P-1 (BS)

Quantitative Aptitude 15
Time and Work, Pipes and Cisterns

Number of Questions : 50 CEX–5315/P1BS/19

1. A can copy 100 pages in 5 hr. A and B 5. Worker A takes 18 days to finish a job.
together can copy 100 pages in 4 hr. In what Worker B takes 27 days to finish the same
job. How long should it take for both A and B,
time can B copy 20 pages?
working together to finish the same job?
(a) 5 hr (b) 4 hr
4
(c) 8 hr (d) 2 hr (a) 11 days (b) 12 days
7
4
2. Mr. Smith can build a shed in x hr. After 2 hr, (c) 10 days (d) 13 days
5
he stops his work. What part of the shed is
left unbuilt? 6. A and B together can complete a piece of
x−3 x−4 work in 15 days while A alone can complete
(a) (b) the work in 21 days. How long will B alone
x x
take to complete the job?
2 x−2 1 1
(c) 1 + (d) (a) 52 days (b) 52 days
x x 2 8
3
3. Five men and two boys working together can (c) 51 days (d) 53 days
4
do four times as much work per hour as a
man and a boy can complete together in an 7. Ravi can finish a piece of work in 21 days and
hour. Compare the work of a man with that of Prem can finish the same work in half the
time taken by Ravi. If they work together then,
a boy.
what part of the same work can they finish in
(a) 1 : 1 (b) 1 : 2 a day?
(c) 2 : 1 (d) 3 : 1 1
1
(a) (b)
7 5
4. Two pipes can fill a tank in 18 min and 36 min
1 1
respectively and a waste pipe can empty 2 (c) (d)
4 3
gallons per minute. If all the three pipes work
together, then the tank is filled in 15 min. The 8. A certain number of men can complete a job
capacity of the tank is: in 10 days. If there were 2 more men, the job
(a) 120 gallons (b) 60 gallons can be completed in 2 days less. Initially,
(c) 240 gallons (d) 180 gallons how many men were there?
(a) 10 (b) 8
(c) 6 (d) 5

QA / Exercise - 15 Page 1
9. Two pipes A and B can fill a tank in 10 min 14. To complete a certain work, Y would take
and 15 min respectively. If both the pipes are three times as long as X and Z together, and
opened simultaneously, then how long will it Z takes twice as long as X and Y together.
take to fill the tank? The three men together can complete the work
(a) 6 min (b) 8 min in 10 days. How long would each take to
complete the work separately?
(c) 10 min (d) 5 min
(a) 24, 40, 30 days
(b) 30, 20, 10 days
10. Pipe A can fill a tank in 18 min; Pipe B can fill (c) 15, 20, 35 days
the tank in 27 min and Pipe C can empty the (d) 30, 24, 40 days
full tank in 36 min. If all of them work together,
then find the time taken to fill the empty tank. 15 . Five men can complete a piece of work in 1
day whereas 4 women can complete the
4
(a) 16 minutes (b) 20 minutes same piece of work in 3 days. How much
7 time will a man and 2 women take to complete
3 the same piece of work?
(c) 12 minutes (d) 15 minutes 3 8
7 (a) 1 days (b) 2 days
7 11
11. A works twice as fast as B and three times 5 2
(c) 5 days (d) 2 days
as fast as C. If C can complete a job in 12 hr, 11 9
then what part of the job can B complete in
1 hr? 16. A and B can complete a job in 8 days working
together. B alone can complete it in 12 days.
1 1 Both of them worked together for 4 days and
(a) (b)
8 4 then B left. How long will A take to complete
the remaining work?
1
(c) (d) 1 3 1
2 (a) 10 days (b) 11 days
4 2
(c) 16 days (d) 12 days
12. A tap can fill an empty tank completely in
10 hr while another tap can empty the full 17. Ten men can complete a work in 18 days.
tank in 20 hr. If both the taps are kept open, After 6 days, 5 more men joined. In how many
then in how much time would an empty tank days will the remaining work be completed?
gets filled? (a) 6 days (b) 12 days
(a) 15 hr (b) 20 hr (c) 8 days (d) 10 days
(c) 10 hr (d) 40 hr
18. A cistern can be filled by a supply pipe in
13. A team of labourers promises to complete a 4
30 min and emptied by a waste pipe in hr.
piece of work in 10 days, but 5 of them do not 5
turn up. If the rest of the team takes 12 days If both pipes are opened together, then in what
to complete the work, then find the original time will the cistern be filled?
number of labourers. 1
(a) hr (b) 1 hr
(a) 32 (b) 25 2
(c) 35 (d) 30 1
(c) 1 hr (d) 2 hr
3

