Time And Work
Class 8th Mathematics RS Aggarwal Solution
- Rajan can do a piece of work in 24 days while Amit can do it in 30 days. In how…
- Ravi can do a piece of work in 15 hours while Raman can do it in 12 hours. How…
- A and B, working together can finish a piece of work in 6 days, while A alone…
- Two motor mechanics, Raju and Siraj, working together can overhaul a scooter in…
- A, B and C can do a piece of work in 10 days, 12 days and 15 days respectively.…
- A can do a piece of work in 24 hours while B alone can do it in 16 hours. If A,…
- A, B and C working together can finish a piece of work in 8 hours. A alone can…
- A and B can finish a piece of work in 16 days and 12 days respectively. A…
- A can do a piece of work in 14 days while B can do it in 21 days. They began…
- A can do 2/3 of a certain work in 16 days and B can do 1/4 of the same work in…
- A, B and C can do a piece of work in 15, 12 and 20 days respectively. They…
- A and B can do a piece of work in 18 days; B and C can do it in 24 days while…
- A and B can do a piece of work in 12 days, B and C in 15 days, and C and A in…
- Pipes A and B can fill an empty tank in 10 hours and 15 hours respectively. If…
- Pipe A can fill an empty tank in 5 hours while pipe B can empty the full tank…
- Three taps A, B and C can fill an overhead tank in 6 hours, 8 hours and 12…
- A cistern has two inlets A and B which can fill it in 12 minutes and 15…
- A pipe can fill a cistern in 9 hours. Due to a leak in its bottom, the cistern…
- Pipe A can fill a cistern in 6 hours and pipe B can fill it in 8 hours. Both…
- A alone can do a piece of work in 10 days and B alone can do it in 15 days. In…
- A man can do a piece of work in 5 days. He and his son working together can…
- A can do a job in 16 days and B can do the same job in 12 days. With the help…
- To complete a work, A takes 50% more time than B. If together they take 18 days…
- A works twice as fast as B. If both of them can together finish a piece of work…
- A alone can finish a piece of work in 10 days which B alone can do in 15 days.…
- The rates of working of A and B are in the ratio 3 : 4. The number of days…
- A and B together can do a piece of work in 12 days; B and C can do it in 20…
- 3 men or 5 women can do a work in 12 days. How long will 6 men and 5 women take…
- A can do a piece of work in 15 days. B is 50% more efficient than A. B can…
- A does 20% less work than B. If A can finish a piece of work in 7 1/2 hours,…
- A can do a piece of work in 20 days while B alone can do In 12 days. B worked…
- A can do a piece of work in 25 days. While B alone can do in 20 days. A…
- Two pipes can fill a tank in 20 minutes,end 30 minutes respectively. If both…
- A tap can fill a cistern in 8 hours and another tap can empty the full cistern…
- A pump can fill a tank in 2 hours. Due to a leak in the tank it takes 2 1/3…
- Two pipes can fill a tank in 10 hours and 12 hours respectively, while a third…
- A can do a piece of work in 10 days while B alone can do it in 15 days. In how many…
- A and B can do a piece of work in 15 days; B and C in 12 days; C and A in 20 days. How…
- Tap A can fill a cistern in 8 hours and tap B can empty it in 12 hours. How long will…
- 2 men or 3 women can do a piece of work in 16 days. In how many days can 4 men and 6…
- A pipe can fill a cistern in 9 hours. Due to a leak in its bottom, the cistern fills up…
- The rates of working of two taps A and B are in the ratio 2:3. The ratio of the time…
- A can finish a piece of work in 12 hours while B can finish it in 15 hours. How long…
- A can do a piece of work in 14 days and B is 40% more efficient than A. In how many…
- A pump can fill a cistern in 2 hours. Due to a leak in the tank it takes 2 1/3 hours to…
- A works twice as fast as B. If both of them can together finish a piece of work in 12…
- Fill in the blanks. (i) A tap can fill a tank in 6 hours. The part of the tank filled…
Exercise 13a
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?
