Time and Work | Mathematics (Maths) Class 8 PDF Download

 Page 1


Question:1
Rajan can do a piece of work in 24 days while Amit can do it in 30 days. In how many days can they complete it, if they work together?
Solution:
Work done by Rajan in 1 day = 
1
24
Work done by Amit in 1 day = 
1
30
Work done by Amit and Rajan together in 1 day = 
1
24
+
1
30
=
54
720
=
3
40
? They can complete the work in 
40
3
 days, i. e. , 13
Question:2
Ravi can do a piece of work in 15 hours while Raman can do it in 12 hours. How long will both take to do it, working together?
Solution:
Time taken by Ravi = 15 hTime taken by Raman = 12 hWork done per hour by Ravi = 
1
15
Work done per hour by Raman = 
1
12
Work done per hour by Ravi and Raman together = 
1
15
+
1
12
Question:3
A and B, working together can finish a piece of work in 6 days, while A alone can do it in 9 days. How much time will B alone take to finish it?
Solution:
Time taken by A and B to finish a piece of work = 6 daysWork done per day by A ?and B = 
1
6
Time taken by A ?alone = 9 daysWork done per day by A ?alone = 
1
9
Work done per day by B
Question:4
Two motor mechanics, Raju and Siraj, working together can overhaul a scooter in 6 hours. Raju alone can do the job in 15 hours. In how many hours can Siraj alone do it?
Solution:
Time taken by Raju = 15 hWork done by Raju in 1 h =
1
15
Time taken by Raju and Siraj working together = 6 hWork done by Raju and Siraj in 1 h = 
1
6
Work done by Siraj in 1 h = work
Question:5
A, B and C can do a piece of work in 10 days, 12 days and 15 days respectively. How long will they take to finish it if they work together?
Solution:
Time taken by A to complete the work = 10 daysTime taken by B ?to complete the work = 12 daysTime taken by C ?to complete the work = 15 daysWork done per day by A =
1
10
Work done
Question:6
A can do a piece of work in 24 hours while B alone can do it in 16 hours. If A, B and C working together can finish it in 8 hours, in how many hours can C alone finish the work?
Solution:
Time taken by A to complete the piece of work = 24 hWork done per hour by A = 
1
24
Time taken by B to complete the work = 16 hWork done per hour by B ? = 
1
16
Total time taken when A
Question:7
A, B and C working together can finish a piece of work in 8 hours. A alone can do it in 20 hours and B alone can do it in 24 hours. In how many hours will C alone do the same work?
Solution:
A can complete the work in 20 h. Work done per hour by A =
1
20
B can complete the work in 24 h. Work done per hour by B =
1
24
It takes 8 h to complete the work if A, B and C work together.
Question:8
A and B can finish a piece of work in 16 days and 12 days respectively. A started the work and worked at it for 2 days. He was then joined by B. Find the total time taken to finish the
work.
Solution:
Time taken by A ?to complete the work = 16 daysWork done per day by A = 
1
16
Time taken by B to complete the work = 12 daysWork done per day by B = 
1
12
Work done per day by A and
Question:9
A can do a piece of work in 14 days while B can do it in 21 days. They began together and worked at it for 6 days. Then, A fell ill and B had to complete the remaining work alone. In how
many days was the work completed?
Solution:
Time taken by A to complete the work = 14 daysWork done by A ?in one day = 
1
14
Time taken by B to complete the work = 21 daysWork done by B in one day = 
1
21
Work done jointly by
Question:10
A can do 
2
3
of a certain work in 16 days and B can do 
1
4
of the same work in 3 days. In how many days can both finish the work, working together?
Solution:
A can do 
2
3
 work in 16 daysSo, work done by ?A ?in one day = 
2
48
=
1
24
B can do 
1
4
 work in 3 daysSo, work done by B ?in one day =
1
12
Work done jointly by A and B in one day =
1
24
 + 
1
12
 = 
1 + 2
24
Question:11
A, B and C can do a piece of work in 15, 12 and 20 days respectively. They started the work together, but C left after 2 days. In how many days will the remaining work be completed by
A and B?
Solution:
Time taken by A = 15 daysTime taken by B = 12 daysTime taken by C = 20 daysWork d by A in one day =
1
15
Work done by B in one day = 
1
12
Work done by C in one day =
1
20
Work don
Question:12
A and B can do a piece of work in 18 days; B and C can do it in 24 days while C and A can finish it in 36 days. In how many days can A, B, C finish it, if they all work together?
Solution:
Time needed by A and B to finish the work = 18 daysTime needed by B and C to finish the work = 24 daysTime needed by C and A to finish the work = 36 daysWork done by A and B in one
(
Page 2


Question:1
Rajan can do a piece of work in 24 days while Amit can do it in 30 days. In how many days can they complete it, if they work together?
Solution:
Work done by Rajan in 1 day = 
1
24
Work done by Amit in 1 day = 
1
30
Work done by Amit and Rajan together in 1 day = 
1
24
+
1
30
=
54
720
=
3
40
? They can complete the work in 
40
3
 days, i. e. , 13
Question:2
Ravi can do a piece of work in 15 hours while Raman can do it in 12 hours. How long will both take to do it, working together?
Solution:
Time taken by Ravi = 15 hTime taken by Raman = 12 hWork done per hour by Ravi = 
1
15
Work done per hour by Raman = 
1
12
Work done per hour by Ravi and Raman together = 
1
15
+
1
12
Question:3
A and B, working together can finish a piece of work in 6 days, while A alone can do it in 9 days. How much time will B alone take to finish it?
Solution:
Time taken by A and B to finish a piece of work = 6 daysWork done per day by A ?and B = 
1
6
Time taken by A ?alone = 9 daysWork done per day by A ?alone = 
1
9
Work done per day by B
Question:4
Two motor mechanics, Raju and Siraj, working together can overhaul a scooter in 6 hours. Raju alone can do the job in 15 hours. In how many hours can Siraj alone do it?
Solution:
Time taken by Raju = 15 hWork done by Raju in 1 h =
1
15
Time taken by Raju and Siraj working together = 6 hWork done by Raju and Siraj in 1 h = 
1
6
Work done by Siraj in 1 h = work
Question:5
A, B and C can do a piece of work in 10 days, 12 days and 15 days respectively. How long will they take to finish it if they work together?