Page 2 QA / Exercise - 15
19. A is thrice as fast as B, and therefore is able 24. A pump can fill a tank in 6 hours. Because of
to finish a work in 60 days less than B. Find 1
a leak in the tank, it took 6 hours to fill the
the time in which they can complete it, 2
working together. tank. If the tank is full, then how much time
(a) 20 days (b) 10 days will the leak take to empty it?
(c) 22.5 days (d) 40 days (a) 52 hours (b) 72 hours
(c) 91 hours (d) 78 hours
20. Three taps A, B and C together can fill a tank
25. Two pipes A and B can fill a tank in 12 min.
in 6 hours. After 1 hour C is closed and the
and 16 min respectively. If both the pipes are
tank is filled in 8 more hours. Find the time in opened simultaneously, after how much time
which C alone can fill the tank. should B be closed so that the tank fills in
(a) 16 hours (b) 19 hours 9 minutes?
(c) 12 hours (d) 8 hours (a) 4 min (b) 2 min
(c) 5 min (d) 8 min
21. Tejas can complete as much work in 4 days
as Aniket in 5 days. Ketan can complete as 26. A, B and C can complete a assigned work in
much work in 5 days as Aniket in 3 days. If 8, 16 and 24 days respectively. They all begin
Tejas takes 30 days to complete a work, in together. A continues to work till it is finished,
what time would Ketan complete the same C leaves 2 days before its completion and B
leaves one day before its completion. In what
work?
time will the work gets finished?
(a) 50 days (b) 62.5 days
(a) 5 days (b) 3 days
(c) 28 days (d) 75 days (c) 4 days (d) 2 days
(e) 1 day
22. Rahul can finish a piece of work in 16 days.
When he had worked for 4 days Rohit joined 27. An amount of !99 is paid for a task which A
him. If they complete the work in 4 more days, can complete in 32 days, B in 20 days and C
then in how many days can Rohit alone finish in 12 days and D in 24 days. If A, B, C and D
the job? work together, then how much money should
(a) 6 days (b) 4 days each receive?
(c) 8 days (d) 12 days (a) !15, !20, !50, !24
(b) !32, !20, !12, !24
(c) !15, !20, !12, !50
1 (d) !15, !24, !40, !20
23. A can finish th of a work in 12 days. B can
6 (e) !40, !20, !15, !60
complete 40% of the same work in 40 days
28. Two inlet pipes A and B can fill a tank in 15
1 min and 20 min respectively. A leak in the
while C can finish th of the work in 14 days. pipe can empty the tank in 15 min. Initially
5
pipe A is opened for 5 minutes. Then, pipe B
Who will complete the work first?
is also opened. How much more time will it
(a) A (b) B take to fill the tank?
(c) C (d) At the same time (a) 10 mins (b) 15 mins
(c) 20 mins (d) 25 mins
(e) 12 mins

QA / Exercise - 15 Page 3
29. A can finish a piece of work in 4 days working 33. Six men earn as much as 8 women, 2 women
9 hours per day and B can finish it in 6 days earn as much as 3 boys and 4 boys can earn
working 7 hours per day. How long will they as much as 5 girls. If a girl earns !50 a day,
take to finish the work, working together then each man earns
2 (a) !115 (b) !135
8 hours a day?
5 (c) !125 (d) !150
(a) 3 days (b) 4 days (e) None of these

