹, C»‹ A»‹ «ê˜‰¶ 4
7 of the work is completed in 42 days
èO½‹ º®Šð˜ âQ™, Üõ˜èœ
8
Íõ¼‹ «ê˜‰¶ Üš«õ¬ô¬ò âˆî¬ù
7 èO™ º®‚è Þò½‹.
B= =
8x 426 If A and B can do a work in 6 days. B and C
1
B= can do it in 12 days, C and A can do it in 4
48
days how many days it would take to finish
1 1
A+ B = + the same work by all the three together ?
80 48
(A) 8 days (B) 4 days
3+5 8 (C) 10 days (D) 2 days
= =
240 240
30 Solution:
1 A+ B =
=
30

22
 TNPSC èí‚°
1 º®Šð£˜. B â¡ðõ˜ A-¬ò Mì 60%
B+C = ÜFèñ£ù Fø¬ñ»¬ìòõ˜ âQ™, º¿
12
«õ¬ô¬ò»‹ º®‚è BŸ° «î¬õò£ù
1
C+ A= èœ
4
A Can do a job in 16 days. B is 60% more
1 1 1 efficient than A. Find the number of days for
A+ B + B +C +C + A = + +
6 12 4 B to finish the same work
2 +1+ 3 A) 16 B) 12
=
12 C) 10 D) 15
6 Solution:
2( A + B + C) =
12 1
2 A→
16
1 1 1 Ratio of time taken by a and b
A + B +=
C x=
2 2 4 8 5
= 16 0 : 10 0
Answer = 4 days
= 8:5
8 : 5 = 16 : x
48. A, B Þ¼õ˜ å¼ «õ¬ô¬ò º¬ø«ò 12
2
èœ, 18 èO™ º®Šð˜. 4  8 16
=

ê˜è£˜ ä.ã.âv Üè£ìI

«õ¬ô 𣘈î Hø° A cƒA M´Aø£˜. 5 x
eF «õ¬ô¬ò B ñ†´‹ º®‚Aø£˜
x = 10 days
âQ™ Üš«õ¬ô¬ò º¿õ¶‹ º®‚è
Ý°‹ èœ?
A and B can complete a work individually in 50. A å¼ «õ¬ô¬ò 12 èO™
12 days and 18 days. They started doing the ªêŒò‚ô‹. B â¡ðõ˜ Aä Mì 60%
work together but after 4 days A had to leave ÜFè Fø¬ñ»¬ìòõ˜. Ü«î «õ¬ô¬ò
and B alone completed the remaining work. B ñ†´‹ º®‚è âˆî¬ù ï£†èœ â´ˆ¶‚
The whole work was completed in ªè£œõ£˜?
(A) 30 days (B) 20 days A can do a certain job in 12 days. B is 60%
(C) 12 days (D) 8 days more efficient then A. How many days does
Solution: B alone take to do the same job?
1 1 (A) 8 days (B) 7 days
A→ , B→ 1
12 18 (C) 7 days (D) 8 1 days
2 2
Solution:
1 1
A’s 4 days work = x4 = 1
12 3 A→
3 12
1 3 −1 2 2

Remaining Work = 1 −= = 1.6 16 2

3 3 3 = =
B’s One day Work =
12 120 15
15

2 work done by B
1
3 =7 days
2
6 2 Another method:
= 18 x
3 Ratio of time taken by A and B
=12 days 160 : 100 = 8 : 5
8 : 5 = 12 : x
49. å¼ «õ¬ô¬ò A 16 èO™

23
 TNPSC èí‚°
 1 1 
8 12 = 8 + 
=  40 60 
5 x
 60 + 40 
3
12 x 5 3x5 15 1 = 8 
x= = = = 7 days  2400 
8 2 2 2 2
 100  1
51. 5 ݇èÀ‹ 2 CÁõ˜èÀ‹ «ê˜‰¶ = 8 =
 24 00  3
ªêŒ»‹ «õ¬ôˆ Føù£ù¶ å¼ Ýµ‹,  3 
å¼ CÁõ‹ ªêŒ»‹ «õ¬ôˆ Fø¬ùŠ 1
«ð£™ 4 ñ샰 âQ™ æ˜ Ý‡ ñŸÁ‹ = 1−
3
å¼ CÁõ¡ ªêŒ»‹ «õ¬ôˆ FøQ¡
3 −1 2
MAî‹ â¶? = =
3 3
5 men and 2 boys working together can do
four times as much work as a man and a boy Let a be days remaining work is completed
TNPSC group- IV & VAO │ (èEî‹ ¬è«ò´)