Solution:
Time taken by A to complete the work = 10 daysTime taken by B ?to complete the work = 12 daysTime taken by C ?to complete the work = 15 daysWork done per day by A =
1
10
Work done
Question:6
A can do a piece of work in 24 hours while B alone can do it in 16 hours. If A, B and C working together can finish it in 8 hours, in how many hours can C alone finish the work?
Solution:
Time taken by A to complete the piece of work = 24 hWork done per hour by A = 
1
24
Time taken by B to complete the work = 16 hWork done per hour by B ? = 
1
16
Total time taken when A
Question:7
A, B and C working together can finish a piece of work in 8 hours. A alone can do it in 20 hours and B alone can do it in 24 hours. In how many hours will C alone do the same work?
Solution:
A can complete the work in 20 h. Work done per hour by A =
1
20
B can complete the work in 24 h. Work done per hour by B =
1
24
It takes 8 h to complete the work if A, B and C work together.
Question:8
A and B can finish a piece of work in 16 days and 12 days respectively. A started the work and worked at it for 2 days. He was then joined by B. Find the total time taken to finish the
work.
Solution:
Time taken by A ?to complete the work = 16 daysWork done per day by A = 
1
16
Time taken by B to complete the work = 12 daysWork done per day by B = 
1
12
Work done per day by A and
Question:9
A can do a piece of work in 14 days while B can do it in 21 days. They began together and worked at it for 6 days. Then, A fell ill and B had to complete the remaining work alone. In how
many days was the work completed?
Solution:
Time taken by A to complete the work = 14 daysWork done by A ?in one day = 
1
14
Time taken by B to complete the work = 21 daysWork done by B in one day = 
1
21
Work done jointly by
Question:10
A can do 
2
3
of a certain work in 16 days and B can do 
1
4
of the same work in 3 days. In how many days can both finish the work, working together?
Solution:
A can do 
2
3
 work in 16 daysSo, work done by ?A ?in one day = 
2
48
=
1
24
B can do 
1
4
 work in 3 daysSo, work done by B ?in one day =
1
12
Work done jointly by A and B in one day =
1
24
 + 
1
12
 = 
1 + 2
24
Question:11
A, B and C can do a piece of work in 15, 12 and 20 days respectively. They started the work together, but C left after 2 days. In how many days will the remaining work be completed by
A and B?
Solution:
Time taken by A = 15 daysTime taken by B = 12 daysTime taken by C = 20 daysWork d by A in one day =
1
15
Work done by B in one day = 
1
12
Work done by C in one day =
1
20
Work don
Question:12
A and B can do a piece of work in 18 days; B and C can do it in 24 days while C and A can finish it in 36 days. In how many days can A, B, C finish it, if they all work together?
Solution:
Time needed by A and B to finish the work = 18 daysTime needed by B and C to finish the work = 24 daysTime needed by C and A to finish the work = 36 daysWork done by A and B in one
(
Question:13
A and B can do a piece of work in 12 days, B and C in 15 days, and C and A in 20 days. How much time will A alone take to finish the job?
Solution:
A +B can complete the work in 12 days. B +C ?can complete the work in 15 days. C +A can complete the work in 20 days. A +B 's 1 day work = 
1
12
B +C 's 1 day work =
1
15
C
Question:14
Pipes A and B can fill an empty tank in 10 hours and 15 hours respectively. If both are opened together in the empty tank, how much time will they take to fill it completely?
Solution:
A can fill a tank in 10 hours. B can fill a tank in 15 hours. Pipe A fills 
1
10
 of the tank in one hour.Pipe B fills 
1
15
of the tank in one hour.Part of tank filled by pipes A and B together = 
1
10
+
1
15
=
Question:15
Pipe A can fill an empty tank in 5 hours while pipe B can empty the full tank in 6 hours. If both are opened at the same time in the empty tank, how much time will they take to fill it up
completely?
Solution:
Pipe A can fill a tank in 5 hours. Pipe B can empty a full tank in 6 hours. Pipe A fills 
1
5
 of the tank in one hour.Pipe B empties 
1
6
 of the tank in one hour.Part of the tank filled in one hour using both pipes A and B 
Question:16
Three taps A, B and C can fill an overhead tank in 6 hours, 8 hours and 12 hours respectively. How long would the three taps take to fill the empty tank, if all of them are opened
together?
Solution:
Time taken by tap A to fill the tank = 6 hoursTime taken by tap B to fill the tank = 8 hoursTime taken by tap C to fill the tank = 12 hoursA fills 
1
6
 of the tank in one hour.B fills 
1
8
 of the tank
Question:17
A cistern has two inlets A and B which can fill it in 12 minutes and 15 minutes respectively. An outlet C can empty the full cistern in 10 minutes. If all the three pipes are opened
together in the empty tank, how much time will they take to fill the tank completely?
Solution:
Inlet A can fill the cistern in 12 minutes. Inlet B can fill the cistern in 15 minutes. Outlet C empties the filled cistern in 10 minutes. Part of the cistern filled by inlet A in one minute = 
1
12
Part of the cistern filled by inlet B in one minute
Question:18
A pipe can fill a cistern in 9 hours. Due to a leak in its bottom, the cistern fills up in 10 hours. If the cistern is full, in how much time will it be emptied by the leak?
Solution:
A ?pipe can fill a cistern in 9 hours. Part of the cistern filled by the pipe in one hour = 
1
9
Let the leak empty the cistern in x hours. Part of the cistern emptied by the leak in one hour = -
1
x
 
The leak will empty the filled cistern in 90 hours.
Question:19
Pipe A can fill a cistern in 6 hours and pipe B can fill it in 8 hours. Both the pipes are opened and after two hours, pipe A is closed. How much time will B take to fill the remaining part of
the tank?
