3.

256 UniT 3 – ChapTer 6

6.63. A tank has a leak at its bottom which empties it at 1 1 1

6 litres/minute. It also has a filling tap which can \ − =
6 x 18
fill the tank in 6 hours. The tank takes 18 hours
to become full. Find the capacity of the tank. x=9
Sol: Let the time that would be taken by the leak to \Capacity of the tank = (6) (9) (60)
empty the full tank be x hours. = 3240 litres.

exeRCISe-1

Directions for questions 1 to 50: For the multiple choice ques- 7. X and Y can complete a job in 15 days working together. Y
tions, select the correct alternative from the given choices. and Z can complete the job in 20 days working together.
For the non-multiple choice questions, write your answer in X and Z can complete the job in 30 days working together.
the space provided. Who is the slowest of the 3 workers?
(A) X (B) Y
1. If 30 men can do a job in 30 days, find the part of the job
(C) Z (D) Cannot be determined
that can be completed by 1 man in 1 day.
1 1 8. A, B and C can do a piece of work in 18 days, 24 days and
(A) (B) 36 days, respectively. In how many days can they complete
30 90
the work working together?
1 (A) 10 (B) 8 (C) 6 (D) 12
(C) (D) None of these
900
9. Tap A takes 4 hours to fill a tank. Tap B takes 6 hours to
2. A can do a work in 9 days and B can do the same work in fill the tank. If both the taps were opened simultaneously,
18 days. If they work together, in how many days will they by the time the tank was full, what fraction of the tank was
Difficulty level-1: Foundation

complete the work? ______ filled by tap A?

3. A can do a work in 21 days and B in 28 days. Together they 2 3

(A) 3.2 hours, (B) 3.2 hours,
started the work and B left after 4 days. In how many days 5 5
can A alone do the remaining work?
2 3
(A) 12 (B) 10 (C) 16 (D) 14 (C) 2.4 hours, (D) 2.4 hours,
5 5
4. A, B and C can do a work in 7, 14 and 21 days, respectively.
10. A and B can do a piece of work in 12 days and 18 days, re-
They completed the work together and got ` 220. The
spectively. They worked together and earned ` 300. What
share of C is (` ) ______.
is the share of A in this amount?
5. If the ratio of the individual times taken by P, Q and R to (A) ` 120 (B) ` 180 (C) ` 150 (D) ` 100
complete a job is 2 : 3 : 6, find the ratio of the parts of the
11. If a man completes a job in 6 days working 6 hours a day,
jobs done by P, Q and R in an hour.
in how many days can he complete the job working 9
(A) 2 : 3 : 6 (B) 6 : 3 : 2
hours a day? ______
(C) 3 : 2 : 1 (D) 1 : 2 : 3
12. A is 30% more efficient than B. If B can do a piece of
6. A, B and C together can do a work in 22 days. B and C to-
work in 26 days then in how many days can A alone do
3 the work?
gether can do of the work in 30 days. In how many days
4 (A) 20 (B) 24 (C) 22 (D) 26
can A alone do the work?
13. P can complete a job in 30 days. Q can complete the job
8 7 in 60 days. If they work on alternate days, the job would
(A) 47 (B) 48
9 9 be completed in the
(A) least possible time, if P starts the job.
8 7
(C) 48 (D) 47 (B) least possible time, if Q starts the job.
9 9
(C) same time, irrespective of who starts the job.

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 TIME AND WORK 3.257

3 5 26. Two pipes can fill a tank in 20 minutes and 26 minutes.