can do. Then ratio of working capacities of a

man and a boy are in the ratio 2 a
=
(A) 5 : 2 (B) 1 : 3 3 60
(C) 2 : 1 (D) 2 : 5 40
120
=a
Solution: 3
1 man 1 day Work = x
a = 40 days
1boy 1 day work = y
5x + 2 y = 4 ( x + y )
53. A ñŸÁ‹ B â¡ðõ˜èœ Þ¼õ¼‹ «ê˜‰¶
5x − 4 x = 4 y − 2 y å¼ «õ¬ô¬ò 4 èO™ º®Šð£˜èœ.
x = 2y Ýù£™ A ñ†´‹ Ü‰î «õ¬ô¬ò 6
èO™ º®Šð˜. Ü«î «õ¬ô¬ò B
x 1
= ñ†´‹ ªêŒ¶ º®‚è ............. èœ
y 2 Ý°‹.
= 2 :1 A and B together can do a piece of work in 4
days, but A alone can do it in 6 days. B alone
take to do the same work in ____________
52. X ñŸÁ‹ Y º¬ø«ò å¼ «õ¬ô¬ò
days.
40 ñŸÁ‹ 60 èO™ îQˆîQò£è
ªêŒ¶ º®Šð£˜èœ. 8 èO™ 1
(A) 12 (B)
Üõ˜èœ «ê˜‰¶ º®ˆî H¡ X â¡ðõ˜ 12
10
Mô°Aø£˜. Ü‰î «õ¬ô º®ò âšõ÷¾ (C) (D) 24
24 10
ï£†èœ Ý°‹? Solution:
X and Y can complete a job separately in 40 1 1
A+B= A=
and 60 days. After working together for 8 4 6
days, X leaves. What is the total time in which
the work is completed ? B = A+ B − B
(A) 48 days (B) 44 days 1 1
(C) 46 days (D) 40 days = −
4 6
Solution: 6−4 2
1 1 = =
X= Y= 24 24
40 60 12

24
 TNPSC èí‚°
12 days
x + 2x = 1
1 18
Answer = 12 days 3x =
18
54. A, B-&ä Mì 2 ñ샰 «õèñ£è «õ¬ô 1
x=
ªêŒAø£˜. B-Ý™ å¼ «õ¬ô¬ò îQò£è 54
º®‚è 12 ï£†èœ Ýù£™, A ñŸÁ‹ 1
B Þ¼õ¼‹ «ê˜‰¶ Ü‰î «õ¬ô¬ò A = 2x
54
º®‚è «î¬õŠð´‹ ï£†èœ 27

A works twice as fast as B. If B can complete 27 days

a work in 12 days independently, the number
of days in which A and B can together finish
the work is 56. å¼ «õ¬ô¬ò 2 ñQî˜èÀ‹ 3
A) 4 days B) 6 days ¬ðò¡èÀ‹ «ê˜‰¶ 10 èO½‹,
C) 8 days D) 18 days Ü«î «õ¬ô¬ò 3 ñQî˜èÀ‹ 2
Solution: ¬ðò¡èÀ‹ «ê˜‰¶ 8 èO½‹
º®‚è º®»‹. 2 ñQî˜èÀ‹, 1
Ratio of rates of working of A and B = 2:1
¬ðò‹ «ê˜‰¶ Üš«õ¬ô¬ò âˆî¬ù
Time taken = 1:2 èO™ ªêŒ¶ º®‚è º®»‹?
1
B’s One day work = 2 men and 3 boys can do a piece of work in

ê˜è£˜ ä.ã.âv Üè£ìI

12
1 10 days while 3 men and 2 boys do the same
= ( 2 times of work B )
6 work in 8 days. In how many days can 2 men
and 1 boy do the work?
1 1
= + 2
6 2 1
(A) 25 (B) 12
2 +1 3 2
= = (C) 13 (D) 12
12 12
4 Solution:
4 days 1
2 M + 3b = → (i )
10
1
3M + 2b = → (ii )
55. A, B äŠ «ð£ô Þó‡´ ñ샰 8
Fø¬ñò£ù ï™ô «õ¬ôò£œ. Üõ˜èœ
Þ¼õ¼‹ å¼ «õ¬ô¬ò, 18 èO™ 3
(i )x3 ⇒ 6 M + 9b =
º®‚Aø£˜èœ. A ñ†´‹ Üš«õ¬ô¬ò 10
âˆî¬ù èO™ º®Šð£˜?
2
A is twice as good a workman as B and (i i )x2 ⇒ 6 M + 4b =
8
together they finish a piece of work in 18 days. 4

In how many days A alone finish the work? (i) - (ii)

(A) 26 days (B) 27 days 3 1
(C) 25 days (D) 24 days 5=
b −
10 4
Solution:
6−5
B= x 5b =
20
Work done by A = 2x
A and B=18 days 1 1 1
b= x =
1 20 5 100
A+B=
18

25
 TNPSC èí‚°
3 1 4 èO™ º®‚è‚ô‹ âQ™ 10
2M + =
100 10 Ý†èœ å¼ ï£¬÷‚° 8 ñE «ïó‹
«õ¬ô ªêŒî£™ Üš«õ¬ô¬ò
1 3
2M
= − âˆî¬ù èO™ º®‚è º®»‹?
10 100
20 men working 6 hours a day can finish a
10 − 3 7 work in 4 days. In how many days can 10 men
2M
= =
100 100 working 8 hours a day finish the work?
7 (A) 8 days (B) 6 days
M=
200 (C) 4 days (D) 10 days
Now Solution:
20 men take 24 hours
7 1 10 Men = 1
2M + b = 2 x +
200100 100 1 24x2
= hours
TNPSC group- IV & VAO │ (èEî‹ ¬è«ò´)