4 4
(c) 3 days (d) 2 days 34. Harish, Ramesh and Suresh can finish a
13 13 project in 22, 33 and 44 days respectively.
(e) 5 days How soon can they finish the project if they
work jointly?
30. A and B each working alone can complete a
job in 12 and 18 days, respectively. They 2 2
(a) 10 days (b) 12 days
started working together but B left after 13 13
sometime and A finished the remaining job in
6 days. After how many days from the start 2
(c) 15 days (d) 17.5 days
did B leave? 13
3 (e) None of these
(a) 2 days (b) 5 days
5
3 35. A, B and C together can complete a job in 15
(c) 3 days (d) 4 days
5 days. After working with B and C for 5 days,
2 A leaves and then B and C take 20 days more
(e) 3 days to finish that job. In how many days can A
5
complete the job alone?
31. 20 men and 30 women take 5 days to (a) 25 (b) 27
complete a piece of work. It takes 20 days (c) 32 (d) 30
for the same work to be completed by 6 men (e) None of these
and 5 women. How many days will it take for
40 men to complete the same work? 36. Two inlet pipes can seperately fill a tank in
(a) 2 days (b) 3 days 20 min and 15 min respectively and a
(c) 4 days (d) 6 days waste pipe can empty the completely filled
(e) None of these
tank in 12 min. On a certain day, the two inlet
pipes are turned on simultaneously to fill the
1 empty tank. But after 9 min it was found that
32. A and B can mow a field in 3 days, A and C
2 the waste pipe was also left opened, it was
in 4 days, B and C in 5 days. If all are working closed immediately. How much additional time
together, then in how many days they can is required to fill the tank completely?
mow the complete field? (a) 5.5 min (b) 5 min
74 (c) 6 min (d) 6.2 min
(a) 2 days (b) 2 days
103 (e) 6.5 min
63
(c) 2 days (d) 3 days
103
(e) None of these

Page 4 QA / Exercise - 15
37. Twenty seven men can complete a piece of 42. To complete a task in 45 days, a contractor
work in 21 days working 6 hrs in a day. In employs 45 people. Upon reviewing the work
how many days 18 men working 9 hrs a day after 30 days, he notices that only half the
can complete twice the amount of work. Three task is completed. In order to meet the
person of first group can complete same deadline of 45 days, then how many more
amount of work in 3 days as 3 person of people must he employ now?
second group can complete in two days. (a) 25 (b) 15
(a) 34 days (b) 42 days (c) 60 (d) 45
(c) 28 days (d) 21 days (e) None of these
(e) 14 days
43. In order to build a wall, A can lay bricks at 30
38. A and B can complete a piece of work in bricks per minute and B at 40 bricks per
10 days, B and C in 12 days while C and A in minute. How much time will it take for A and
15 days. They all work together for 6 days B, working together to build a wall 14 m in
and then A left. In how many more days can height and 6 m in length. If the dimensions of
B and C together finish the remaining work? the bricks are length = 15 cm, height = 5 cm
(a) 3 days (b) 5 days and width = 7 cm. (Assume that area taken
(c) 9 days (d) 12 days by cement is negligible)
(e) 4 days (a) 2 hrs 20 mins (b) 2 hrs 30 mins
(c) 2 hrs 40 mins (d) 2 hrs 50 mins
39. Twenty men can complete a job in 12 days. (e) None of these
Four days after they started working, 12 more
men joined them. How many days will they 44. In a tank there are four outlets A, B, C and D.
now take to complete the remaining job? These outlets can empty the tank in 10 min,
(a) 7 days (b) 5 days 12 min, 15 min and 18 min respectively. If the
(c) 4 days (d) 8 days tank is full and all the outlets are opened how
(e) 6 days much time will it take to empty the whole
tank, the outlet A , B are closed after 1 min
40. Two pipes can fill a cistern in 12 hours and and 2 min respectively and the outlet C is
18 hours respectively. The pipes are opened closed 5 minutes before the tank gets empty.
simultaneously and it is found due to leakage 8
8
in the bottom it took 48 min more to fill the (a) 6 min (b) 8 min
cistern. When the cistern is full, then in what 11 11
time will the leak empty it? 8
(c) 7 min (d) 9 min
(a) 48 hours (b) 84 hours 13
(c) 72 hours (d) 112 hours
(e) None of these
(e) None of these
45. A and B working separately can complete a
41. If two pipes are opened simultaneously, the
piece of work in 6 and 8 days respectively. If
reservoir will be filled in 6 hr. One pipe fills the
they work for a day alternately, beginning with
reservoir 5 hr faster than the other. How much
A, then in how many days the work will be
time does the slower pipe take to fill in the
completed?
reservoir?
(a) 5 days (b) 6 days
(a) 10 hr (b) 3 hr
(c) 11 hr (d) 20 hr 3 3
(c) 6 days (d) 7 days
(e) None of these 4 4
(e) 7 days