Answer:
Number of days Rajan required do a piece of work : 24
Number of days Amit required do a piece of work : 30
Work done by Rajan in one day: 
Work done by Amit in one day: 
Work done by Rajan and Amit together in one day: 
= 
= 
They can do the work together in 
days = 
days
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?
Answer:
Number of hours Ravi required do a piece of work : 15 hours
Number of hours Raman required do a piece of work : 12 hours
Work done by Ravi in one hour: 
Work done by Raman in one hour: 
Work done by Ravi and Raman together in one hour: 
= 
= 
They can do the work together in 
hours = 
= 6 hours 40 min
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?
Answer:
Number of days A required do a piece of work : 9 days
Let number of days B required do a piece of work : X days
Number of hours required by A and B together to do a piece of work : 6 days
Work done by A in one day: 
Work done by B in one day: 
Work done by A and B together in a day : 
Work done by A and B together in one day : 
= 
=
⇒ 6X + 54 = 9X
⇒ 3X = 54
⇒ X = 54/3 = 18
B can do the work 18 days
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?
Answer:
Number of hours Raju required to overhaul a scooter : 15 hours
Let number of hours siraj required to overhaul a scooter : X hours
Number of hours required by Raju and Siraj together to do a piece of work : 6 hours
Work done by Raju in one hour:
Work done by Siraj in one hour:
Work done by Raju and Siraj together in a one hour :
Work done by Raju and Siraj together in one hour : 
= 
=
⇒ 6X +90 = 15X
⇒ 9X = 90
⇒ X = 
= 10 hours
Siraj can do the work 10 hours.
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?
Answer:
Number of days A required do a piece of work : 10
Number of days B required do a piece of work : 12
Number of days C required do a piece of work : 15
Work done by A in one day: 
Work done by B in one day:
Work done by C in one day:
Work done by A, B and C together in one day: 
= 
= 
They can do the work together in 4 days .
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?
Answer:
Number of hours A required do a piece of work : 24 hours
Number of hours B required do a piece of work : 16 hours
Let number of hours C required to do a piece of work : X hours
Number of hours required by A, B and C together to do a piece of work : 8 hours
Work done by A in one hour:
Work done by B in one hour: 
Work done by C in one hour:
Work done by A, B and C together in a one hour : 
Work done by A, B and C together in one hour : 
= 
= 
=
=
⇒ 40X +384 = 48X
⇒ 8X = 384
⇒ X = 
= 48 hours
Siraj can do the work 48 hours.
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?
Answer:
Number of hours A required do a piece of work : 20 hours
Number of hours B required do a piece of work : 24 hours
Let number of hours C required to do a piece of work : X hours
Number of hours required by A, B and C together to do a piece of work : 8 hours
Work done by A in one hour: 
Work done by B in one hour:
Work done by C in one hour:
Work done by A, B and C together in a one hour :
Work done by A, B and C together in one hour : 
= 
= 
=
=
⇒ 88X +960 = 120X
⇒ 32X = 960
⇒ X = 
= 30 hours
C can do the work 30 hours.
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.
Answer:
Number of days A required do a piece of work : 16
Number of days B required do a piece of work : 12
Work done by A in one day:
Work done by B in one day:
A works alone for 2 days, so work completed by A in 2 days : 
=
Work left = 
Work done by A and B together in one day: 
= 
They can do the work together in 
days .
But 
th of the work is done by both A and B
Time required to complete th of the work together by A and B : 
6 days
Time taken to finish the work 6 + 2 = 8days ( here 2 is added because work is done by A alone).
Total time taken to finish the work: 8days
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?
Answer:
Number of days A required do a piece of work : 14 days
Number of days B required do a piece of work : 21 days
Work done by A in one day: 
Work done by B in one day: 
Work done by A and B together in one day: 
= 
They can do the work together in 
days .