48 6
48 hours 48
a day = = 6 days
2
4
8 2 = 1 = 1 8 hours 8
= = 25 1
100 25 12
50
25 2 2
59. A â¡ðõ˜ ñ†´‹ Ï. 800‚è£ù å¼
1 «õ¬ô¬ò 8 ï£O™ º®Šð£˜. ܉î
= 12
2 «õ¬ô¬ò Üõ˜ å¼ àîMò£÷¬ó
¬õˆ¶‚ ªè£‡´ 5 ï£O™ º®ˆî£™
57. å¼ «õ¬ô¬ò A, B Þ¼õ¼‹ «ê˜‰¶
àîMò£÷¼‚° Üõ˜ ªè£´‚è «õ‡®ò
8 èO™ º®Šð˜. A ñ†´‹
ðƒ° âšõ÷¾?
Üš«õ¬ô¬ò 12 èO™ º®Šð˜.
B ñ†´‹ Üš«õ¬ô¬ò âˆî¬ù A alone can complete a piece of work of Rs.
800 in 8 days, but by engaging an assistant, the
èO™ º®Šð˜?
work is completed in 5 days. Find the share to
A and B together can do a piece of work in 8 be received by the assistant
days, but A alone can do it in 12 days. How
many days would B alone take to do the same (A) 500 (B) 300
work? (C) 800 (D) 600
(A) 24 days (B) 16 days Solution:
(C) 32 days (D) 10 days A+B = 5
Solution: B can do the work = 8 - 5
1 1 B=? =3
A+ B
= A→
8 12 8 days = 800
B = A+ B − A
100

=
1 1
− 1 day = 800 = 100
8 12 8
for 3 days = 100 x 3
3− 2 1 = 300 Rupees
= =
24 24
24 days 60. A ñŸÁ‹ B ÝAòõ˜èœ «ê˜‰¶ å¼
Answer = 24 days «õ¬ô¬ò 7 èO™ º®‚A¡øù˜.
3
A â¡ðõ˜ Bä Mì 1 ñ샰 M¬óõ£è
4
58. 20 Ý†èœ å¼ ï£¬÷‚° 6 ñE º®Šð£˜ âQ™ Ü«î «õ¬ô¬ò A
«ïó‹ «õ¬ô ªêŒî£™ å¼ «õ¬ô¬ò îQò£è âˆî¬ù èO™ º®Šð£˜?

26
 TNPSC èí‚°
A and B can do a job together in 7 days. A is =(6 men + 5 Women)
3 =(10 Women + 5 Women)
1 times as efficient as B. the same job can
be4 done by A alone in = 15 Women
1 5W = 12
9
(A) 3 days (B) 11 days = 12 x 5=60
1 1
12 16
(C) 4 days (D) 3 days 4
12 x 5
15W =
Solution: 15 3
= 4 days
1
A+ B =
7
62. ó£‹ â¡ðõ˜ å¼ «õ¬ô¬ò 15 èO™
3
A â¡ðõ˜ B ¬ò 1 Mì ñ샰 º®‚Aø£˜. óq‹ â¡ðõ˜ ó£‹&¬ò
M¬óõ£è º®Šð£˜ 4 Mì 50% M¬óõ£è º®Šð£˜ âQ™,
3 7 óq‹ ñ†´‹ îQò£è Ü«î «õ¬ô¬ò
1 =
4 4 âˆî¬ù èO™ º®Šð£˜?
1 Ram can do a work in 15 days. Rahim is 50%
7x + 4x = more efficient than Ram. The number of days,
7
Rahim will take to do the same piece of work
1
is

ê˜è£˜ ä.ã.âv Üè£ìI

11x =
7
A. 7½ B. 10
1 C. 12 D. 14
x=
77 Solution:
1 1
= x 7 = 11 Ram →
77 15
11
Rahim is 50% more efficient than Ram
11 days 3
Ram 150
= = 3: 2
Rahim 100
` 2
61. 3 Ý‡èœ Ü™ô¶ 5 ªð‡èœ å¼
«õ¬ô¬ò 12 èO™ ªêŒ¶ 3 : 2 = 15 : X
º®‚A¡øù˜. âQ™ 6 Ý‡èœ ñŸÁ‹ 3 15
=
5 ªð‡èœ Ü‰î «õ¬ô¬ò âˆî¬ù 2 X
èO™ ªêŒ¶ º®Šð˜ ? 3 X = 30
3 men or 5 women can do a piece of work in 10
12 days. How long will 6 men and 5 women 30
X= = 10
take to finish the work? 3
A) 20 B) 10 10 days
C) 4 D) 5
63. A can finish a job in 20 days and B can com-
Solution: plete it in 30 days. They work together and
3 Men = 5 Women finish the job. If Rs. 600 is paid as wages,
then the share of A and B
5 A â¡ðõ˜ å¼ «õ¬ô¬ò 20 èO½‹,
1 Men =
3 2 B â¡ðõ˜ Ü«î «õ¬ô¬ò 30 èO½‹
6 men = 5 x 6 º®Šð˜. Þ¼õ¼‹ «ê˜‰¶ «õ¬ô ªêŒ¶,
3 Üš«õ¬ô¬ò º®ˆ¶ Ï. 600 ä îƒèœ
= 10 Women õ¼õ£ò£èŠ ªðŸøù˜ âQ™ A ñŸÁ‹ B

27
 TNPSC èí‚°
¡ ðƒ° â¡ù? å¼ «õ¬ô¬ò 8 ï£†èœ ñŸÁ‹ 20
(A) 240, 360 (B) 300, 300 èO™ º®Šð£˜èœ. Þ¼õ¼‹ «ê˜‰¶
(C) 360, 240 (D) 400, 200 4 ï£†èœ «õ¬ô ªêŒî H¡ º®‚èŠðì
«õ‡®ò «õ¬ôJ¡ ð£è‹ â¡ùõ£è
Solution:
Þ¼‚°‹?
1 1
A= B= Two men A and B can do a work alone in
20 30
1 1 8 days and 20 days respectively. They did
A+ B = + work together for 4 days. Find the remaining
20 30
portion of work to be completed ?
30 + 20
A+ B = Solution:
600 7 3
ªñ£ˆî‹ = 600 (A) 10 (B) 10
12 10 10
600
ðƒ° = = 12 (C) 7 (D) 3
50
TNPSC group- IV & VAO │ (èEî‹ ¬è«ò´)