Solution:
Pipe A can fill a cistern in 6 hours. Pipe B can fill a cistern in 8 hours. Part of the cistern filled by pipe A in one hour = 
1
6
Part of the cistern filled by pipe B in one hour = 
1
8
Part of the cistern filled by pipes A and B in one hour
Question:20
Tick
? the correct answer:
A alone can do a piece of work in 10 days and B alone can do it in 15 days. In how many days will A and B together do the same work?
a
5 days
b
6 days
c
8 days
d
9 days
Solution:
b
6 days
A can do a work in 10 days. A's 1 day work = 
1
10
B can do a work in 15 days. B's 1 day work = 
1
15
A +B 's 1 day work = 
1
10
+
1
15
=
5
30
=
1
6
A and B together will take 6 days to complete the work
Question:21
Tick
? the correct answer:
A man can do a piece of work in 5 days. He and his son working together can finish it in 3 days. In how many days can the son do it alone?
a
6
1
2
days
b
7 days
c
7
1
2
days
( ) ( ) ( ) ( ) ( ) (
(
( )
Page 3


Question:1
Rajan can do a piece of work in 24 days while Amit can do it in 30 days. In how many days can they complete it, if they work together?
Solution:
Work done by Rajan in 1 day = 
1
24
Work done by Amit in 1 day = 
1
30
Work done by Amit and Rajan together in 1 day = 
1
24
+
1
30
=
54
720
=
3
40
? They can complete the work in 
40
3
 days, i. e. , 13
Question:2
Ravi can do a piece of work in 15 hours while Raman can do it in 12 hours. How long will both take to do it, working together?
Solution:
Time taken by Ravi = 15 hTime taken by Raman = 12 hWork done per hour by Ravi = 
1
15
Work done per hour by Raman = 
1
12
Work done per hour by Ravi and Raman together = 
1
15
+
1
12
Question:3
A and B, working together can finish a piece of work in 6 days, while A alone can do it in 9 days. How much time will B alone take to finish it?
Solution:
Time taken by A and B to finish a piece of work = 6 daysWork done per day by A ?and B = 
1
6
Time taken by A ?alone = 9 daysWork done per day by A ?alone = 
1
9
Work done per day by B
Question:4
Two motor mechanics, Raju and Siraj, working together can overhaul a scooter in 6 hours. Raju alone can do the job in 15 hours. In how many hours can Siraj alone do it?
Solution:
Time taken by Raju = 15 hWork done by Raju in 1 h =
1
15
Time taken by Raju and Siraj working together = 6 hWork done by Raju and Siraj in 1 h = 
1
6
Work done by Siraj in 1 h = work
Question:5
A, B and C can do a piece of work in 10 days, 12 days and 15 days respectively. How long will they take to finish it if they work together?
Solution:
Time taken by A to complete the work = 10 daysTime taken by B ?to complete the work = 12 daysTime taken by C ?to complete the work = 15 daysWork done per day by A =
1
10
Work done
Question:6
A can do a piece of work in 24 hours while B alone can do it in 16 hours. If A, B and C working together can finish it in 8 hours, in how many hours can C alone finish the work?
Solution:
Time taken by A to complete the piece of work = 24 hWork done per hour by A = 
1
24
Time taken by B to complete the work = 16 hWork done per hour by B ? = 
1
16
Total time taken when A
Question:7
A, B and C working together can finish a piece of work in 8 hours. A alone can do it in 20 hours and B alone can do it in 24 hours. In how many hours will C alone do the same work?
Solution:
A can complete the work in 20 h. Work done per hour by A =
1
20
B can complete the work in 24 h. Work done per hour by B =
1
24
It takes 8 h to complete the work if A, B and C work together.
Question:8
A and B can finish a piece of work in 16 days and 12 days respectively. A started the work and worked at it for 2 days. He was then joined by B. Find the total time taken to finish the
work.
Solution:
Time taken by A ?to complete the work = 16 daysWork done per day by A = 
1
16
Time taken by B to complete the work = 12 daysWork done per day by B = 
1
12
Work done per day by A and
Question:9
A can do a piece of work in 14 days while B can do it in 21 days. They began together and worked at it for 6 days. Then, A fell ill and B had to complete the remaining work alone. In how
many days was the work completed?
Solution:
Time taken by A to complete the work = 14 daysWork done by A ?in one day = 
1
14
Time taken by B to complete the work = 21 daysWork done by B in one day = 
1
21
Work done jointly by
Question:10
A can do 
2
3
of a certain work in 16 days and B can do 
1
4
of the same work in 3 days. In how many days can both finish the work, working together?
Solution:
A can do 
2
3
 work in 16 daysSo, work done by ?A ?in one day = 
2
48
=
1
24
B can do 
1
4
 work in 3 daysSo, work done by B ?in one day =
1
12
Work done jointly by A and B in one day =
1
24
 + 
1
12
 = 
1 + 2
24
Question:11
A, B and C can do a piece of work in 15, 12 and 20 days respectively. They started the work together, but C left after 2 days. In how many days will the remaining work be completed by
A and B?
Solution:
Time taken by A = 15 daysTime taken by B = 12 daysTime taken by C = 20 daysWork d by A in one day =
1
15
Work done by B in one day = 
1
12
Work done by C in one day =
1
20
Work don
Question:12
A and B can do a piece of work in 18 days; B and C can do it in 24 days while C and A can finish it in 36 days. In how many days can A, B, C finish it, if they all work together?
Solution:
Time needed by A and B to finish the work = 18 daysTime needed by B and C to finish the work = 24 daysTime needed by C and A to finish the work = 36 daysWork done by A and B in one
(
Question:13
A and B can do a piece of work in 12 days, B and C in 15 days, and C and A in 20 days. How much time will A alone take to finish the job?
Solution:
A +B can complete the work in 12 days. B +C ?can complete the work in 15 days. C +A can complete the work in 20 days. A +B 's 1 day work = 
1
12
B +C 's 1 day work =
1
15
C
Question:14
Pipes A and B can fill an empty tank in 10 hours and 15 hours respectively. If both are opened together in the empty tank, how much time will they take to fill it completely?
Solution:
A can fill a tank in 10 hours. B can fill a tank in 15 hours. Pipe A fills 
1
10
 of the tank in one hour.Pipe B fills 
1
15
of the tank in one hour.Part of tank filled by pipes A and B together = 
1
10
+
1
15
=
Question:15
Pipe A can fill an empty tank in 5 hours while pipe B can empty the full tank in 6 hours. If both are opened at the same time in the empty tank, how much time will they take to fill it up
completely?
Solution:
Pipe A can fill a tank in 5 hours. Pipe B can empty a full tank in 6 hours. Pipe A fills 
1
5
 of the tank in one hour.Pipe B empties 
1
6
 of the tank in one hour.Part of the tank filled in one hour using both pipes A and B 
Question:16
Three taps A, B and C can fill an overhead tank in 6 hours, 8 hours and 12 hours respectively. How long would the three taps take to fill the empty tank, if all of them are opened
together?