QA / Exercise - 15 Page 5
46. A and B can separately do a piece of work in 49. A can do a work in 12 days. When he had
20 and 15 days respectively. They worked worked for 3 days, B joined him. If they
together for 6 days after which B was replaced complete the work in 3 more days, in how
by C. The work was finished in next 4 days. many days can B alone finish the work ?
The number of days in which C alone could (a) 6 days (b) 12 days
do the work is (c) 4 days (d) 8 days
(a) 30 days (b) 45 days (e) 10 days
(c) 40 days (d) 35 days
(e) 50 days 50. A does half as much work as B in three-fourth
of the time. If together they take 18 days to
complete a work, how much time shall B take
47. A and B can complete a piece of work in 8
to do it alone?
days, B and C can do it in 12 days, C and A
can do it in 8 days. A, B and C together can (a) 30 days (b) 35 days
complete it in (c) 40 days (d) 45 days
(a) 4 days (b) 5 days (e) 15 days
(c) 6 days (d) 7 days
(e) 8 days

48. X is 3 times as fast as Y and is able to

complete the work in 40 days less than Y.
Then the time in which they can complete
the work together is
(a) 15 days (b) 10 days
1
(c) 7 days (d) 5 days
2
(e) 20 days

Page 6 QA / Exercise - 15
 Time and work

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 CEX–5315/P1BS/19 Quantitative Aptitude - 15 P-1(BS)
Time and Work, Pipes and Cisterns
Answers and Explanations

1 b 2 d 3 c 4 a 5 c 6 a 7 a 8 b 9 a 10 d
11 a 12 b 13 d 14 a 15 b 16 d 17 c 18 c 19 c 20 a
21 b 22 c 23 c 24 d 25 a 26 a 27 d 28 c 29 d 30 c
31 c 32 a 33 c 34 a 35 d 36 c 37 c 38 a 39 b 40 c
41 a 42 d 43 c 44 b 45 c 46 c 47 c 48 a 49 a 50 a

1. b A can copy 100 pages in 5 hr.

1 1 5
∴ A can copy 20 pages in 1 hr. (A + B)’s 1 day’s work = + =
18 27 54
100
Given 20 + B = .
4 54 4
∴ Both A and B will finish the work in = 10 days.
⇒ 20 + B = 25 ⇒ B = 5 pages per hour 5 5
∴ For 20 pages, B needs 4 hr

1
2 6. a (A + B)’s 1 day’s work =
2. d Smith’s 2 hr work = 15
x
2 x–2 1
Work left = 1– = A’s 1 day’s work =
x x 21

3. c Let the work done by a man and a boy in one hour be 1 1 2

‘m’ and ‘b’ respectively. B’s 1 day’s work = − =
15 21 105
∴ 5 m + 2 b = 4(m + b) = 4 m + 4 b
⇒ 1m=2b 105 1
= 52 days.
∴ B alone can finish the work in
Therefore, work done by man : work done by a boy 2 2
= 2 : 1.