A and B worked together for 6 days, so work completed by A and B in 6 days : 
Work left = 
Number of days taken by B to complete the left over work : 
= 6 ( here 21 is days required by B to complete a piece of work).
Time taken to finish the work: 6 + 6 = 12 days.
Total time taken to finish the work: 12 days
Question 10.
A can do 
of a certain work in 16 days and B can do 
of the same work in 3 days. In how many days can both finish the work, working together?
Answer:
A can do 
of a work in 16 days
B can do 
of a work in 3 days
Work done by A in one day: 
Work done by B in one day: 
Work done by A and B together in one day: 
= 
They can do the work together in 8 days.
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?
Answer:
Number of days A required do a piece of work : 15 days
Number of days B required do a piece of work : 12 days
Number of days C required do a piece of work : 20 days
Work done by A in one day:
Work done by B in one day:
Work done by C in one day:
Work done by A, B and C together in one day: 
= 
They can do the work together in 5 days.
A, B and C worked together for 2 days, so work completed by A, B and C in 2 days : 2
= 
Work left = 
Work done by A and B together in one day: =
They can do the work together in days.
Number of days taken by A and B to complete the left over work : 
= 4 ( here is days required by A and B to complete the work).
Time taken to finish the left over work: 4 days.
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?
Answer:
Number of days required by A and B to finish the work : 18 days
Number of days required by A and B to finish the work : 24 days
Number of days required by A and B to finish the work : 36 days
Work done by A and B in one day: 
Work done by B and C in one day:
Work done by C and A in one day: 
Work done by (A and B) , (B and C ) and (C and A) in one day that is work done by
(A +B) + (B + C) + (C + A) = 2(A+B+C) = 
Work done by A, B and C = 
=
They can do the work in 16 days
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?
Answer:
Number of days required by A and B to finish the work : 12 days
Number of days required by A and B to finish the work : 15 days
Number of days required by A and B to finish the work : 20 days
Work done by A and B in one day:
Work done by B and C in one day:
Work done by C and A in one day:
Work done by (A and B) , (B and C ) and (C and A) in one day that is work done by
(A +B) + (B + C) + (C + A) = 2(A+B+C) = 
Work done by A, B and C = 
=
A ‘s one day work = (A +B + C ) ‘s one day work – (B + C) ‘s one day work = – =
A alone can complete the work in 30 days.
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?
Answer:
Number of hours Pipe A requires to fill an empty tank : 10 hours
Number of hours Pipe B requires to fill an empty tank : 15 hours
Amount of water filled by Pipe A in empty tank in one hour:
Amount of water filled by Pipe B in one hour:
Amount of water filled by Pipe A and Pipe B together in one hour: 
= 
=
They can fill the tank together in 6 hours.
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?
Answer:
Number of hours Pipe A requires to fill an empty tank : 5 hours
Number of hours Pipe B requires to empty the full tank : 6 hours
Amount of water filled by Pipe A in empty tank in one hour:
Amount of water Pipe B empties in one hour:
Amount of water filled by Pipe A and Pipe B together in one hour: 
= =
They can fill the tank together in 30 hours.
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?
Answer:
Number of hours tap A requires to fill the tank : 6
Number of hours tap B requires to fill the tank : 8
Number of hours tap C requires to fill the tank : 12
Amount of water filled by tap A in one hour:
Amount of water filled by tap B in one hour:
Amount of water filled by tap C in one hour:
Amount of water filled by taps A, B and C together in one hour: 
= 
= 
They can fill the tank together in 
hours = 
hours = 2 hours 40 min.
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?
Answer:
Number of hours inlet A requires to fill the cistern : 12 min = 
= hours
Number of hours inlet B requires to fill the cistern : 15 min = = hours
Number of hours outlet C requires to empty the cistern : 10 min = 
= hours
Part of the cistern filled by inlet A in one hour: 5
Part of the cistern filled by inlet B in one hour: 4
Part of the cistern emptied by outlet C in one hour: 6
Work done by pipes A, B and C together in one hour: 5 + 4 – 6 = 3
They can fill the cistern together in 
hours = 20 min
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?