Solution:
Time taken by tap A to fill the tank = 6 hoursTime taken by tap B to fill the tank = 8 hoursTime taken by tap C to fill the tank = 12 hoursA fills 
1
6
 of the tank in one hour.B fills 
1
8
 of the tank
Question:17
A cistern has two inlets A and B which can fill it in 12 minutes and 15 minutes respectively. An outlet C can empty the full cistern in 10 minutes. If all the three pipes are opened
together in the empty tank, how much time will they take to fill the tank completely?
Solution:
Inlet A can fill the cistern in 12 minutes. Inlet B can fill the cistern in 15 minutes. Outlet C empties the filled cistern in 10 minutes. Part of the cistern filled by inlet A in one minute = 
1
12
Part of the cistern filled by inlet B in one minute
Question:18
A pipe can fill a cistern in 9 hours. Due to a leak in its bottom, the cistern fills up in 10 hours. If the cistern is full, in how much time will it be emptied by the leak?
Solution:
A ?pipe can fill a cistern in 9 hours. Part of the cistern filled by the pipe in one hour = 
1
9
Let the leak empty the cistern in x hours. Part of the cistern emptied by the leak in one hour = -
1
x
 
The leak will empty the filled cistern in 90 hours.
Question:19
Pipe A can fill a cistern in 6 hours and pipe B can fill it in 8 hours. Both the pipes are opened and after two hours, pipe A is closed. How much time will B take to fill the remaining part of
the tank?
Solution:
Pipe A can fill a cistern in 6 hours. Pipe B can fill a cistern in 8 hours. Part of the cistern filled by pipe A in one hour = 
1
6
Part of the cistern filled by pipe B in one hour = 
1
8
Part of the cistern filled by pipes A and B in one hour
Question:20
Tick
? the correct answer:
A alone can do a piece of work in 10 days and B alone can do it in 15 days. In how many days will A and B together do the same work?
a
5 days
b
6 days
c
8 days
d
9 days
Solution:
b
6 days
A can do a work in 10 days. A's 1 day work = 
1
10
B can do a work in 15 days. B's 1 day work = 
1
15
A +B 's 1 day work = 
1
10
+
1
15
=
5
30
=
1
6
A and B together will take 6 days to complete the work
Question:21
Tick
? the correct answer:
A man can do a piece of work in 5 days. He and his son working together can finish it in 3 days. In how many days can the son do it alone?
a
6
1
2
days
b
7 days
c
7
1
2
days
( ) ( ) ( ) ( ) ( ) (
(
( )
d
8 days
Solution:
c
 7
1
2
 days
A man can do a work in 5 days. The man's 1 day work = 
1
5
The man and the son can do the work in 3 days. The man and his son's 1 day work =
1
3
Let the son's 1 day work be 
1
x
. Therefore,
1
3
Question:22
Tick
? the correct answer:
A can do a job in 16 days and B can do the same job in 12 days. With the help of C, they can finish the job in 6 days only. Then, C alone can finish it in
a
34 days
b
22 days
c
36 dyas
d
48 days
Solution:
d
48 days
A can do a job in 16 days. B can do the job in 12 days. Suppose C can do the job in x days. A's 1 day work = 
1
16
B's 1 day work = 
1
12
C's 1 day work = 
1
x
A, B and C together can complete
Question:23
Tick
? the correct answer:
To complete a work, A takes 50% more time than B. If together they take 18 days to complete the work, how much time shall B take to do it?
a
30 days
b
35 days
c
40 days
d
45 days
Solution:
a
30 days
Let B ?take x days to complete the work. Then A takes x +
50
100
x = 1. 5xA's 1 day's work = 
1
1.5x
 = 
2
3x
B's 1 day's work = 
1
x
A +B ?takes 18 days to complete the work. A +B 's 1 day's ne
Question:24
Tick
? the correct answer:
A works twice as fast as B. If both of them can together finish a piece of work in 12 days, then B alone can do it in
a
24 days
b
27 days
c
36 days
d
48 days
Solution:
c
36 days
Let A take x days to complete the work. Then B takes 2x days to complete the work. A's 1 day's work =
1
x
B's 1 day's work =
1
2x
A and B take 12 days to complete the work. Net work done by
Question:25
Tick
? the correct answer:
A alone can finish a piece of work in 10 days which B alone can do in 15 days. If they work together and finish it, then out of total wages of Rs 3000, A will get
a
Rs 1200
b
Rs 1500
c
Rs 1800
d
Rs 2000
Solution:
c
Rs. 1800
Since the wage distribution will follow the work distribution ratio, we have:
Work done by A in 1 day =
1
10
( ) ( ) ( )
Page 4


Question:1
Rajan can do a piece of work in 24 days while Amit can do it in 30 days. In how many days can they complete it, if they work together?
Solution:
Work done by Rajan in 1 day = 
1
24
Work done by Amit in 1 day = 
1
30
Work done by Amit and Rajan together in 1 day = 
1
24
+
1
30
=
54
720
=
3
40
? They can complete the work in 
40
3
 days, i. e. , 13
Question:2
Ravi can do a piece of work in 15 hours while Raman can do it in 12 hours. How long will both take to do it, working together?
Solution:
Time taken by Ravi = 15 hTime taken by Raman = 12 hWork done per hour by Ravi = 
1
15
Work done per hour by Raman = 
1
12
Work done per hour by Ravi and Raman together = 
1
15
+
1
12
Question:3
A and B, working together can finish a piece of work in 6 days, while A alone can do it in 9 days. How much time will B alone take to finish it?
Solution:
Time taken by A and B to finish a piece of work = 6 daysWork done per day by A ?and B = 
1
6
Time taken by A ?alone = 9 daysWork done per day by A ?alone = 
1
9
Work done per day by B
Question:4
Two motor mechanics, Raju and Siraj, working together can overhaul a scooter in 6 hours. Raju alone can do the job in 15 hours. In how many hours can Siraj alone do it?
Solution:
Time taken by Raju = 15 hWork done by Raju in 1 h =
1
15
Time taken by Raju and Siraj working together = 6 hWork done by Raju and Siraj in 1 h = 
1
6
Work done by Siraj in 1 h = work
Question:5
A, B and C can do a piece of work in 10 days, 12 days and 15 days respectively. How long will they take to finish it if they work together?