1
4. a Work done by the waste pipe in 1 min. 7. a Ravi’s 1 day’s work = and
21
1  1 1 
= − +
15  18 36  1 2
Prem’s 1 day’s work = =
1 21
1 10
=− (minus sign means emptying) 2
60
∴ (Ravi + Prem)’s 1 day work
1 1 2 3 1
∴ Volume of part = 2 gallons = + = = th part of the work.
60 21 21 21 7
∴ Capacity of the tank = 2 × 60 = 120 gallons.
8. b Let initial number of men be x.
1 Number of days is 10, so number of man days is 10x.
5. c A’s 1 day’s work = , If there were 2 more men i.e. (x + 2), it can be completed
18
in 8 days.
1 So, 10x = (x + 2)8
B’s 1 day’s work = ⇒ x = 8.
27

QA / Exercise - 15 Page 1
 1 1 1 1 1
9. a Part of the tank filled by A in 1 minute = + + = ...(iii)
10 a b c 10
Subtracting (i) from (iii), we get b = 40 days.
1
Part of the tank filled by B in 1 minute = Subtracting (ii) from (iii), we get c = 30 days.
15 Substituting the values of b and c in (iii), we get
Part of the tank filled by both the pipes in one minute a = 24.
∴ X, Y and Z complete the work in 24, 40 and 30 days
1 1 1
= + = respectively.
10 15 6
∴ The tank can be filled in 6 minutes. 1
15. b One man can complete th part of the work in one
5
10. d Work done by the 3 pipes together in 1 minute day.
1 1 1 5 1 7 1
= + − = − = Also, 1 woman can complete th part of the work in
18 27 36 54 36 108 12
one day.
108 3 Therefore, part of the work completed by a man and
So, the empty tank will be filled in = 15 minutes.
7 7
1 2 1 1 11
2 women = + = + =
11. a Time taken by A, B and C to complete a work 5 12 5 6 30
= 1x, 2x and 3x. Hence, the number of days required for completing the
3x = 12 ⇒ x = 4 30 8
Time taken by B to complete the work = 8 hr piece of work = =2 days .
11 11
1
∴ In 1 hr, B will complete th of the work.
8 1
16. d (A + B)’s 1 day’s work = ;
8
Alternate method:
1 1
According to the question, (A + B)’s 4 day’s work = ; Remaining work =
A = 2B and A = 3C 2 2
1 1 1
3 Work completed by A in 1 day = − =
Thus 2B = 3C ⇒ B = C 8 12 24
2
∴ A alone takes 24 days to complete the job.
1
Now work completed by C in 1 hr = 1
12 Since only of the work is left, A will complete the
2
3 1 1
∴ Work completed by B in 1 hr = × = th part. 1
2 12 8 remaining work in × 24 = 12 days.
2

12. b Let x hr be the required time to fill the tank. 1

17. c Amount of work completed by 10 men in 1 day is th.
 1 1  18
∴  –  x=1
 10 20  Therefore, amount of work completed by 10 men in 6
days
x
⇒ = 1 ⇒ x = 20
20 6 1
= =
∴ The tank can be filled in 20 hr. 18 3

13. d Let original labourers = x. 1 2

10 × x = (x – 5) × 12 ⇒ x = 30 Amount of work left = 1 − =
3 3
14. a Let X, Y and Z be the three persons and they complete Since 10 men require 12 days to complete the remaining
the work in a, b and c days respectively. 2
1 1 3 work, time required by 1 man is 12 × 10 = 120 days.
+ = 3
...(i)
a c b Therefore, time required for (10 + 5) = 15 men
1 1 2 120
+ = ...(ii)
a b c = = 8 days.
15