1 1
A→ B→
A = 30 x 12 = 360 8 20
° ï£†èœ «õ¬ô ªêŒî H¡
º®‚èðì «õ‡®ò «õ¬ôJ¡ ð£è‹
B = 20 x 12 =240
1 1
A→ B→
8 20
64. å¼ «õ¬ô¬ò 10 èO½‹, ܬî
15 èO½‹, ªêŒ¶ º®Šð˜.
 5−2
Þ¼õ¼‹ «ê˜‰¶ Üš«õ¬ô¬ò„ ªêŒ¶ = 4 
Ï.1,500ä ߆®ù£™, ܈ªî£¬è¬ò  40 
âšõ£Á HKˆ¶‚ ªè£œõ˜-? 3 3
= 4x =
A can do a piece of work in 10 days . B can do 40 10
10
it in 15 days. How much does each of them
get if they finish the work and earn Rs. 1,500? 66. X, Y, Z îQˆîQ«ò å¼ «õ¬ô¬ò
A. Rs. 700, Rs. 800 B. Rs. 500, Rs. 1,000 º®‚è 6 ñE«ïó‹, 4 ñE «ïó‹,
C. Rs. 600, Rs. 900 D. Rs. 800, Rs. 700 12ñE «ïó‹ â´ˆ¶‚ ªè£œA¡øù˜.
Íõ¼‹ «ê˜‰¶ Üš«õ¬ô¬ò º®‚è
Solution: âšõ÷¾ «ïó‹ â´ˆ¶‚ ªè£œõ˜ ?
1 1
A= B= X and Y and Z can independently complete a
10 15
1 1 piece of work in 6 hours, 4 hours and 12 hours
A+ B = + respectively. If they work together how much
10 15
time will they take to complete that piece of
15 + 10 work ?
A+ B =
150
Solution:
ªñ£ˆî‹ = 1500 A) 3 hours B) 5 hours
D) 2hours
60
300 C) 6 hours
1500
ðƒ° = = 60 1 1 1
25 =A = B C=
5 6 4 12
1 1 1
A = 15 x 60 = 900 A+ B +C = + +
6 4 12
B = 10 x 60 =600
2 + 3 +1 6 1
= = =
12 12 2
65. A ñŸÁ‹ B â¡ø ñQî˜èœ îQˆîQ«ò 2

28
 TNPSC èí‚°
= 2 hours 1 1
A+ B = +
9 12
4+3
67. A â¡ðõ˜ B&¬ò 裆®½‹ Þ¼ñ샰 =
36
CøŠð£è «õ¬ô¬ò ªêŒõ£˜ ,Þ¼õ¼‹ 1
7
«ê˜‰¶ Ü‰î «õ¬ô¬ò 14 èO™ = =
36 36
º®Šð£˜èœ. âù«õ A ñ†´‹ ܉î
7
«õ¬ô¬ò º®‚è âˆî¬ù ï£†èœ 1
Ý°‹? = 5 days
7
A is twice as good a workman as B and
69. A â¡ðõ˜ å¼ «õ¬ô¬ò 20
together they finish a piece of work in 14 days.
èO½‹ B â¡ðõ˜ Ü«î «õ¬ô¬ò
In how many days can A alone finish the work?
30 èO½‹ ªêŒ¶ º®Šð£˜èœ.
A) 11 B) 21 ÜšM¼õ¼‹ «ê˜‰¶ Üš«õ¬ô¬ò„
C) 28 D) 42 ªêŒ¶ º®‚è âˆî¬ù ï£†èœ Ý°‹?
Solution: A can do a piece of work in 20 days and B can
B=X do it in 30 days. How long will they take to do
A = 2X the work together?
1 (A) 12 days (B) 14 days
A+ B=
14 (C) 16 days (D) 20 days

ê˜è£˜ ä.ã.âv Üè£ìI

1
X + 2X = Solution:
14
1 1
1 A= B=
3X = 20 30
14 1 1
A+ B = +
1 20 30
X=
42 30 + 20
A+ B =
600
1 1 12
A = 2x = 600
42 21 21 = = 12
50
12 days
21 Days

70. å¼ «õ¬ô¬ò 4 ݇èÀ‹,

68. å¼ «õL- ÜÁõ¬ì ªêŒò bLŠ-‚° 9
6 ªð‡èÀ‹ «ê˜ˆ¶ 8 èœ
ï£†èœ Ý°‹. ܬî«ò, ó£‹ îQò£è
ªêŒAø£˜èœ, «ñ½‹ Ü«î «õ¬ô¬ò
ÜÁõ¬ì ªêŒò 12 ï£†èœ Ý°‹.
3 ݇èÀ‹, 7 ªð‡èÀ‹ «ê˜‰¶
Þó‡´ «ð¼‹ «ê˜‰¶ ܬî ÜÁõ¬ì
10 ï£†èœ ªêŒAø£˜èœ. 10 ªð‡èœ
ªêŒò âˆî¬ù ï£†èœ Ý°‹?
ñ†´‹ Ü‰î «õ¬ô¬ò âˆî¬ù
Dilip can reap a field in 9 days, which Ram
èO™ ªêŒ¶ º®Šð£˜èœ
alone can reap in 12 days. In how many days
both together, can reap this field? 4 men and 6 women can complete a work in 8
days, while 3 men and 7 women can complete
Solution:
it in 10 days. In how many days will 10 women
1 1
5 4 complete it.
(A) 7 days (B) 7 days (A) 35 (B) 40
1 36 (C) 45 (D) 50
6
(C) 7 days (D) days Solution:
1 1 1
A→ B→ 4 M + 6W = → (i )
9 12 8
29
 TNPSC èí‚°