Solution:
Time taken by A to complete the work = 10 daysTime taken by B ?to complete the work = 12 daysTime taken by C ?to complete the work = 15 daysWork done per day by A =
1
10
Work done
Question:6
A can do a piece of work in 24 hours while B alone can do it in 16 hours. If A, B and C working together can finish it in 8 hours, in how many hours can C alone finish the work?
Solution:
Time taken by A to complete the piece of work = 24 hWork done per hour by A = 
1
24
Time taken by B to complete the work = 16 hWork done per hour by B ? = 
1
16
Total time taken when A
Question:7
A, B and C working together can finish a piece of work in 8 hours. A alone can do it in 20 hours and B alone can do it in 24 hours. In how many hours will C alone do the same work?
Solution:
A can complete the work in 20 h. Work done per hour by A =
1
20
B can complete the work in 24 h. Work done per hour by B =
1
24
It takes 8 h to complete the work if A, B and C work together.
Question:8
A and B can finish a piece of work in 16 days and 12 days respectively. A started the work and worked at it for 2 days. He was then joined by B. Find the total time taken to finish the
work.
Solution:
Time taken by A ?to complete the work = 16 daysWork done per day by A = 
1
16
Time taken by B to complete the work = 12 daysWork done per day by B = 
1
12
Work done per day by A and
Question:9
A can do a piece of work in 14 days while B can do it in 21 days. They began together and worked at it for 6 days. Then, A fell ill and B had to complete the remaining work alone. In how
many days was the work completed?
Solution:
Time taken by A to complete the work = 14 daysWork done by A ?in one day = 
1
14
Time taken by B to complete the work = 21 daysWork done by B in one day = 
1
21
Work done jointly by
Question:10
A can do 
2
3
of a certain work in 16 days and B can do 
1
4
of the same work in 3 days. In how many days can both finish the work, working together?
Solution:
A can do 
2
3
 work in 16 daysSo, work done by ?A ?in one day = 
2
48
=
1
24
B can do 
1
4
 work in 3 daysSo, work done by B ?in one day =
1
12
Work done jointly by A and B in one day =
1
24
 + 
1
12
 = 
1 + 2
24
Question:11
A, B and C can do a piece of work in 15, 12 and 20 days respectively. They started the work together, but C left after 2 days. In how many days will the remaining work be completed by
A and B?
Solution:
Time taken by A = 15 daysTime taken by B = 12 daysTime taken by C = 20 daysWork d by A in one day =
1
15
Work done by B in one day = 
1
12
Work done by C in one day =
1
20
Work don
Question:12
A and B can do a piece of work in 18 days; B and C can do it in 24 days while C and A can finish it in 36 days. In how many days can A, B, C finish it, if they all work together?
Solution:
Time needed by A and B to finish the work = 18 daysTime needed by B and C to finish the work = 24 daysTime needed by C and A to finish the work = 36 daysWork done by A and B in one
(
Question:13
A and B can do a piece of work in 12 days, B and C in 15 days, and C and A in 20 days. How much time will A alone take to finish the job?
Solution:
A +B can complete the work in 12 days. B +C ?can complete the work in 15 days. C +A can complete the work in 20 days. A +B 's 1 day work = 
1
12
B +C 's 1 day work =
1
15
C
Question:14
Pipes A and B can fill an empty tank in 10 hours and 15 hours respectively. If both are opened together in the empty tank, how much time will they take to fill it completely?
Solution:
A can fill a tank in 10 hours. B can fill a tank in 15 hours. Pipe A fills 
1
10
 of the tank in one hour.Pipe B fills 
1
15
of the tank in one hour.Part of tank filled by pipes A and B together = 
1
10
+
1
15
=
Question:15
Pipe A can fill an empty tank in 5 hours while pipe B can empty the full tank in 6 hours. If both are opened at the same time in the empty tank, how much time will they take to fill it up
completely?
Solution:
Pipe A can fill a tank in 5 hours. Pipe B can empty a full tank in 6 hours. Pipe A fills 
1
5
 of the tank in one hour.Pipe B empties 
1
6
 of the tank in one hour.Part of the tank filled in one hour using both pipes A and B 
Question:16
Three taps A, B and C can fill an overhead tank in 6 hours, 8 hours and 12 hours respectively. How long would the three taps take to fill the empty tank, if all of them are opened
together?
Solution:
Time taken by tap A to fill the tank = 6 hoursTime taken by tap B to fill the tank = 8 hoursTime taken by tap C to fill the tank = 12 hoursA fills 
1
6
 of the tank in one hour.B fills 
1
8
 of the tank
Question:17
A cistern has two inlets A and B which can fill it in 12 minutes and 15 minutes respectively. An outlet C can empty the full cistern in 10 minutes. If all the three pipes are opened
together in the empty tank, how much time will they take to fill the tank completely?
Solution:
Inlet A can fill the cistern in 12 minutes. Inlet B can fill the cistern in 15 minutes. Outlet C empties the filled cistern in 10 minutes. Part of the cistern filled by inlet A in one minute = 
1
12
Part of the cistern filled by inlet B in one minute
Question:18
A pipe can fill a cistern in 9 hours. Due to a leak in its bottom, the cistern fills up in 10 hours. If the cistern is full, in how much time will it be emptied by the leak?
Solution:
A ?pipe can fill a cistern in 9 hours. Part of the cistern filled by the pipe in one hour = 
1
9
Let the leak empty the cistern in x hours. Part of the cistern emptied by the leak in one hour = -
1
x
 
The leak will empty the filled cistern in 90 hours.
Question:19
Pipe A can fill a cistern in 6 hours and pipe B can fill it in 8 hours. Both the pipes are opened and after two hours, pipe A is closed. How much time will B take to fill the remaining part of
the tank?