Page 2 QA / Exercise - 15
 1
18. c Time required to fill the cistern =
1
=
1 22. c Rahul’s 1 day’s work =
5 3 16
2– Number of days Rahul worked = 4 + 4 = 8
4 4
1 1
4 1 ∴ Total work done by Rahul = 8 × =
= hr = 1 hr 16 2
3 3
1
The remaining of the work is done by Rohit in
19. c !A = 3 B 2
Let A takes x days to complete the work alone. 4 days.
∴ B takes (x + 60) days to complete the work alone. ∴ Complete work will be done by Rohit in
1 2
A’s one day’s work = 4× = 8 days.
x 1
1
B’s one day’s work =
x + 60 23. c Whole work completed by A = 12 × 6 = 72 days.
1 3
Whole work completed by B =  40 ×
∴ x = x + 60 100 
 = 100 days.
 40 
⇒ x + 60 = 3x ⇒ 2x = 60 ⇒ x = 30 days Whole work completed by C = 14 × 5 = 70 days.
A can complete the work in 30 days. ∴ C will complete the work first.
B can complete the work in 90 days.
1 1 4 2 1 1
In 1 day + = = work is completed. 24. d Work done by the leak in 1 hour = −
30 90 90 45 6 61
2
45
∴ The work will take days = 22.5 days.
2 1 2 1
=− =
6 13 78
1 ∴ The leak will empty the tank in 78 hours.
20. a (A + B + C)’s 1 hour’s work =
6
25. a Let B closed after x minutes. Then, part filled by
1 5 (A + B) in x min. + part filled by A in (9 – x) min. = 1.
Remaining part of tank = 1 − =
6 6  1 1 1
⇒ x +  + (9 − x ) × 12 = 1,
5  12 16 
Time taken by (A + B) to fill this of the tank = 8 hours.
7x (9 − x )
6
⇒ + = 1 ⇒ x = 4 min.
48 48 12
⇒ A and B together fill the tank is hours Hence, B must be closed after 4 min.
5
Now, we know A + B + C = 6 hours
48 1
A +B = hours 26. a A in 1 day can complete
8
th of work.
5

1 5 1 1
∴ C= − = B in 1 day can complete
16
th of work.
6 48 16
Hence, C alone can fill the tank in 16 hours. 1
C in 1 day can complete th of work.
24
21. b Ratio in number of days taken by Tejas:Aniket:Ketan
= 12 : 15 : 25 Let the work completed in x days.
Let us assume that Ketan can complete the work in 1 1 1
x days. Then, Then, x+ [ x – 1] + [ x – 2] = 1
8 16 24
30 12
= 6x + 3x – 3 + 2x – 4
x 25 ⇒ = 1 ⇒ 11x – 7 = 48
⇒ x = 62.5 days. 48
⇒ 11x = 55 ⇒ x = 5 days.

QA / Exercise - 15 Page 3
27. d Ratios of one day’s work of A, B, C and D 31. c (20 M + 30 W) × 5 = (6 M + 5 W) × 20
1 1 1 1 ⇒ 20 M + 30 W = 24 M + 20 W
= : : : = 15 : 24 : 40 : 20 2
32 20 12 24 ⇒1W= M
Total amount = !99 5
∴ 30 W = 12 M
15 Now, we have 20 M + 30 W takes 5 days
A’s share " × 99 = !15
99 or (20 + 12) men can complete the work in 5 days
32× 5
24 40 men will complete the work in = = 4 days.
B’s share = × 99 = ! 24 40
99

40
× 99 = ! 40  1 1 2
C’s share " 32. a  + =
99 A B 7
20 1 1 1
D’s share " × 99 = ! 20  + =
99 B C 5