15. A can do th of a work in 12 days and B can do th An outlet pipe can empty the tank in 13 minutes. If all
4 8
the pipes are opened simultaneously, in how many min-
of it in 20 days. In how many days can A and B together
utes will the tank become full?
complete the work?
2 1 1 2
1 1 2 2 (A) 87 (B) 86 (C) 87 (D) 86
(A) 11 (B) 10 (C) 11 (D) 10 3 3 3 3
3 3 3 3
16. P and Q completed a job working together in x days. P 27. A, B and C can do a work in 15, 30 and 45 days respec-
takes (x + 8) days to complete the job, Q takes (x + 18) tively. C started the work. A and B joined after one day. In
days to complete the job. Find x. ______ how many days was the work completed?
(A) 6 (B) 8 (C) 7 (D) 9
17. A, B and C together can do a work in 20 days. If A and C
together can do the work in 40 and 60 days respectively, 28. P and Q can complete a job in 12 days working together.
B alone can do the work in ______ days. Q and R can complete the job in 20 days working to-
gether. P and R can complete the job in 15 days working
18. Three men and seven boys can do a piece of work in 45
together. In how many days can P, Q and R complete the
days. In how many days can 9 men and 21 boys do the
job working together?
work?
(A) 5 (B) 10 (C) 15 (D) 20
(A) 15 (B) 12
(C) 18 (D) Cannot be determined 29. A is twice as fast as B. If B alone can do the work in 30
days, A and B together can complete the work in ______
19. If the ratio of the work done by (x + 1) men in (x − 2)
days.
days to the work done by (x + 2) men in (x − 4) days is 9
: 8, then the value of x is 30. P, Q and R take 20 days, 30 days and 40 days respectively
(A) 12 (B) 14 (C) 10 (D) 16 to complete a job. The three work on a rotation basis to
complete the job with only 1 person working on a day.
20. 9 men can complete a job in 20 days. If a woman works
Who should start the job so that the job is completed in
at one-third the rate of a man, in how many days can 15

Difficulty Level-1: Foundation

the least possible time?
women complete the job? ______
(A) P (B) Q
21. Kavitha can do a piece of work in K days. What part of the (C) R (D) Any one of the three
work can she complete in X days?
31. 6 men can do a piece of work in 10 days. If a woman
(A) K/X (B) XK (C) 1/XK (D) X/K
works half as fast as a man, in how many days can 10 wom-
22. A can complete a job in 2 days. B can complete the job en complete the work?
in 4 days. If they work on alternate days, the job would be (A) 24 (B) 6 (C) 18 (D) 12
completed in the
32. If A is thrice as fast as B. Together they can do a work in
(A) least possible time, if A starts the job.
27 days. A alone can do the work in ______ days.
(B) least possible time, if B starts the job.
(C) same time, irrespective of who starts the job 33. Varma can read a book in k minutes. What part of the
book can he read in 8 minutes?(k > 8)
23. 215 men can construct a 677 m long wall in 13×5 days.
How many men are required to construct a wall twice the 8 k k −8
(A) 8 + k (B) (C) (D)
length of the previous wall in half the time? ______ k 8 k
34. Two pipes can fill a tank in 30 minutes and 20 minutes
24. Work done by (k – 1) men in (k – 8) days is equal to the
respectively. If they are opened simultaneously, in what
work done by (k + 4) men in (k – 11) days. What is the
time will the tank become full?
value of k?
(A) 15 minutes (B) 12 minutes
(A) 22 (B) 26 (C) 24 (D) 28
(C) 18 minutes (D) 9 minutes
25. 2 men can complete a job in 8 days working 8 hours a day.
35. P and Q working together can complete a piece of work
(i) How many men are required to complete the job in in 24 days. The ratio of their efficiencies is 2 : 3. In how
4 days working 4 hours a day? ______ many days can the faster person complete the work work-
(ii) How many men are required to complete twice the ing alone?
job working 4 hours a day for 4 days? ______ (A) 40 (B) 50 (C) 60 (D) 90

