Time And Work
Class 8th Mathematics RD Sharma Solution
- Rakesh can do a piece of work in 20 days. How much work can he do in 4 days.…
- Rohan can paint 1/3 of a painting in 6 days. How many days will he take to…
- Anil can do a piece of work in 5 days and Ankur in 4 days. How long will they…
- Mohan takes 9 hours to mow a large lawn. He and Sohan together can mow in4…
- Sita can finish typing a 100 page document in 9 hours, Mita in 6 hours and Rita…
- A, B and C working together can do a piece of work in 8 hours. A alone can do…
- A and B can do a piece of work in 18 days, B and C in 24 days and A and C in 36…
- A and B can do a piece of work in 12 days; B and C in 15 days; C and A in 20…
- A, B and C can reap a field in 15 3/4 days; B, C and D in 14 days; C, D and A…
- A and B can polish the floors of a building in 10 days. A alone can do 1/4 th…
- A and B can finish a work in 20 days. A alone can do 1/5 th of the work in 12…
- A and B can do a piece of work in 20 days and B in 15 days. They work together…
- A can do a piece of work in 40 days and B in 45 days. They work together for…
- Aasheesh can paint his doll in 20 minutes and his sister Chinki can do so in…
- A and B can do a piece of work in 6 days and 4 days respectively. A started…
- 6 men can complete the electric fitting in a building in 7 days. How many days…
- 8 men can do a piece of work in 9 days. In how many days will 6 men do it?…
- Reema weaves 35 baskets in 25 days. In how many days will she weave 55…
- Neha types 75 pages in 14 hours. How many pages will she type in 20 hours?…
- If 12 boys earn Rs 840 in 7 days, what will 15 boys earn in 6 days?…
- If 25 men earn Rs 1000 in 10 days, how much will 15 men earn in 15 days?…
- Working 8 hours a day, Ashu can copy a book in 18 days. How many hours a day…
- If 9 girls can prepare 135 garlands in 3 hours, how many girls are needed to…
- A cistern can be filled by one tap in 8 hours, and by another in 4 hours. How…
- Two taps A and B can fill an overhead tank in 10 hours and 15 hours…
- A pipe can fill a cistern in 10 hours. Due to a leak in the bottom it is…
- A cistern has two inlets A and B which can fill it in 12 hours and 15 hours…
- A cistern can be filled by a tap in 4 hours and emptied by an outlet pipe in 6…
Exercise 11.1
Question 1.Rakesh can do a piece of work in 20 days. How much work can he do in 4 days.
Answer:
Given,
Time taken by Rakesh to do a piece of work = 20 day
∵Work done by Rakesh in 1 day = 
∴ work done by him in 4 days = 
Question 2.
Rohan can paint 
of a painting in 6 days. How many days will he take to complete painting?
Answer:
Given,
Number of days taken by Rohan for painting 
of painting = 6 days
∴Number of days taken by him to complete the painting = 
Question 3.
Anil can do a piece of work in 5 days and Ankur in 4 days. How long will they will do the same work, if they work together?
Answer:
Given,
Anil can do a piece of work in 5 days
Work done by him in 1 day = 
Ankur can do same work in 4 days
Work done by Ankur in 1 day = 
∵ Work done by both in 1 day = 
∴ Total work done in = 
Question 4.
Mohan takes 9 hours to mow a large lawn. He and Sohan together can mow in4 hours. How long will Sohan take to mow the lawn if he works alone?
Answer:
Given,
Mohan can mow a lawn in 9 hours.
Work done by Mohan in 1 hour = 
Mohan and Sohan can mow it together in = 4 hours
Work done by them together in 1 hour =
Work done by Sohan in 1 hour = (work done by both in 1 hour) – (work done by Mohan in 1 hr)
∴ Time taken by Sohan to complete the work = 
Question 5.
Sita can finish typing a 100 page document in 9 hours, Mita in 6 hours and Rita in 12 hours. How long will they take to type a 100 page document if they work together?
Answer:
Work done by Sita in 1 hour = 
Work done by Mita in 1 hour = 
Work done by Rita in 1 hour = 
Work done by them together in 1 hour = 
∴ Time taken by them to complete the work together = 
Question 6.
A, B and C working together can do a piece of work in 8 hours. A alone can do it in20 hours and B alone can do it in 24 hours. In how many hours will C alone do the same work?
Answer:
Given,
A can do a piece of work in 20 hours
Work done by A in 1 hour =
B can do same work in = 24 hours
Work done by B in 1 hour = 
A,B and C working together can do that work in = 8 hours
Work done by A, B, C together in 1 hour = 
∵ work done by C in 1 hour = (work done by A,B,C in 1 hour) – ( work done by A And B in 1 hr)
∴ Time taken by C to complete the work = 
Question 7.
A and B can do a piece of work in 18 days, B and C in 24 days and A and C in 36 days. In what time can they do it, all working together?