1 72. æ˜ «õ¬ôJ¡ å¼ ð°F¬ò A â¡ðõ˜

3M + 7W = → (ii )
10 10 èO½‹ B â¡ðõ˜ 15 èO½‹
3 ªêŒõ˜. Þ¼õ¼‹ 5 ï£†èœ «õ¬ô
(i) x 3 ⇒ 12M + 18W = ªêŒîù˜. eF «õ¬ô¬ò C â¡ðõ˜
8
2 2 èO™ ªêŒ¶ º®ˆî£˜. ªñ£ˆî
4 «õ¬ô‚°Kò ÃL Ï. 5,000 âQ™ B
(ii )x4 ⇒ 12 M + 28W =
10 ñŸÁ‹ C J¡ Fù‚ÃL
5

(i) - (ii) A can do a piece of work in 10 days ; B in 15

days. They work for 5 days. The rest of the
3 2
−10W =− work was finished by C in 2 days. If they get
8 5
Rs.5,000 for the whole work, the daily wages
15 − 16 of B and Care
−10W =
40 (A) Rs.150 (B) Rs.225
TNPSC group- IV & VAO │ (èEî‹ ¬è«ò´)

−1 (C) Rs. 250 (D) Rs. 300

−10W =
40 Solution:
1 1 1 1
10W = A→ = x5=
40 10 10 2
2

40 èO™ ªêŒ¶ º®Šð˜ 1 1 1

B→ = x5=
15 15 3
3
71. 4 Ý‡èœ Ü™ô¶ 6 ¬ðò¡èœ å¼
«õ¬ô¬ò 20 èO™ º®Šð£˜èœ. Proof of C
Üš«õ¬÷¬ò 6 Ý‡èœ ñŸÁ‹ 1 1
=1-  + 
11 ¬ðò¡èœ âˆî¬ù èO™  2 3
º¯Šð£˜èœ?
 3+ 2 
If 4 men or 6 boys can finish a piece of work =1-  
 6 
in 20 days, in how many days can 6 men and
11 boys finish it? 1
C=
(A) 5 days (B) 6 days 6
(C) 7 days (D) 8 days
1 1
Solution: A= 3 2
x 6 = 3, B = x 6 = 2,
2 3
Ý‡èœ ¬ðò¡èœ èœ
1 1
4 6 20 C= x 6 =1
6
6 11 ? 1 1 1
A: B :C = = : :
2 3 6
6x 11x = 3 : 2 :1
+ 1
=
20x4 6x20 3
A share= x1500=750
36 x + 44 x 6
=1
20x4x6 2
B share= x1500=500
4 6
80 x
=1 1
20 x 4 x6 C share= x1500=250
6
x = 6 days

30
 TNPSC èí‚°
750 6
A daily wages = = 150 = +4
5 2
(5 days) 14
= = 7 Women
500 2
B daily wages = = 100
5
(5 days) 74. å¼ «õ¬ô¬ò A ñŸÁ‹ B ÝAò
250 Þ¼õ¼‹ «ê˜‰¶ 12 èO™ º®Šð˜.
C daily wages = = 125
2 A ñ†´‹ Üš«õ¬ô¬ò îQò£è 20
èO™ º®Šð˜, âQ™ B ñ†´‹
(2 days)
îQò£è Üš«õ¬ô¬ò âˆî¬ù
B and C = 100+125=225 èO™ º®Šð˜?
A and B together can do a piece of work in
73. å¼ °PŠH†ì «õ¬ô¬ò 3 ݇èœ, 12 days, but A alone can do it 20 days. How
4 ªð‡èœ, 6 CÁõ˜èœ «ê˜‰¶ 7 many days would B alone take to do the same
èO™ º®Šð˜. å¼ ªð‡, ݇ work?
ªêŒ»‹ «õ¬ôŠ «ð£™ Þ¼ ñ샰 (A) 24 days (B) 30 days
«õ¬ô ªêŒõ£˜. å¼ CÁõ¡ ݇ (C) 36 days (D) 28 days
ªêŒ»‹ «õ¬ôJ™ ð£F «õ¬ô Solution:

ê˜è£˜ ä.ã.âv Üè£ìI

ªêŒõ£˜ âQ™, Ü«î «õ¬ô¬ò 7
1
èO™ º®‚è âˆî¬ù ªð‡èœ A+ B =
12
«î¬õŠð´õ˜?
Three men, four women and six children can 1
A=
complete a work in seven days. A woman does 20
double the work a man does and child does B = A+ B − A
half the work a man do. How many women 1 1
can complete the work in 7 days? = −
12 20
(A) 7 (B) 8 5−3
(C) 12 (D) 9 =
60
Solution:
2 1
2 men = 1 Women = =
60 30
1M= 1 W
30

2 30 days
3
3M= 2 W
75. 8 «ð˜ å¼ «õ¬ô¬ò 24 èO™
2 Children = 1 Man
º®ˆî£™ Ü«î «õ¬ô¬ò 24 «ð˜
2C = 1 Women -__________ èO™ º®Šð˜
2
1 If 8 workers can complete a work in 24 days,
1 Child = 4 Women then 24 workers can complete the same work
3
6 Child = 6 W in
4 (A) 8 days (B) 16 days
2
3 3 (C) 12 days (D) 24 days
= +4+
2 2 Solution:

8W = 24 day (W = Workers)
24w = ?