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 3.258 UNIT 3 – CHAPTER 6

36. Vinay and Varma can do a work in 30 days and 60 days 43. P and Q working together can complete a piece of
respectively. If they work on alternate days beginning work in 6 days. If P alone can complete the work in 15
with Vinay in how many days will the work be completed? days, then in how many days can Q alone complete the
______ work?
(A) 10 (B) 12 (C) 20 (D) 18
37. The ratio of the efficiencies of P, Q and R is 4 : 5 : 6. If
they completed a job working together, find the fraction 44. An inlet pipe takes 8 hours to fill a tank. An outlet pipe
of the job done by P. takes 12 hours to empty it. If both pipes are opened si-
1 1 4 7 multaneously, in how many hours will the tank be filled?
(A) (B) (C) (D) ______
5 3 15 15
45. x men can do a work in 120 days. If there were 20 men
38. Pipe A can fill a tank in 6 hours. Due to a leak at the bot- less, the work would have taken 60 days more. The value
tom, it takes 9 hours to fill the tank. In what time the leak of x is ______.
alone can empty the tank?
(A) 16 hours (B) 15 hours 46. 4 men can complete a piece of work in 4 days working 4
(C) 18 hours (D) 17 hours hours a day. In how many hours can eight men complete
the same work working 8 hours a day?
39. Twenty four men can do a work in 35 days. How many (A) 1/2 (B) 2 (C) 4 (D) 1
men are required to complete the work in 21 days?
______ 47. A and B working together can complete a job in 30 days.
1 The ratio of their efficiencies is 3 : 2. In how many days
40. A and B can do a work in 7 days and 30 days respec- can the faster person complete the job? ______
2
tively. In how many days can they complete the work if 48. If one man can eat one fruit in one day, then how many
they work together? fruits can eight men eat in eight days?
(A) 5 (B) 4 (C) 6 (D) 3 (A) 8 (B) 64
41. If A is 20% more efficient than B, then what is the ratio of (C) 16 (D) None of these
the work completed by A and B in one hour? 49. If 12 men or 20 women can do a work in 54 days, then 9
Difficulty Level-2: Moderate

(A) 5 : 6 (B) 6 : 5 men and 12 women can together do the work in ______
(C) 12 : 1 (D) Cannot be determined days.
42. P is twice as fast as Q and R together. Working together, 50. For how many days will 75 kg of ration be sufficient for a
all three can do a work in 21 days. In how many days can family of 6 members if each member consumes 1.25 kg
Q and R together do the work? of ration per day? ______
(A) 48 (B) 63 (C) 54 (D) 72

EXERCISE-2

Directions for questions 1 to 50 : For the multiple choice ques- of them started the work, but A left after 4 days, B left 2
tions, select the correct alternative from the given choices. days before the completion of the work. In how many
For the non-multiple choice questions, write your answer in days was the work completed?
the space provided. (A) 71/27 (B) 81/14 (C) 91/16 (D) 101/27
1. A, working alone, takes 80 days more than the time taken 3. P, Q and R are 3 small pumps fitted to a tank. S is a large
by A and B working together to complete the work. B, pump fitted to the tank. Q is 50% more efficient than P.
working alone, takes 20 days more than the time taken R is 331/3% more efficient than Q. S is 50% more effi-
by A and B working together to complete the work. Find cient than R. Find the ratio of the time taken by the four
the time taken by A alone to complete the work. (in days) pumps working together to fill the tank and the time
______ taken by the large pump to fill it.
2. A can complete a piece of work in 12 days which B and C 2 3 3 7
(A) (B) (C) (D)
can complete in 16 and 20 days respectively. All the three 5 5 10 20