Solution:
Pipe A can fill a cistern in 6 hours. Pipe B can fill a cistern in 8 hours. Part of the cistern filled by pipe A in one hour = 
1
6
Part of the cistern filled by pipe B in one hour = 
1
8
Part of the cistern filled by pipes A and B in one hour
Question:20
Tick
? the correct answer:
A alone can do a piece of work in 10 days and B alone can do it in 15 days. In how many days will A and B together do the same work?
a
5 days
b
6 days
c
8 days
d
9 days
Solution:
b
6 days
A can do a work in 10 days. A's 1 day work = 
1
10
B can do a work in 15 days. B's 1 day work = 
1
15
A +B 's 1 day work = 
1
10
+
1
15
=
5
30
=
1
6
A and B together will take 6 days to complete the work
Question:21
Tick
? the correct answer:
A man can do a piece of work in 5 days. He and his son working together can finish it in 3 days. In how many days can the son do it alone?
a
6
1
2
days
b
7 days
c
7
1
2
days
( ) ( ) ( ) ( ) ( ) (
(
( )
d
8 days
Solution:
c
 7
1
2
 days
A man can do a work in 5 days. The man's 1 day work = 
1
5
The man and the son can do the work in 3 days. The man and his son's 1 day work =
1
3
Let the son's 1 day work be 
1
x
. Therefore,
1
3
Question:22
Tick
? the correct answer:
A can do a job in 16 days and B can do the same job in 12 days. With the help of C, they can finish the job in 6 days only. Then, C alone can finish it in
a
34 days
b
22 days
c
36 dyas
d
48 days
Solution:
d
48 days
A can do a job in 16 days. B can do the job in 12 days. Suppose C can do the job in x days. A's 1 day work = 
1
16
B's 1 day work = 
1
12
C's 1 day work = 
1
x
A, B and C together can complete
Question:23
Tick
? the correct answer:
To complete a work, A takes 50% more time than B. If together they take 18 days to complete the work, how much time shall B take to do it?
a
30 days
b
35 days
c
40 days
d
45 days
Solution:
a
30 days
Let B ?take x days to complete the work. Then A takes x +
50
100
x = 1. 5xA's 1 day's work = 
1
1.5x
 = 
2
3x
B's 1 day's work = 
1
x
A +B ?takes 18 days to complete the work. A +B 's 1 day's ne
Question:24
Tick
? the correct answer:
A works twice as fast as B. If both of them can together finish a piece of work in 12 days, then B alone can do it in
a
24 days
b
27 days
c
36 days
d
48 days
Solution:
c
36 days
Let A take x days to complete the work. Then B takes 2x days to complete the work. A's 1 day's work =
1
x
B's 1 day's work =
1
2x
A and B take 12 days to complete the work. Net work done by
Question:25
Tick
? the correct answer:
A alone can finish a piece of work in 10 days which B alone can do in 15 days. If they work together and finish it, then out of total wages of Rs 3000, A will get
a
Rs 1200
b
Rs 1500
c
Rs 1800
d
Rs 2000
Solution:
c
Rs. 1800
Since the wage distribution will follow the work distribution ratio, we have:
Work done by A in 1 day =
1
10
( ) ( ) ( )
Work done by B in 1 day =
1
15
Net work done by A +B
in 1 day =
1
10
+
1
15
=
5
30
=
1
6
i.e., A +B
will take 6 days to complete the work.
A's share of work in a day = 
1
10
÷
1
6
=
1
10
×
6
1
=
6
10
=
3
5
? A's wage = 
3
5
×3000 = Rs 1800
Question:26
Tick
? the correct answer:
The rates of working of A and B are in the ratio 3 : 4. The number of days taken by them to finish the work are in the ratio
a
3 : 4
b
9 : 16
c
4 : 3
d
16 : 9
Solution:
c
4:3
The number of days taken for working is the reciprocal of the rate of work.
i. e. , number of days taken =
1
rate of work
=
1
3
4
=
4
3
Question:27
Tick
? the correct answer:
A and B together can do a piece of work in 12 days; B and C can do it in 20 days while C and A can do it in 15 days. A, B and C all working together can do it in
a
6 days
b
9 days
c
10 days
d
10
1
2
days
Solution:
c
10 days
A +B can do a work in 12 days. B +C can do a work in 20 days. C +A ?can do a work in 15 days. Now, we have: Work done by A +B in 1 day = 
1
12
Work done by B +C in 1 day
Question:28
Tick
? the correct answer:
3 men or 5 women can do a work in 12 days. How long will 6 men and 5 women take to do it?
a
6 days
b
5 days
c
4 days
d
3 days
Solution:
c
4 days
Three men can complete the work in 12 days. Thus, one man can complete the work in 36 days. Rate of work done by one man in 1 day =
1
36
Similarly, rate of work done by one woman in
The work can be completed in 4 days.
Question:29
Tick
? the correct answer:
A can do a piece of work in 15 days. B is 50% more efficient than A. A can finish it in
a
10 days
b
( ) ( ) ( ) ( ) ( )
Page 5


Question:1
Rajan can do a piece of work in 24 days while Amit can do it in 30 days. In how many days can they complete it, if they work together?
Solution:
Work done by Rajan in 1 day = 
1
24
Work done by Amit in 1 day = 
1
30
Work done by Amit and Rajan together in 1 day = 
1
24
+
1
30
=
54
720
=
3
40
? They can complete the work in 
40
3
 days, i. e. , 13
Question:2
Ravi can do a piece of work in 15 hours while Raman can do it in 12 hours. How long will both take to do it, working together?
Solution:
Time taken by Ravi = 15 hTime taken by Raman = 12 hWork done per hour by Ravi = 
1
15
Work done per hour by Raman = 
1
12
Work done per hour by Ravi and Raman together = 
1
15
+
1
12
Question:3
A and B, working together can finish a piece of work in 6 days, while A alone can do it in 9 days. How much time will B alone take to finish it?
Solution:
Time taken by A and B to finish a piece of work = 6 daysWork done per day by A ?and B = 
1
6
Time taken by A ?alone = 9 daysWork done per day by A ?alone = 
1
9
Work done per day by B
Question:4
Two motor mechanics, Raju and Siraj, working together can overhaul a scooter in 6 hours. Raju alone can do the job in 15 hours. In how many hours can Siraj alone do it?
Solution:
Time taken by Raju = 15 hWork done by Raju in 1 h =
1
15
Time taken by Raju and Siraj working together = 6 hWork done by Raju and Siraj in 1 h = 
1
6
Work done by Siraj in 1 h = work
Question:5
A, B and C can do a piece of work in 10 days, 12 days and 15 days respectively. How long will they take to finish it if they work together?