Answer:
A pipe can fill a cistern in: 9 hours
Let a leak empty the cistern in: X hours
Due to the leak time taken to fill the cistern : 10 hours
Part of the cistern filled by pipe in one hour:
Part of the cistern emptied by leak in one hour:
=
= 
= 
X = 90 hours
Therefore the leak will empty the 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?
Answer:
Pipe A can fill the cistern in : 6 hours
Pipe B can fill the cistern in : 8 hours
Part of cistern filled by pipe A in one hour:
Part of cistern filled by pipe B in one hour:
Part of cistern filled by pipe A and pipe B together in one hour: 
= 
They can fill the cistern together in 
hours.
Pipes A and B filled cistern together for 2 hours,
So part of the cistern filled pipes by A and B in 2 hours : 
= 
Part of cistern which is empty = 
Number of hours taken by pipe B to fill left over part of cistern : 
= 
( here 8 is hours required by pipe B to fill the remaining part of the cistern).
Time taken by pipe B to fill the remaining part of the cistern: = 
= 3 hours 20 min
Exercise 13b
Question 1.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
Answer:
Number of days A required do a piece of work : 10 days
Number of days B required do a piece of work : 15 days
Work done by A in one day:
Work done by B in one day:
Work done by A and B together in one day: = =
They can do the work together in 6 days
Question 2.
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
days
B. 7 days
C. 7 days
D. 8 days
Answer:
Number of days the man requires to do a piece of work : 5 days
Let Number of days his son requires to do a piece of work : X days
Number of days required by the man and his son together to do a piece of work : 3 days
Work done by the man in one hour:
Work done by his son in one hour:
Work done by the man and his Son together in a one hour :
Work done by the man and his son together in one hour : 
= 
=
⇒ 3X + 15 = 5X
⇒ 2X = 15
⇒ X = 
= 
days
Son alone can do the work days.
Question 3.
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 days
D. 48 days
Answer:
Number of days A required do a piece of work : 16 days
Number of days B required do a piece of work : 12 days
Let number of days C required to do a piece of work : X days
Number of days required by A, B and C together to do a piece of work: 6 days
Work done by A in one day:
Work done by B in one day:
Work done by C in one day:
Work done by A, B and C together in a one day:
Work done by A, B and C together in one hour : 
= 
= 
=
=
⇒ 42X +288 = 48X
⇒ 6X = 288
⇒ X = 
= 48 days
C alone can do the work 48 days.
Question 4.
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
Answer:
Let number of days B required a work be x
Then number of days A takes to complete the work is : 
= 1.5x
Work done by A in one day: 
= 
Work done by B in one day: 
Number of days taken by A and B to do the work together: 18 days
Work done by A and B together in one day:
That is : = +
= 
X = 
= 30
B alone will take 30 days to complete the work.
Question 5.
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
Answer:
Work done by A in one day: 2x
Work done by B in one day: x
Number of days taken by A and B to do the work together: 12 days
Work done by A and B together in one day:
= 2x + x
= 3x
X =
Here X is Work done by B in one day
B alone will take 36 days to complete the work.
Question 6.
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
Answer:
Number of days A required do a piece of work : 10 days
Number of days B required do a piece of work : 15 days
Work done by A in one day:
Work done by B in one day:
Work done by A and B together in a one day: + = =
A and B together take 6 days to complete the work.
A’s share of work is : X 6 = 
We know that wages are divided on basis of the share of the work
A’s wage is X 3000 = 1800
Question 7.
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
Answer:
We know that number of days taken to work is reciprocal of the rate of the work.
Work done by A:
Work done by B:
Ratio of work done is 
Question 8.