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 TIME AND WORK 3.259

4. A pipe which can fill a tank in 12 hours, is opened at 6:00 13. Working together, A and B can complete a work in 12
a.m. A leak which can empty the tank in 24 hours was ob- days. They work together for 9 days after which B leaves.
served at 10:00 a.m. and was immediately stopped. The If A finishes the remaining work in 5 days, then find the
tank would be full at ______ :______ p.m. number of days that B alone would take to complete the
work. ______
5. A man, a woman and a boy can do a piece of work in 3, 4
and 12 days respectively. How many boys must assist one 14. 20 workers can reap 120 acres of land in 30 days work-
man and a one woman to complete the work in one and ing 6 hours a day. How many more acres of land can 30
a half days? workers working 12 hours a day reap in 15 days? ______
(A) 12 (B) 6 (C) 1 (D) 3
15. P and Q can do a work in 12 and 16 days respectively. If
6. A takes 1 day to complete a job. B takes twice the time as they work on alternate days, beginning with Q, then in
A to complete the job. C takes twice the time as B to com- how many days will the work be completed?
plete the job. D takes twice the time as C to complete the 1 2 3 1
job. Two of the four when working together take atmost (A) 13 (B) 13 (C) 13 (D) 13
4 3 4 3
40% of the time to complete the job that the other two
would take working together. Find the faster pair. 16. A tank has two inlet pipes which can fill it in 10 hours
(A) A, D (B) A, C and 15 hours respectively. It also has an outlet pipe which
(C) A, B (D) Cannot be determined can empty it in 30 hours. The inlet pipes are opened at
7. Three taps A, B and C together can fill a tank in 6 hours. 6:00 am. Just when the tank was expected to be full, it was
All the taps are opened simultaneously. After 2 hours, C spotted that the outlet pipe had accidentally been left
was closed and the tank was filled in 8 more hours. Find open. The outlet pipe was then closed. After how much
the time (in hours) in which C can fill the tank. ______ more time will the tank be full? (in hours) ______.

8. Working together, A and B can complete a piece of work 17. There are three taps P, Q and R. P takes thrice as much
in 24 days, B and C can complete the same work in 40 time as Q and R together to fill a tank. Q takes twice as
days while A and C can complete it in 30 days. Find the much time as P and R together to fill the tank. In how
number of days in which each of them can complete the much time (in hours) can R fill the tank individually, if
the three together require 10 hours to fill the tank when

Difficulty Level-2: Moderate

same work. ______, ______, ______
opened simultaneously? ______
9. Three taps P, Q and R can fill a tank in 8, 10 and 12 hours
respectively. Tap P is opened at 8:00 a.m., tap Q at 10:00 18. A can complete a work in 20 days. B can complete the
a.m. and tap R at 11:00 a.m. At what time would the tank same work in 30 days while C can complete the work in
be full? 60 days. They start working together. A leaves after 3 days
(A) 12:12 p.m. (B) 12:25 p.m. and B leaves 4 days before the work was originally sched-
(C) 12:42 p.m. (D) 12:58 p.m. uled to be completed. For how many days did C work?
______
10. Naveen, Praveen and Lenin are three brothers. The rate of
work of Naveen is one-third of that of Praveen and Lenin 19. Pipe A can fill a tank in half the time in which pipe B can
together. If Praveen can complete the work in 8 days, while fill the same tank. If both the pipes are opened simul-
Lenin can complete it in 24 days, then in how many days taneously, it takes 8 hours to fill the tank. In how many
can they together complete the same work? ______ hours can A alone fill the tank? ______

11. Pipe A can fill a tank in 12 hours and pipe B can empty 20. Two pipes can fill a tank in 18 minutes and 27 minutes. A
the tank in 18 hours. Both pipes are opened at 6 am and third pipe can empty the tank (when full) in 6 minutes.
2
after some time B is closed, and the tank is full at 8 p.m. All the three pipes are opened when the tank was rd
on the same day. At what time was B closed? 3
full. In how many minutes will the tank become empty?
(A) 10 am (B) 8 am (C) 9 am (D) 11 am
______
12. The ratio of the rates of work of A, B and C is 1 : 3 : 2. The
21. A certain quantity of work can be completed by A, B, C in
total wages of A, B and C for working for 15, 20 and 25
20, 15 and 30 days respectively and an amount of ` 4000
days respectively are ` 5000. Find the total wages of the
is paid for that work. Another quantity of work can be
three (in ` ), if A works for 10 days, B for 15 days and C
completed by A, B, C in 15, 25, 10 days respectively and
for 12 days. ______