31
 TNPSC èí‚°
8W=24 d A can do a piece of work in 20 days and B can
do it in 30 days. How long will they take to do
24 the work together ?
1W =
8 (A) 10 days (B) 12 days
24 1
24W = x
(C) 11 days (D) 20 days
8 24
1 1
1 A→ B=
= 20 30
8 1 1
A+ B = +
8 days 20 30
30 + 20
Another method =
` 600
8 x 24 = 24 x x
50 1
= =
192 600 12
x= x = 8 days 12
TNPSC group- IV & VAO │ (èEî‹ ¬è«ò´)

24
12 days
76. å¼ °PŠH†ì «õ¬ô¬ò A 25
ï£À‚°œ º®Šð£˜. «ñ½‹ B îQò£è
78. 8 Ý‡èœ ñŸÁ‹ 12 CÁõ˜èœ «ê˜‰¶
Ü‰î «õ¬ô¬ò 20 èO™ º®Šð£˜.
å¼ «õ¬ô¬ò 10 èO™ ªêŒ¶
A «õ¬ô¬ò ªî£ìƒA 10 èœ
º®Šð˜. Ü«î «õ¬ô¬ò 6 ݇èœ
èNˆ¶ B «ê˜Aø£˜ âQ™ Ü‰î «õ¬ô
ñŸÁ‹ 8 CÁõ˜èœ «ê˜‰¶ 14 èO™
º®»‹ èœ,
ªêŒ¶ º®Šð˜. å¼ Ý‡ îQò£è
A alone can do a certain job in 25 days which Üš«õ¬ô¬ò âˆî¬ù èO™
B alone can do in 20 days. A started the work ªêŒ¶ º®Šð£˜? å¼ CÁõ¡ îQò£è
and was joined by B after 10 days. The work Üš«õ¬ô¬ò âˆî¬ù èO™
lasted for: ªêŒ¶ º®Šð£¡?
1
(A) 12 days (B) 14 2 days Eight men and twelve boys can finish a piece
2
29 of work in 10 days while six men and eight
(C) 15 days (D) 6 days boys can finish the same work in 14 days. Find
3
Solution: the number of days taken by one man alone to
1 1 complete the work and also one boy alone to
A→ B=
25 20 complete the work
1 1
A:B = : (A) Man - 140 days, boy - 280 days
25 20
5 4 (B) Man - 280 days, boy - 140 days
= 4:5 (C) Man - 150 days, boy - 300 days
(D) Man - 300 days, boy - 150 days
A = 10 x 4 =40
20 Solution:
60 20 1
Total = 100 - 40 = 60 = = 8M + 12b = → (i )
9 3 10
2 3
=6
3 1
6 M + 8b = → (ii )
14
77. A â¡ðõ˜ å¼ «õ¬ô¬ò 20
èO½‹ B â¡ðõ˜ Ü«î «õ¬ô¬ò 3
(i ) x 3 ⇒ 24 M + 36b =
30 èO½‹ ªêŒ¶ º®Šð£˜èœ. 10
2
ÜšM¼õ¼‹ «ê˜‰¶ Üš«õ¬ô¬ò„ 4
ªêŒ¶ º®‚è âˆî¬ù ï£†èœ Ý°‹? (ii ) x 4 ⇒ 24 M + 32b =
14
7

32
 TNPSC èí‚°
(i) - (ii) = 25, C = 65
3 2 (C) Together = 20 days Separately A = 40, B
4=
b −
10 7 = 30, C = 70
21 − 20 (D) Together = 25 days Separately A = 45, B
4b =
70 = 35, C = 75
1 1 1 Solution:
=b =x
70 4 280 1 1 1
A+B → B+C= C+A=
Boy = 280 days 12 15 20
1 1 1
A + B+ B+ C + C + A = + +
2
4 1 1 12 15 20
6M + 8 x = 5+ 4+3
280 14 2( A + B + C) =
140
70
35
60
6
12 1 1
1 1 ( A+ B +C) = x =
6M = − 60 2 10
14 35 10

10 − 4 6 10
A+ B +C =
6M = =
140 140

ê˜è£˜ ä.ã.âv Üè£ìI

1 1
6 1 1 +C =
M= = x = 12 10
140 6 140
1 1 12 − 10 2 1
C= − = = =
140 days 10 12 120 120 60 60