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
days
Answer:
Number of days required by A and B to finish the work : 12 days
Number of days required by A and B to finish the work : 20 days
Number of days required by A and B to finish the work : 15 days
Work done by A and B in one day:
Work done by B and C in one day:
Work done by C and A in one day:
Work done by (A and B) , (B and C ) and (C and A) in one day that is work done by
(A +B) + (B + C) + (C + A) = 2(A+B+C) = 
Work done by A, B and C = =
They can do the work in 10 days
Question 9.
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
Answer:
Number of days required by 3 men to finish the work : 12 days
Number of days required by 5 women to finish the work : 12 days
Number of days required by 1 man to finish the work : 3 x 12 = 36 days
Number of days required by 1 woman to finish the work : 5 x 12 = 60 days
Work done by a man in one day:
Work done by a woman in one day: 
Work done by 6 men in one day: 6 x =
Work done by 5 women in one day: 5 x =
Work done by 6 men and 5 women together in one day: + = 
=
6 men and 5 women together take 4 days to complete the work.
Question 10.
A can do a piece of work in 15 days. B is 50% more efficient than A. B can finish it in
A. 10 days
B. 7 days
C. 12 days
D. 10 days
Answer:
Number of days required by A to finish the work : 15 days
Work done by A in one day:
B can work 50% more efficiently than A,
B's one day work = 150% of 
= 
B alone can complete the work in 10 days.
Question 11.
A does 20% less work than B. If A can finish a piece of work in 7 hours, then B can finish it in
A. 5 hours
B. 5hours
C. 6 hours
D. 6 hours
Answer:
Number of hours taken by A to finish the work = hours = hours
Work done by A in one hour : 
Let number of hours taken by B to finish the work :
A can work 20% less than B that is 
= 
times of B’s work.
Here , : 1 = :
= 
X = 
= 6 hours.
Question 12.
A can do a piece of work in 20 days while 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
Answer:
Number of days A required do a piece of work : 20
Number of days B required do a piece of work : 12
Work done by A in one day:
Work done by B in one day:
B works alone for 9 days, so work completed by B in 9 days : 
= 
Work left = 
But th of the work is already done by B
Time required to complete the remaining th of the work by A : 
5 days
Time taken to finish the work 9 + 5 = 14 days
A can finish the remaining work in : 5 days
Question 13.
A can do a piece of work in 25 days. While 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 days
B. 15 days
C. 6
hours
D. 25 hours
Answer:
Number of hours A required do a piece of work : 25
Number of hours B required do a piece of work : 20
Work done by A in one hour: 
Work done by B in one hour:
A works alone for 10 hours, so work completed by A in 10 hours : 10
=
Work left =
Work done by A and B together in one hour: 
= 
They can do the work together in 
hours.
But th of the work is done by both A and B
Time required to complete th of the work together by A and B : 
hours
Time taken to finish the work: = 
hours
Question 14.
Two pipes can fill a tank in 20 minutes,end 30 minutes respectively. If both the pipes are opened simultaneously then the lank will he filled
A. 10 minutes
B. 12 minutes
C. 15 minutes
D. 25 minutes
Answer:
Number of minutes Pipe A requires to fill an empty tank : 20 minutes
Number of minutes Pipe B requires to fill an empty tank : 30 minutes
Amount of water filled by Pipe A in empty tank in one minute:
Amount of water filled by Pipe B in one minute:
Amount of water filled by Pipe A and Pipe B together in one minute: 
= 
=
They can fill the tank together in 12 minutes.
Question 15.
A tap can fill a cistern in 8 hours and another tap can empty the full cistern in 16 hours. If both the taps are open then time taken to fill the cistern is
A. 5
hours
B. 10 hours
C. 16 hours
D. 20 hours
Answer:
Number of hours Tap A requires to fill an empty tank : 8 hours
Number of hours Tap B requires to empty the full tank : 16 hours
Amount of water filled by Tap A in empty tank in one hour:
Amount of water Tap B empties in one hour:
Amount of water filled by Tap A and Tap B together in one hour: 
=
They can fill the tank together in 16 hours.