Answer:
Given,
A and B can do a piece of work in = 18 days
Work done by A and B in 1 day = 
B and C can do a piece of work in = 24 days
Work done by C and B in 1 day =
A and c can do a piece of work in = 36 days
Work done by A and C in 1 day = 
Now adding, we get,
2(A+B+C)’s 1 day work = 
A+B+C one day work = 
∴ A, B and C can finish the work in = 
Question 8.
A and B can do a piece of work in 12 days; B and C in 15 days; C and A in 20 days. How much time will A alone take to finish the work?
Answer:
A and B can do a piece of work in = 12 days
Work done by A and B in 1 day = 
B and C can do a piece of work in = 15 days
Work done by C and B in 1 day = 
A and c can do a piece of work in = 20 days
Work done by A and C in 1 day =
Now adding, we get,
2(A+B+C)’s 1 day work = 
A+B+C one day work = 
∵ A’s 1 day work = (A+B+C)’s 1 day work – ( B+C)’s 1 day work
= 
∴ A can finish the work in = 
Question 9.
A, B and C can reap a field in 
days; B, C and D in 14 days; C, D and A in 18 days; D, A and B in 21 days. In what time can A, B, C and D together reap it?
Answer:
Given,
A, B and C can reap the field in = 
days
B, C and D can reap it in = 14 days
C, D and A can reap it in = 18 days
D, A and B can reap it in = 21 days
So,
A, B and C’s 1 day work = 
B, C and D’s 1 day work = 
C, D and A’s 1 day work =
D, A and B’s 1 day work = 
Now, adding up,
3[A+B+C+D] = 
A+B+C+D = 
Thus A, B, C, D can finish the work in = 
days.
Question 10.
A and B can polish the floors of a building in 10 days. A alone can do 
th of it in 12 days. In how many days can B alone polish the floor?
Answer:
Given,
A and B can polish a building in = 10 days
A alone can do 
of it in 12 days
(A+B)’s 1 day work = 
A’s I day work = 
B’s 1 day work = (A+B)’s 1 day work – A’s 1 day work = 
Thus B can finish the work in = 
days.
Question 11.
A and B can finish a work in 20 days. A alone can do 
th of the work in 12 days. In how many days can B alone do it?
Answer:
Given,
A and B can finish a work in = 20 days
A can 
work in = 12 days
∴ A+ B ‘s 1 day work =
∴ A’s 1 day work = 
B’s 1 day work = (A+B)’s 1 day work – A’s 1 day work
= 
Thus B can finish the work in = 
Question 12.
A and B can do a piece of work in 20 days and B in 15 days. They work together for 2 days and then A goes away. In how many days will B finish the remaining work?
Answer:
Given,
A and B can do a piece of work in = 20 days
B can do it in = 15 days
∴ A and B’s 1 day work =
B’s 1 day work =
∵ A and B work for 2 days, hence work done by them in 2 days = 
Remaining work = 
∵ B do work in = 1 day
B do 1 complete work in = 
∴ B will do 
work in = 
days
Question 13.
A can do a piece of work in 40 days and B in 45 days. They work together for 10 days and then B goes away. In how many days will A finish the remaining work?
Answer:
Given,
A can do a piece of work in 40 days
B can do it in = 45 days
A’s 1 day work = 
B’s 1 day work = 
(A+B)’s 1 day work together = 
A+B’s 10 day work = 
Remaining work = 
∴ Remaining work will be done by A = 
days.
Question 14.
Aasheesh can paint his doll in 20 minutes and his sister Chinki can do so in 25 minutes. They paint the doll together for five minutes. At this juncture, they have a quarrel and Chinki withdraws from painting. In how many minutes will Aasheesh finish the painting of the remaining doll?
Answer:
Given,
Aasheesh can paint his doll in = 20 minutes
Chinki can paint the same in = 25 minutes
∵ Aasheesh can paint in 1 minute = 
Chinki can paint in 1 munute = 
∵ They both can paint in 1 minute = 
Work done by them in 5 minute = 
Remaining work = 1
So, Aasheesh can paint remaining doll in = 
Question 15.
A and B can do a piece of work in 6 days and 4 days respectively. A started the work, worked at it for 2 days and then was joined by B. Find the total time taken to complete the work.
Answer:
Given,
A can do a piece of work in = 6 days
B can do same piece of work in = 4 days
∵ Work done by A in 1 day =
∴ In 2 Days he finished = 
part of work
Remaining work = 
So, Remaining work will be finished by A and B in = 
days
∴ Total time taken to complete the work = 2 + 
= 3
days
Question 16.
6 men can complete the electric fitting in a building in 7 days. How many days will it take if 21 men do the job?
Answer:
Given,
6 men can complete the work in = 7 days
∵ 1 man can complete it in = 6 × 7 = 42 days
∴ 21 man will complete it in = 
Question 17.
8 men can do a piece of work in 9 days. In how many days will 6 men do it?