79. A, B Þ¼õ¼‹ å¼ «õ¬ô¬ò 12 C = 60

èO™ ªêŒ¶ º®Šð˜. B, C Ü«î 1 1
B+ =
«õ¬ô¬ò 15 èO™ ªêŒ¶ º®Šð˜. 60 15
C, A Ü«î «õ¬ô¬ò 20 èO™
1 1 4 −1 3 1
ªêŒ¶ º®Šð˜. Íõ¼‹ «ê˜‰¶ ñŸÁ‹ C= − = = =
îQˆîQò£è¾‹ Üš«õ¬ô¬ò 15 60 60 60 20 20
âˆî¬ù èO™ ªêŒ¶ º®Šð˜? B = 20
(A) «ê˜‰¶ = 10 ï£†èœ îQˆîQò£è A 1 1
= 30, B = 20, C = 60 A+ =
20 12
(B) «ê˜‰¶ = 15 ï£†èœ îQˆîQò£è A
1 1 20 − 12 8 1
= 35, B = 25, C = 65 A= − = = =
20 12 240 240 30
(C) «ê˜‰¶ = 20 ï£†èœ îQˆîQò£è A 30

= 40, B = 30, C = 70 A = 30, B=20, C=60

(D) «ê˜‰¶ = 25 ï£†èœ îQˆîQò£è A A+B+C = 10
= 45, B = 35, C = 75
A and B can do a piece of work in 12 days. B
80. A, å¼ «õ¬ô¬ò 9 ñE «ïó‹ ªè£‡ì 7
and C in 15 days, C and A in 20 days. In how
«õ¬ô èO½‹,B Ü«î «õ¬ô¬ò 7
many days will they finish it together and
ñE «ïó‹ ªè£‡ì 6 «õ¬ô èO½‹
separately?
º®‚è‚ô‹. Üõ˜èœ Þ¼õ¼‹
(A) Together = 10 days Separately A = 30, 2
B = 20, C = 60 «ê˜‰¶ å¼ ï£¬÷‚° 8 5 ñE «ïó‹
(B) Together = 15 days Separately A = 35, B «õ¬ô ªêŒî£™, Üš«õ¬ô¬ò º®‚è
âšõ÷¾ è£ô‹ â´Šð£˜èœ?

33
 TNPSC èí‚°
A can do a piece of work in 7 days of 9 hours 3+ 2 5
each and B can do it in 6 days of 7 hours each. = =
18 18
How long will they take to do it, working to-
5
2 = 1−
gether 8 hours a day? 18
5
(A) 4 days (B) 5 days 18 − 5
1 =
2 days 18
(C) 3 days (D) 4
Solution: 13
=
1 8
A → 7x9 =63 =
63 13
1 boys = x 18 = 13
B → 6x7 =42 = 18
42
Answer = 13
1 1 2+3
TNPSC group- IV & VAO │ (èEî‹ ¬è«ò´)

A+ B = + =
63 42 126 82. 2 Ý‡èœ ñŸÁ‹ 7 CÁõ˜èœ å¼
5 «õ¬ô¬ò 14 èO™ ªêŒ¶
=
126 º®‚A¡øù˜. ñŸÁ‹ 3 Ý‡èœ ñŸÁ‹
8 CÁõ˜èœ Ü«î «õ¬ô¬ò 11
2 èO™ ªêŒ¶ º®‚A¡øù˜. âQ™
å¼ ï£¬÷‚° 8 ñE«ïó‹ «õ¬ô
5 8 Ý‡èœ ñŸÁ‹ 6 CÁõ˜èœ, ܉î
42 «õ¬ô¬òŠ «ð£™ 3 ñ샰 «õ¬ô¬ò
= âˆî¬ù èO™ ªêŒ¶ º®Šð˜?
53
126 5 2 men and 7 boys can do a piece of work in
= x
5 42 14 days, 3 men and 8 boys can do the same in
11 days. 8 men and 6 boys can do 3 times the
3 Days
amount of this work in
(A) 21 days (B) 18 days
81. æ˜ «õ¬ô¬ò å¼ Ý‡, å¼ ªð‡
(C) 24 days (D)36 days
ñŸÁ‹ å¼ ¬ðò¡ º¬ø«ò 6, 9 ñŸÁ‹
18 èO™ º®Šð£˜èœ âQ™ å¼ Solution:
ݵ‹ ñŸÁ‹ å¼ ªð‡µ‹ âˆî¬ù 1
2 M + 7b = → (i )
¬ðò¡èœ ¶¬í¹K‰î£™ å¼ ï£O™ 14
«õ¬ô¬ò º®‚è º®»‹-? 1
3M + 8b = → (ii )
A man, a woman and a boy can do a piece of 11
work in 6, 9 and 18 days respectively. How
many boys must assist one man and one wom- 3
(i) x 3 → 6M + 21 b =
an to do the work in 1 day? 14
(A) 5 (B) 6 2
(ii) x 2 → 6M + 16b =
(C) 9 (D) 13 11
( -) (-) (-)
Solution:
1 1 3 2
1M → W= 5b= −
6 9 14 11
1 33 − 28
1b = 5b =
18 154
1 1 5 1 1
1M + 1W = + =b = x
6 9 154 5 154

34
 TNPSC èí‚°
1 1
2M + 7 x =
154 14 6 X − 48 + 4 X − 48 + 3 X
22 =1
216
1 1
2M
= − 13 X − 96
14 22 =1
216
11 − 7
2M = 13 X = 312
154
24
2 312
4 1 1 X= = 24
M= x = 13
154 2 77
77