28. c Rate of pipe A and the leakage is same i.e. 15 min.  1 1 1  1 1 1  2 1 1 103
 + = ⇒2 + + = + + =
Thus, when only ‘A’ is opened, by the end of 5 min, the  A C 4  A B C  7 5 4 140
tank would still be empty.
When A, B and leak work together,  1 1 1  103
⇒ + + =
Construction by pipe A = destruction by the leak in the  A B C  280
tank. Hence, only pipe B will help in filling the tank. A, B and C together can complete the work in
Hence, it takes 20 min to fill the tank.
280 74
=2 days.
29. d A can complete the work in 4 × 9 = 36 hours 103 103
B can complete the work in 6 × 7 = 42 hours
1 1 13 33. c Earning of men, women, boys and girls are
∴ (A + B)’s 1 hour’s work = + = 8
36 42 252 1 man earning = woman earning
6
252 3
∴ Both will finish the work in hrs. 1 woman earning = boy earning
13 2
2 252 5 5 5
Number of days of 8 hrs. each = × 1 boy earning = girl earning = × 50
5 13 42 4 4
8 3 5
30 4 ∴ 1 man earning = × × × 50 = !125.
= =2 days. 6 2 4
13 13
Alternate method:
1 work Initials used
30. c A’s work for 6 days = 6 × work =
12 2 Man : M, Woman : W, Girl : G, Boy : B
Now according to the question
1 6M = 8W
The remaining work was completed by A and B
2 2W = 3B
together. 4B = 5G
1 1 5 8 3 5 5
Work completed by A and B in a day = + = Thus, M = × × ×G = × 50 = !125.
12 18 36 6 2 4 2
∴ Number of days they worked together
34. a Given Harish, Ramesh and Suresh can finish a project
1 in 22, 33 and 44 days respectively. Let they take x
2 36 18 3 days to complete the job while working together.
= = = = 3 days .
5 10 5 5
 1 1 1  6+4+3
36  + +  x = 1 ⇒   x =1
 22 33 44   132 
3
Hence, B left after 3 days from the start of the work. 132 2
5 ⇒ x= ⇒ x = 10 days .
13 13

Page 4 QA / Exercise - 15
35. d As A, B and C together require 15 days to complete the 32 2
32 men 1 day’s work = =
1 240 15
job, they can complete rd of the job in 5 days.
3 2
Therefore, amount of work left when A leaves is Now, work is completed by them in 1 day.
15
1 2 2 15 2
1– = . It is given that B and C together take 20 ∴ work is completed by them in × = 5 days.
3 3 3 2 3
2
days for rd work. Therefore, B and C need 30 days
3 1 1 5
40. c Work completed by two pipes in 1 hour = + =
to complete the job. 12 18 36
A’s 1 day’s work ∴ Time taken by these pipes to fill the tank
= (A + B + C)’s 1 day’s work – (B + C)’s 1 day’s work 36 1
= = 7 hours = 7 hr 12 min.
1 1 1 5 5
= – = Due to leakage, time taken = 7 hr. 12 min. + 48 min.
15 30 30
A can finish the work in 30 days. = 8 hours.
∴ Work completed by (two pipes + leak) in an hour
36. c Let total work be 60 units. 1st tap fills 3units per minute, 1
2nd tap fills 4 units per minute and waste pipe empties =
8
5 units per minute. So, when opened together all three 5 1 1
will fill (3 + 4 – 5) = 2 units per min. Hence, in first 9 min, Work completed by the leak in 1 hour = − =
36 8 72
18 units of tank is filled. Since the waste pipe is closed ∴ Leak will empty the full cistern in 72 hours.
∴ The remaining 42 units will require
42
= 6 min to fill.
3+4 41. a Let the slower pipe takes x hr to fill the reservoir. Then,
1 1 1
37. c From the given data men in the first group are two-third + =
x ( x + 5) 6
as efficient as men from the second group. Hence, 27
⇒ 12x + 30 = x2 + 5x ⇒ x2 – 7x – 30 = 0
2
men of the first group are equivalent to   × 27 ⇒ x(x – 10) + 3(x – 10) = 0
3
= 18 men of second group. Further more ⇒ (x – 10) (x + 3) = 0, i.e x = 10 hr. (! x ≠ −3)
(Men × hours per day × number of days ) = cons tan t
Work done 1
42. d In 30 days, of the work was done by 45 people.
18 × 6 × 21 18 × 9 × D 2
= ⇒ D = 28 days
x 2x So, 45 people require 60 days to complete the work.
1 person requires 60 × 45 days.
1 ∴ To complete the entire job in 15 days,
38. a (A + B+ C)’s 1 day’s work =
8 60 × 45
Work completed by A, B and C in 6 day’s = 180 people are required.
1 3 15
= 6× = 180
8 4 Only half the work is left, = 90 people are
2
3 1
∴ Remaining work = 1 − = required. As there are already 45 people, 45 more
4 4
people are required to complete the job.
1
∴ B and C can finish the remaining th of the work in
4 43. c If A and B work together, then they can lay 30 + 40
1 = 70 bricks per minute.
× 12 = 3 days. = (70 × 15 cm × 5 cm) of the wall in 1 minute
4
(Note → here width of brick = width of wall.
39. b (20 × 12) men can complete the work in 1 day. So, ‘w’ of brick is not required)
Dimensions of the wall = 14 m × 6 m
1
∴ 1 man’s 1 day’s work = 14 × 6 × 100 × 100
240
... Total time = (convert cm to m)
1 1 70 × 15 × 5
20 men 4 day’s work = ×4 =
12 3 = 160 minutes = 2 hrs and 40 mins.
1 2
Remaining work = 1 − =
3 3