Solution:
Time taken by A to complete the work = 10 daysTime taken by B ?to complete the work = 12 daysTime taken by C ?to complete the work = 15 daysWork done per day by A =
1
10
Work done
Question:6
A can do a piece of work in 24 hours while B alone can do it in 16 hours. If A, B and C working together can finish it in 8 hours, in how many hours can C alone finish the work?
Solution:
Time taken by A to complete the piece of work = 24 hWork done per hour by A = 
1
24
Time taken by B to complete the work = 16 hWork done per hour by B ? = 
1
16
Total time taken when A
Question:7
A, B and C working together can finish a piece of work in 8 hours. A alone can do it in 20 hours and B alone can do it in 24 hours. In how many hours will C alone do the same work?
Solution:
A can complete the work in 20 h. Work done per hour by A =
1
20
B can complete the work in 24 h. Work done per hour by B =
1
24
It takes 8 h to complete the work if A, B and C work together.
Question:8
A and B can finish a piece of work in 16 days and 12 days respectively. A started the work and worked at it for 2 days. He was then joined by B. Find the total time taken to finish the
work.
Solution:
Time taken by A ?to complete the work = 16 daysWork done per day by A = 
1
16
Time taken by B to complete the work = 12 daysWork done per day by B = 
1
12
Work done per day by A and
Question:9
A can do a piece of work in 14 days while B can do it in 21 days. They began together and worked at it for 6 days. Then, A fell ill and B had to complete the remaining work alone. In how
many days was the work completed?
Solution:
Time taken by A to complete the work = 14 daysWork done by A ?in one day = 
1
14
Time taken by B to complete the work = 21 daysWork done by B in one day = 
1
21
Work done jointly by
Question:10
A can do 
2
3
of a certain work in 16 days and B can do 
1
4
of the same work in 3 days. In how many days can both finish the work, working together?
Solution:
A can do 
2
3
 work in 16 daysSo, work done by ?A ?in one day = 
2
48
=
1
24
B can do 
1
4
 work in 3 daysSo, work done by B ?in one day =
1
12
Work done jointly by A and B in one day =
1
24
 + 
1
12
 = 
1 + 2
24
Question:11
A, B and C can do a piece of work in 15, 12 and 20 days respectively. They started the work together, but C left after 2 days. In how many days will the remaining work be completed by
A and B?
Solution:
Time taken by A = 15 daysTime taken by B = 12 daysTime taken by C = 20 daysWork d by A in one day =
1
15
Work done by B in one day = 
1
12
Work done by C in one day =
1
20
Work don
Question:12
A and B can do a piece of work in 18 days; B and C can do it in 24 days while C and A can finish it in 36 days. In how many days can A, B, C finish it, if they all work together?
Solution:
Time needed by A and B to finish the work = 18 daysTime needed by B and C to finish the work = 24 daysTime needed by C and A to finish the work = 36 daysWork done by A and B in one
(
Question:13
A and B can do a piece of work in 12 days, B and C in 15 days, and C and A in 20 days. How much time will A alone take to finish the job?
Solution:
A +B can complete the work in 12 days. B +C ?can complete the work in 15 days. C +A can complete the work in 20 days. A +B 's 1 day work = 
1
12
B +C 's 1 day work =
1
15
C
Question:14
Pipes A and B can fill an empty tank in 10 hours and 15 hours respectively. If both are opened together in the empty tank, how much time will they take to fill it completely?
Solution:
A can fill a tank in 10 hours. B can fill a tank in 15 hours. Pipe A fills 
1
10
 of the tank in one hour.Pipe B fills 
1
15
of the tank in one hour.Part of tank filled by pipes A and B together = 
1
10
+
1
15
=
Question:15
Pipe A can fill an empty tank in 5 hours while pipe B can empty the full tank in 6 hours. If both are opened at the same time in the empty tank, how much time will they take to fill it up
completely?
Solution:
Pipe A can fill a tank in 5 hours. Pipe B can empty a full tank in 6 hours. Pipe A fills 
1
5
 of the tank in one hour.Pipe B empties 
1
6
 of the tank in one hour.Part of the tank filled in one hour using both pipes A and B 
Question:16
Three taps A, B and C can fill an overhead tank in 6 hours, 8 hours and 12 hours respectively. How long would the three taps take to fill the empty tank, if all of them are opened
together?
Solution:
Time taken by tap A to fill the tank = 6 hoursTime taken by tap B to fill the tank = 8 hoursTime taken by tap C to fill the tank = 12 hoursA fills 
1
6
 of the tank in one hour.B fills 
1
8
 of the tank
Question:17
A cistern has two inlets A and B which can fill it in 12 minutes and 15 minutes respectively. An outlet C can empty the full cistern in 10 minutes. If all the three pipes are opened
together in the empty tank, how much time will they take to fill the tank completely?
Solution:
Inlet A can fill the cistern in 12 minutes. Inlet B can fill the cistern in 15 minutes. Outlet C empties the filled cistern in 10 minutes. Part of the cistern filled by inlet A in one minute = 
1
12
Part of the cistern filled by inlet B in one minute
Question:18
A pipe can fill a cistern in 9 hours. Due to a leak in its bottom, the cistern fills up in 10 hours. If the cistern is full, in how much time will it be emptied by the leak?
Solution:
A ?pipe can fill a cistern in 9 hours. Part of the cistern filled by the pipe in one hour = 
1
9
Let the leak empty the cistern in x hours. Part of the cistern emptied by the leak in one hour = -
1
x
 
The leak will empty the filled cistern in 90 hours.
Question:19
Pipe A can fill a cistern in 6 hours and pipe B can fill it in 8 hours. Both the pipes are opened and after two hours, pipe A is closed. How much time will B take to fill the remaining part of
the tank?