84. 56 «ð˜ å¼ «õ¬ô¬ò 24 èO™

1 1
(8M + 6b) = 8x + 3 6 x ªêŒ¶ º®‚A¡øù˜. âQ™ 42 «ð˜
77 15477 Ü‰î «õ¬ô¬ò âˆî¬ù èO™
8 3
= + ªêŒ¶ º®Šð˜?
77 77
11 1 56 man can complete a piece of work in
=
8M + 6b = = 7 days 24 days. In how many days can 42 man
77 7
complete the same piece of work ?
3 ñ샰 (8M + 6b) = 3(7) = 21 days (A) 18 (B) 32

ê˜è£˜ ä.ã.âv Üè£ìI

(C) 98 (D) 48
83. A, B, C â¡ø Í¡Á «ð˜ å¼ «õ¬ô¬ò 56M → 24d
º¬ø«ò 36,54,72 èO™ º®Šð˜.
ÞF™ A â¡ðõ˜ «õ¬ô º®õ 42M → ?
8 èÀ‚° º¡ð£è¾‹, B â¡ðõ˜ 12

12 èÀ‚° º¡ð£è¾‹ MôA‚ 56x 24

D= = 32
ªè£‡ìù˜. C â¡ðõ˜ Üš«õ¬ô¬ò 42
21
âˆî¬ù èO™ º®Šð£˜?
A, B and C can do a piece of work in 36, 54 and
85. A å¼ «õ¬ô¬ò 12 èO™ º®Šð£˜.
72 days respectively. They started the work
Ü«î «õ¬ô¬ò B, 20 èO™
but A left 8 days before the completion of work
º®Šð£˜. A ñŸÁ‹ B «ê˜‰¶ 3 èœ
while B left 12 days before the completion.
«õ¬ô ªêŒîH¡ A ªê¡Á M†ì£˜.
The number of days for which C worked.
eF «õ¬ô¬ò B º®‚è «î¬õŠð´‹
(A) 24 (B) 26 èœ
(C) 28 (D) 30
A can complete a work in 12 days. B call
Solution: complete a work in 20 days. A and B together
1 1 1 work for 3 days after that A left the work. B
A→ B= C=
36 54 72 can complete the remaining work in
Let the work is finished in x days (A) 9 days (B) 11 days
(C) 12 days (D) 13 days
x −8
A= Solution:
36
1 1
x −8 x − 12 x A→ B=
A= B= C= 12 20
36 54 72 1 1
A+ B = +
x − 8 x − 12 x 12 20
+ + =1
36 54 72

35
 TNPSC èí‚°
6 men can finish a work in 24 days, if they
5+3 8 work for 10 hours a day. How many days
= =
60
2 60 will 9 men take to finish the same work if they
4
8 2 work for 8 hours a day ?
= =
60 5 (A) 20 days (B) 40 days
30
15 (C) 10 days (D) 60 days
2
3 days joining = 5 Solution:
6 men x 10 hours x 24 days = 9 men x 8
Remining Work = − hours x ? days
5−2 6 x 10 x 24 = 9 x 8 x d
=
5 2 3
6 x10x 24
3 4 d= = 20
= X 20 9x 8
5 3
TNPSC group- IV & VAO │ (èEî‹ ¬è«ò´)

=12 days d=20 days

86. A ñŸÁ‹ B Þ¼õ¼‹ å¼ «õ¬ô¬ò
12 èO™ ªêŒ¶ º®Šð˜. B ñŸÁ‹ C 88. A ñŸÁ‹ B ÝAò Þ¼õ¼‹ ެ퉶
Ü«î «õ¬ô¬ò 15 èO™ º®Šð˜. å¼ «õ¬ô¬ò 16 èO™ º®Šð˜.
C ñŸÁ‹ A Ü«î «õ¬ô¬ò 20 A îQ«ò Ü‰î «õ¬ô¬ò 48
èO™ º®Šð˜ âQ™ A, B ñŸÁ‹ C èO™ º®Šð£˜ âQ™, B îQ«ò
Íõ¼‹ «ê˜‰¶ Üš«õ¬ô¬ò º®‚è Ü‰î «õ¬ô¬ò âˆî¬ù èO™
«î¬õŠð´‹ èœ. º®Šð£˜?
A and B together can complete in 12 days, B A and B together can do a piece of work in 16
and C together can complete in 15 days, C and days and A alone can do it in 48 days. How
A together can complete in 20 days A, B and long will B alone take to complete the work?
C together can complete in (A) 18 days (B) 24 days
(A) 10 days (B) 12 days (C) 28 days (D) 30 days
(C) 14 days (D) 15 days Solution:
Solution: 1
A+ B =
1 1 1 16
A+B= B+C
= C+A
= 1
12 15 20 A=
48
1 1 1 B=?
2( A + B + C) = + +
12 15 20 B = A+ B − A
5+ 4+3 1 1
= = −
60 16 48
12 1 1 3 −1
= x = =
60 2 10 48
5

10 days 2
= = 24
48
87. 6 Ý‡èœ å¼ «õ¬ô¬ò ÷£¡Á‚° 24

10 ñE «ïó‹ «õ¬ô ªêŒ¶, 24 èO™ 24 days

º®Šð˜. 9 Ý‡èœ ï£ª÷£¡Á‚° 8
ñE «ïó‹ «õ¬ô ªêŒî£™ âˆî¬ù
èO™ Üš«õ¬ô¬ò º®Šð˜ ?

36
 ê˜è£˜ ä.ã.âv Üè£ìI
èí‚°
TNPSC

37
(èEî‹)
TNPSC group- I │

Anna Nagar West, Chennai - 600012

Phone: 9962600037, 9962600038
www.sarkariasacademy.com