Question 16.
A pump can fill a tank in 2 hours. Due to a leak in the tank it takes 2hours to fill the tank. The leak can empty the full tank in
A. 2 hours
B. 7 hours
C. 8 hours
D. 14 hours
Answer:
A pipe can fill a cistern in: 2 hours
Let a leak empty the cistern in: X hours
Due to the leak time taken to fill the cistern : 2
= 
hours
Part of the cistern filled by pipe in one hour: 
Part of the cistern emptied by leak in one hour:
= 
= 
= 
X = 14 hours
Therefore the leak will empty the cistern in 14 hours.
Question 17.
Two pipes can fill a tank in 10 hours and 12 hours respectively, while a third pipe empties the full tank in 20 hours. If all the three pipes operate simultaneously, in how much time will the tank be full?
A. 7 hrs 15 min
B. 7 hrs 30 min
C. 7 hrs 45 min
D. 8 hrs
Answer:
Number of hours inlet A requires to fill the cistern : 10 hours
Number of hours inlet B requires to fill the cistern : 12 hours
Number of hours outlet C requires to empty the cistern : 20 hours
Part of the cistern filled by inlet A in one hour:
Part of the cistern filled by inlet B in one hour:
Part of the cistern emptied by outlet C in one hour:
Work done by pipes A, B and C together in one hour: + – = 
=
They can fill the cistern together in hours = 7 hrs 30 min
Cce Test Paper-13
Question 1.A can do a piece of work in 10 days while B alone can do it in 15 days. In how many days can both finish the same work?
Answer:
Number of days A required do a piece of work : 10
Number of days B required do a piece of work : 15
Work done by A in one day:
Work done by B in one day:
Work done by A and B together in one day: 
= =
They can do the work together in 6 days.
Question 2.
A and B can do a piece of work in 15 days; B and C in 12 days; C and A in 20 days. How many days will be taken by A, B and C working together to finish the work?
Answer:
Number of days required by A and B to finish the work : 15 days
Number of days required by A and B to finish the work : 12 days
Number of days required by A and B to finish the work : 20 days
Work done by A and B in one day:
Work done by B and C in one day:
Work done by C and A in one day:
Work done by (A and B) , (B and C ) and (C and A) in one day that is work done by
(A +B) + (B + C) + (C + A) = 2(A+B+C) = 
Work done by A, B and C = =
They can do the work in 10 days
Question 3.
Tap A can fill a cistern in 8 hours and tap B can empty it in 12 hours. How long will it take to fill the cistern if both of them are opened together?
Answer:
Number of hours Tap A requires to fill an empty tank : 8 hours
Number of hours Tap B requires to empty the full tank : 12 hours
Amount of water filled by Tap A in empty tank in one hour:
Amount of water Tap B empties in one hour:
Amount of water filled by Tap A and Tap B together in one hour: 
=
They can fill the tank together in 24 hours.
Question 4.
2 men or 3 women can do a piece of work in 16 days. In how many days can 4 men and 6 women do the same work?
Answer:
Number of days required by 2 men to finish the work : 16 days
Number of days required by 3 women to finish the work : 16 days
Number of days required by 1 man to finish the work : 2 x 16 = 32 days
Number of days required by 1 woman to finish the work : 3 x 16 = 48 days
Work done by a man in one day: 
Work done by a woman in one day: 
Work done by 4 men in one day: 4 x =
Work done by 6 women in one day: 6 x =
Work done by 4 men and 6 women together in one day: + = 
=
4 men and 6 women together take 4 days to complete the work.
Question 5.
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?
Answer:
A pipe can fill a cistern in: 9 hours
Let a leak empty the cistern in: X hours
Due to the leak time taken to fill the cistern : 10 hours
Part of the cistern filled by pipe in one hour:
Part of the cistern emptied by leak in one hour:
=
=
=
X = 90 hours
Therefore the leak will empty the cistern in 90 hours.
Question 6.