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 3.260 UNIT 3 – CHAPTER 6

an amount of ` 10,000 is paid for this work. If both the 2. If starting from the second day, one additional person
works are completed by A, B, C together, who got the with the same working capacity joins every day, then in
minimum amount of the three? how many days will the work be completed? ______
(A) A (B) B
(C) C (D) Cannot be determined 30. 20 men can finish a piece of work in 30 days. After how
many days should 5 men leave the work so that it is fin-
22. The rate of work of B is twice that of A. A can complete a
ished in 35 days? ______
piece of work in 15 days. A started the work and B joined
him after a few days. The work was completed in 11 days. 31. A rectangular tank has dimensions 6 m × 5 m × 4 m.
For how many days did A work alone? ______ Three inlet pipes X, Y, Z have filling rates of 4 m3/hr, 5
m3/hr, 6 m3/hr respectively. At 8 a.m., X was opened and
23. Pipes A and B are inlet pipes while pipe C is an
at 8.30 a.m., Y was opened. At 10.30 a.m., Z was opened.
outlet pipe. Pipe A supplies water at 50 ltrs/hour. Pipe
The time at which the tank would be full is
B can fill a tank in 4 hours while pipe C can empty it in
(A) 4:50 p.m. (B) 5:40 p.m.
12 hours. All the pipes are simultaneously opened and
(C) 4:20 p.m. (D) 5:10 p.m.
the tank gets filled in 1 hour. What is the capacity of the
tank? 32. A, B and C can complete a piece of work in 10, 20 and
(A) 120 ltrs (B) 60 ltrs 40 days respectively. They work on a rotation basis with A
(C) 54 ltrs (D) None of these working on the first day, B on the second, C on the third,
then again A on the fourth day and so on. In how many
24. If four men, or three women, or two children can com-
days will the work be completed? ______
plete a work in 183 days, then how long would it take
for three men, four women, and six children working 33. A boy is trying to cover a distance of 100 m up a ramp. He
together to finish the work? ______ days takes a jump forward and covers 2 m, but every time he
jumps forward he also slips backwards by 1 m. In all, how
25. 20 cows and 40 goats can be kept for 10 days for ` 460.
many jumps would be required to cover the distance?
What would be the cost of keeping 50 cows and 30 goats
(A) 99 (B) 100
for 12 days if the cost of keeping 5 goats is the same as the
(C) 98 (D) None of these
Difficulty Level-2: Moderate

cost of keeping 1 cow?

(A) ` 888 (B) ` 965 34. A piece of work can be completed by ten men in a
(C) ` 1007 (D) ` 1104 certain number of days. If there were two men less, it
would have taken three more days to complete the work.
26. Mahesh, Suresh and Naresh together can complete a
In how many days can 24 men complete the same work?
work in 4 days. The wages paid to Mahesh, Suresh and
______
Naresh for completing the work are ` 6300, ` 7350 and
` 8400 respectively. Find the number of days in which 35. N filling pipes, P1, P2, … PN (where N > 10), are attached
Naresh alone can complete the work. ______ to a tank. The rate of filling of Pi, where i > 1, is equal to
thrice the combined rate of filling of all the lower num-
27. A and B can complete a work in 10 days and 20 days re-
bered pipes. If the time taken by PN – 3 to fill the tank is
spectively. If they work on alternate days, then find the
128 minutes, find the time (in minutes) taken by PN to
least number of days in which the work will be complet-
fill the tank. ______
ed. ______
36. Ram, Shyam and Tarun can complete a work in 24 days,
28. Four persons A, B, C and D produced 256 pieces of item
36 days and 30 days respectively. All the three started
P in 8 hours. B is twice as efficient as A. D is 25% less
working together. After x days, Ram left. Shyam left x
efficient than A but is three times as efficient as C. How
days before the work was completed. The work was com-
many pieces of P did B produce?
pleted at the end of t days. If x and t are integers, the
(A) 128 (B) 64 (C) 48 (D) 16
value of t is ______.
29. A piece of work can be completed by 20 men in 25 days.
37. Twenty four men working 9 hours a day can complete
20 men start the work together.
a piece of work in 35 days. In how many days can thirty
1. If starting from the second day, one person leaves at men working 8 hours a day complete twice the original
the end of every day, then what fraction of the work work? ______
was completed? ______ /50