QA / Exercise - 15 Page 5
44. b Let us consider that the total work = 360 units 8
A+B+C=
A B C D 24 × 2
10 12 15 18 " (minutes ) 1
A+B+C =
36 30 24 20 " ( units / minutes ) 6
A + B + C complete a work in = 6 days.
Let us consider that it takes ‘x’ minutes to empty the
completely full tank.
∴ The outlet C does (x – 5 ) × 24 units 48. a X is 3 times as fast as Y. Therefore, if x complete a
The outlet D does x × 20 units. work in 1 day y take 3 days to complet it.
∴ 36 × 1 + 30 × 2 + (x – 5) × 24 + 20x = 360 Therefore, the difference between the working days
8 is 2.
⇒x=8 min. But in this case the difference is 40 days.
11
Therefore, A completes a work in 20 days and B
completes the work in 60 days.
1 1 7
45. c (A + B)’s 2 day’s work = + = A and B together competes a work
6 8 24
1 1 3 +1 1
7 21 7 = + = = = 15 days.
Work completed in 3 pairs of days = 3 × = = , 20 60 60 15
24 24 8

7 1 49. a A completes a work in 12 days

Remaining work = 1 − = ,
8 8 1
Work done by A in one day =
1 12
On 7th day, it is A’s turn work is completed by him in
6
3 1
1 day. Work done by A in 3 day = =
12 4
1 1 3
work is completed by him in × 6 = day. 1 3
8 8 4
Remaining work = 1 − =
4 4
∴ Total time taken = 6 + 3 = 6 3 days.
4 4 3
A + B completes work in 3 days
46. c If time taken by C to complete the work be x days then 4

10 6 4 4
+ + =1 A + B complete work in = 3 × = 4 days
20 15 x 3

1 2 4 1 1 1
⇒ + + =1 B’s one day work = − =
2 5 x 4 12 6
5+4 4 ∴ B will take 6 days to complete the work.
⇒ + =1
10 x
50. a A complete half as much work as B in three-fourth of
4 9 1
⇒ = 1− = the time.
x 10 10
⇒ A can complete whole work as B in one and a half
∴ x = 10 × 4 = 40 days. times.
Let the number of days taken by A and B to complete
47. c A + B complete a work in 8 days the same piece of work be 3x and 2x respectively.
B + C complete a work in 12 days
 1 1 
C + A complete a work in 8 days A and B completes  +  work in 1 day.
 3x 2x 
 1 1 1
(A + B + C) can complete  + +  work in one 1 1 1
 8 12 8  ∴ + =
day. 3x 2x 18

3+2+3 ⇒ x = 15
2(A + B + C) =
24 ∴ B completes the work in 2x days = 30 days.

Page 6 QA / Exercise - 15