Solution:
Pipe A can fill a cistern in 6 hours. Pipe B can fill a cistern in 8 hours. Part of the cistern filled by pipe A in one hour = 
1
6
Part of the cistern filled by pipe B in one hour = 
1
8
Part of the cistern filled by pipes A and B in one hour
Question:20
Tick
? the correct answer:
A alone can do a piece of work in 10 days and B alone can do it in 15 days. In how many days will A and B together do the same work?
a
5 days
b
6 days
c
8 days
d
9 days
Solution:
b
6 days
A can do a work in 10 days. A's 1 day work = 
1
10
B can do a work in 15 days. B's 1 day work = 
1
15
A +B 's 1 day work = 
1
10
+
1
15
=
5
30
=
1
6
A and B together will take 6 days to complete the work
Question:21
Tick
? the correct answer:
A man can do a piece of work in 5 days. He and his son working together can finish it in 3 days. In how many days can the son do it alone?
a
6
1
2
days
b
7 days
c
7
1
2
days
( ) ( ) ( ) ( ) ( ) (
(
( )
d
8 days
Solution:
c
 7
1
2
 days
A man can do a work in 5 days. The man's 1 day work = 
1
5
The man and the son can do the work in 3 days. The man and his son's 1 day work =
1
3
Let the son's 1 day work be 
1
x
. Therefore,
1
3
Question:22
Tick
? the correct answer:
A can do a job in 16 days and B can do the same job in 12 days. With the help of C, they can finish the job in 6 days only. Then, C alone can finish it in
a
34 days
b
22 days
c
36 dyas
d
48 days
Solution:
d
48 days
A can do a job in 16 days. B can do the job in 12 days. Suppose C can do the job in x days. A's 1 day work = 
1
16
B's 1 day work = 
1
12
C's 1 day work = 
1
x
A, B and C together can complete
Question:23
Tick
? the correct answer:
To complete a work, A takes 50% more time than B. If together they take 18 days to complete the work, how much time shall B take to do it?
a
30 days
b
35 days
c
40 days
d
45 days
Solution:
a
30 days
Let B ?take x days to complete the work. Then A takes x +
50
100
x = 1. 5xA's 1 day's work = 
1
1.5x
 = 
2
3x
B's 1 day's work = 
1
x
A +B ?takes 18 days to complete the work. A +B 's 1 day's ne
Question:24
Tick
? the correct answer:
A works twice as fast as B. If both of them can together finish a piece of work in 12 days, then B alone can do it in
a
24 days
b
27 days
c
36 days
d
48 days
Solution:
c
36 days
Let A take x days to complete the work. Then B takes 2x days to complete the work. A's 1 day's work =
1
x
B's 1 day's work =
1
2x
A and B take 12 days to complete the work. Net work done by
Question:25
Tick
? the correct answer:
A alone can finish a piece of work in 10 days which B alone can do in 15 days. If they work together and finish it, then out of total wages of Rs 3000, A will get
a
Rs 1200
b
Rs 1500
c
Rs 1800
d
Rs 2000
Solution:
c
Rs. 1800
Since the wage distribution will follow the work distribution ratio, we have:
Work done by A in 1 day =
1
10
( ) ( ) ( )
Work done by B in 1 day =
1
15
Net work done by A +B
in 1 day =
1
10
+
1
15
=
5
30
=
1
6
i.e., A +B
will take 6 days to complete the work.
A's share of work in a day = 
1
10
÷
1
6
=
1
10
×
6
1
=
6
10
=
3
5
? A's wage = 
3
5
×3000 = Rs 1800
Question:26
Tick
? the correct answer:
The rates of working of A and B are in the ratio 3 : 4. The number of days taken by them to finish the work are in the ratio
a
3 : 4
b
9 : 16
c
4 : 3
d
16 : 9
Solution:
c
4:3
The number of days taken for working is the reciprocal of the rate of work.
i. e. , number of days taken =
1
rate of work
=
1
3
4
=
4
3
Question:27
Tick
? the correct answer:
A and B together can do a piece of work in 12 days; B and C can do it in 20 days while C and A can do it in 15 days. A, B and C all working together can do it in
a
6 days
b
9 days
c
10 days
d
10
1
2
days
Solution:
c
10 days
A +B can do a work in 12 days. B +C can do a work in 20 days. C +A ?can do a work in 15 days. Now, we have: Work done by A +B in 1 day = 
1
12
Work done by B +C in 1 day
Question:28
Tick
? the correct answer:
3 men or 5 women can do a work in 12 days. How long will 6 men and 5 women take to do it?
a
6 days
b
5 days
c
4 days
d
3 days
Solution:
c
4 days
Three men can complete the work in 12 days. Thus, one man can complete the work in 36 days. Rate of work done by one man in 1 day =
1
36
Similarly, rate of work done by one woman in
The work can be completed in 4 days.
Question:29
Tick
? the correct answer:
A can do a piece of work in 15 days. B is 50% more efficient than A. A can finish it in
a
10 days
b
( ) ( ) ( ) ( ) ( )
7
1
2
days
c
12 days
d
10
1
2
days
Solution:
a
10 days
Work done by A in 1 day =
1
15
B is 50 % more efficient than A. ? Work done by B in 1 day =
150
100
×
1
15
=
1
10
Thus, B can complete the work in 10 days.
Question:30
Tick
? the correct answer:
A does 20% less work than B. If A can finish a piece of work in 7
1
2
hours, then B can finish it in
a
5 hours
b
5
1
2
hours
c
6 hours
d
6
1
2
hours
Solution:
c
6 hours
Time taken by A to finish the piece of work = 7
1
2
 hours =
15
2
 hoursWork done by A in 1 hour =
2
15
Let B take x hours to finish the work. Work done by B in 1 hours =
1
x
A can work 20 % ?less than
Question:31
Tick
? the correct answer:
A can do a piece of work in 20 days which B alone can do in 12 days. B worked at it for 9 days. A can finish the remaining work in
a
3 days
b
5 days
c
7 days
d
11 days
Solution:
b
5 days
A can complete the work in 20 days. Work done by A in 1 day =
1
20
B can complete the work in 12 days. Work done by B in 1 day =
1
12
In 9 days, B completes 
9
12
, i. e. , 
3
4
 of the work and leaves
Question:32
Tick
? the correct answer:
A can do a piece of work in 25 days, which B alone can do in 20 days. A started the work and was joined by B after 10 days. The work lasted for
a
12
1
2
days
b
15 days
c
16
2
3
days
d
14 days
Solution:
c
 
A can do the piece of work in 25 days. Work done by A in 1 day =
1
25
B can do the same work in 20 days. Work done by B in 1 day =
1
20
A alone completes 
10
25
, i, e. , 
2
5
 of the work in 10 days.
Question:33
Tick
? the correct answer:
Two pipes can fill a tank in 20 minutes and 30 minutes respectively. If both the pipes are opened simultaneously, then hte tank will be filled in
a
10 minutes
b