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 TIME AND WORK 3.261

38. 25 men take 20 days to construct a wall 10 m high. How 44. 40 boys can earn ` 40,000 by completing a work in 50
many men would be required to construct a similar wall, days. Some men accompanied 30 boys and the work was
which is 8 m high, if the work is planned to be completed completed in 20 days. What is the difference in the total
in 10 days? ______ earnings of the men and the boys? (in ` ) ______.
39. Shiven and Shalini agreed to do a job for ` 180. They can 45. Six women and two men together take 10 days to com-
complete the work together in 12 days. If they complete plete a work. Four women and eight men together can
the work in 9 days with the help of Sonia, then what is complete the same work in 5 days. Find the number of
the share of Shiven, given that Shalini can complete the days in which six men and eight women together can
entire work on her own in 18 days? complete the work.
(A) ` 30 (B) ` 45 (C) ` 50 (D) ` 6
46. 9 men and 24 women can do a work in 8 days. 8 men and
40. Every day A, B and C work for 6 hours, 8 hours and 10 32 boys can do the same work in 9 days. If 30 women can
hours respectively. A sum of money is sufficient to pay for do the work in 12 days, then how many boys can do the
the daily wages of A, B and C for 15 days, 10 days and 5 same work in 18 days? ______
days respectively. For how many complete days can all of
47. Anil and Bala agreed to complete a work in 14 days. They
them be paid if they work for 8 hours a day?
also agreed to forfeit thrice the amount of wages corre-
(A) 3 (B) 2 (C) 4 (D) 5
sponding to the unfinished if they failed to complete the
41. 64 men working 8 hours a day plan to complete a piece work in 14 days. As they could not complete the work in
of work in 9 days. However 5 days later they find that they 3
had completed only 40% of the work. They now wanted 14 days, they lost th of the amount that they would
8
to finish the remaining portion of the work in 4 more
have together received had they completed the work in
days. Find the number of hours per day that they need to
time. If Anil alone can complete the work in 80 days, the
work in order to achieve the target. ______
time that Bala alone would take to complete the work is
42. A man takes 80 days to complete a job. Four men, 8 wom- (A) 24 days (B) 20 days
en and 4 machines take 5 days to complete the job. Four (C) 30 days (D) 40 days
men, 1 woman and 2 machines take 10 days to complete
48. Two men are as efficient as 3 women who are as efficient

Difficulty Level-2: Moderate

the job. Find the time taken by a woman to complete the
as 4 machines. The number of men, women and ma-
job (in days).
chines that worked together and completed a job is in
(A) 90 (B) 100
the ratio 3 : 4 : 5. They are paid a total of ` 4900 for the
(C) 105 (D) 120
job. Find the total share of women (in ` ).
(A) 1200 (B) 1800
3 (C) 1500 (D) 1600
43. P and Q are filling pipes. If the bottom th of the tank is
4
49. A, B and C working alone, can complete a work in 8, 12
filled by P and the rest is filled by Q, the tank will be filled
and 24 days respectively. All the three of them started the
3 work and then A left after 2 days. B left after another 3
in 45 minutes. If the bottom th of the tank is filled by
4 days and C then completed the remaining work. If the
Q and the rest is filled by P, the tank will be filled in 39 total wages earned by the three of them are ` 6000, find
minutes. Find the time taken by the two pipes working the share of A.
together to fill the tank. (A) ` 1,000 (B) ` 2,500
(C) ` 2,000 (D) ` 1,500
4 6
(A) 18 minutes (B) 24 minutes 50. Sixty men can complete a piece of work in 80 days. They
7 7
started the work but after 20 days, ten of them left. After
4 2 20 more days, another ten men left. In how many days
(C) 20 minutes (D) 16 minutes will the remaining men complete the remaining work?
7 7
______

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