The rates of working of two taps A and B are in the ratio 2:3. The ratio of the time taken by A and B respectively to fill a given cistern is
A. 2 : 3
B. 3 : 2
C. 4 : 9
D. 9 : 4
Answer:
We know that number of days taken to work is reciprocal of the rate of the work.
Rates of working of two taps A and B are in the ratio 2:3
Work done by A:
Work done by B:
Ratio of work done is : = 3:2
Question 7.
A can finish a piece of work in 12 hours while B can finish it in 15 hours. How long will both take to finish it, working together?
A. 9 hours
B. 6
hours
C. 6
hours
D. 8
hours
Answer:
Number of hours A required do a piece of work: 12
Number of hours B required do a piece of work : 15
Work done by A in one hour:
Work done by B in one hour:
Work done by A and B together in one hour: 
= =
They can do the work together in hours = 6
hours.
Question 8.
A can do a piece of work in 14 days and B is 40% more efficient than A. In how many days can B finish it?
A. 10 days
B. 7
days
C. 5
days
D. 5
days
Answer:
Number of days required by A to finish the work : 14 days
Work done by A in one day:
B can work 40% more efficiently than A,
B's one day work = 140% of 
= 
B alone can complete the work in 10 days.
Question 9.
A pump can fill a cistern in 2 hours. Due to a leak in the tank it takes 2hours to fill it. The leak can empty the full tank in
A. 7 hours
B. 14 hours
C. 8 hours
D. 3 hours
Answer:
A pipe can fill a cistern in: 2 hours
Let a leak empty the cistern in: X hours
Due to the leak time taken to fill the cistern : 2
= hours
Part of the cistern filled by pipe in one hour:
Part of the cistern emptied by leak in one hour:
=
=
=
X = 14 hours
Therefore the leak will empty the cistern in 14 hours.
Question 10.
A works twice as fast as B. If both of them can together finish a piece of work in 12 hours, then B alone can do it in
A. 24 hours
B. 27 hours
C. 36 hours
D. 18 hours
Answer:
Work done by A in one hour: 2x
Work done by B in one hour: x
Number of days taken by A and B to do the work together: 12 hours
Work done by A and B together in one hour:
= 2x + x
= 3x
X =
Here X is Work done by B in one hour
B alone will take 36 hours to complete the work.
Question 11.
Fill in the blanks.
(i) A tap can fill a tank in 6 hours. The part of the tank filled in 1 hour is……………
(ii) A and B working together can finish a piece of work in 6 hours while A alone can do it in 9 hours. B alone can do it in ……….. hours.
(iii) A can do a work in 16 hours and B alone can do it in 24 hours. If A, B and C working together can finish it in 8 hours, then C alone can finish it in ……….. hours.
(iv) If A's one day's work is 
, then A can finish the whole work in……… days.
Answer:
(i)
If A can do a piece of work in n days, then A can do 
of the work in on day
(ii) 18
Number of hours A required do a piece of work : 9 hours
Let number of hours B required do a piece of work : X hours
Number of hours required by A and B together to do a piece of work : 6 hours
Work done by A in one hour:
Work done by B in one hour:
Work done by A and B together in a hour:
Work done by A and B together in one hour: = =
=
⇒ 6X +54 = 9X
⇒ 3X = 54
⇒ X = 
= 18
B can do the work 18 hours
(iii) 48
Number of hours A required do a piece of work : 16 hours
Number of hours B required do a piece of work : 24 hours
Let number of hours C required to do a piece of work : X hours
Number of hours required by A, B and C together to do a piece of work : 8 hours
Work done by A in one hour:
Work done by B in one hour:
Work done by C in one hour:
Work done by A, B and C together in a one hour :
Work done by A, B and C together in one hour : 
= = =
=
⇒ 40X +384 = 48X
⇒ 8X = 384
⇒ X = = 48 hours
C can do the work 48 hours.
(iv)
If A can do a piece of work in n days, then A can do of the work in on day
=