Answer:
Given,
8 men can do a piece of work = 9 days
∵ 1 man can complete it in = 8 × 9 = 72 days
∴ 6 men will do it in = 
Question 18.
Reema weaves 35 baskets in 25 days. In how many days will she weave 55 baskets?
Answer:
Given,
Reema weaves 35 baskets in = 25 days
∵ Time taken by her to weave 1 basket = 
∴ Time taken by her to weave 55 baskets = 
days
Question 19.
Neha types 75 pages in 14 hours. How many pages will she type in 20 hours?
Answer:
Given,
Neha types 75 pages in = 14 hours
∵ Number of pages typed by Neha in 14 hour = 75 pages
∴ Number of pages typed by her in 1 hour = 
∴ Number of pages she typed in 20 hour = 
pages
Question 20.
If 12 boys earn Rs 840 in 7 days, what will 15 boys earn in 6 days?
Answer:
Given,
∵ Earning of 12 boys in 7 days = Rs.840
∴ Earning of 12 boys in 1 day = 
∴ Earning of 1 boy in 1 day = 
∴ Earning of 1 boy in 6 days = 
Hence, Earning of 15 boys in 6 days = 60 × 15 = Rs. 900
Question 21.
If 25 men earn Rs 1000 in 10 days, how much will 15 men earn in 15 days?
Answer:
∵ 25 men in 10 days can earn = Rs.1000
∴ 25 men can earn in 1 day = 
∴ 1 man can earn in 1 day = 
∵ 1 man can earn in 15 days = 15 × 4 = Rs.60
∴ 15 man can earn in 15 days = 60 × 15 = Rs.900
Question 22.
Working 8 hours a day, Ashu can copy a book in 18 days. How many hours a day should he work so as to finish the work in 12 days?
Answer:
∵Working 8 hours a day Ashu can complete a work in = 18 days
∴ Working 1 hours a day he can complete it in = 18 × 8 = 144 days
∴ Number of hours he should work to complete the work in 12 days = 
hours/day
Question 23.
If 9 girls can prepare 135 garlands in 3 hours, how many girls are needed to prepare 270 garlands in 1 hour?
Answer:
∵ 9 Girls in 3 hours can prepare = 135 garlands
∴ 9 girls in 1 hour can prepare = 
∴ 1 girl in 1 hour can prepare = 
garland
∴ Number of girl needed to make 270 garlands in 1 hour = 
girls
Question 24.
A cistern can be filled by one tap in 8 hours, and by another in 4 hours. How long will it take to fill the cistern if both taps are opened together?
Answer:
Given,
A cistern can filled by one tap = 8 hours
Another can filled it in = 4 hours
∵ Cistern filled by first tap in 1 hour = 
Cistern filled by another tap in 1 hour = part
∴ Net cistern filled in 1 hour = 
Thus, both cistern can fill the cistern in = 
hours
Question 25.
Two taps A and B can fill an overhead tank in 10 hours and 15 hours respectively. Both the taps are opened for 4 hours and then B is turned off. How much time will A take to fill the remaining tank?
Answer:
Given,
Tap A can fill a tank in= 10 hours
Tap B can fill the tank in = 15 hours
Work done by Tap A in 1 hour =
Work done by tap B in 1 hour =
∴ Work done by both tap in 1 hour = 
Work done by both tap in 4 hours = 
Remaining part = 
Hence, time taken by A to fill remaining part = 
hours
Question 26.
A pipe can fill a cistern in 10 hours. Due to a leak in the bottom it is filled in 12 hours. When the cistern is full, in how much time will it be emptied by the leak?
Answer:
Given,
A pipe can fill a cistern in = 10 hours
Due to leakage it get filled in = 12 hours
∵ Without leakage work done by pipe in 1 hour = 
∵ With leakage work done by pipe in 1 hour = 
∴ Work done by leakage in 1 hour = 
Hence, the cistern will be emptied by leakage in = 
Question 27.
A cistern has two inlets A and B which can fill it in 12 hours and 15 hours respectively. An outlet can empty the full cistern in 10 hours. If all the three pipes are opened together in the empty cistern, how much time will they take to fill the cistern completely?
Answer:
Given,
Inlet A can fill the cistern in = 12 hours
Inlet B can fill it in = 15 hours
Outlet pipe can empty it in = 10 hours
∵ Work done by pipe A in 1 hour =
∵ Work done by pipe B in 1 hour =
∵ work done by outlet pipe in 1 hour =
∴ Net work done by 3 pipe in 1 hour = 
Hence, time taken by 3 pipes to fill the tank = 
Question 28.
A cistern can be filled by a tap in 4 hours and emptied by an outlet pipe in 6 hours. How long will it take to fill the cistern if both the tap and the pipe are opened together?
Answer:
Given,
Inlet tap can fill a cistern in = 4 hours
Outlet tap can emptied it in = 6 hours
∵ Work done by inlet tap in 1 hour =
∵ Work done by outlet pipe in 1 hour =
∴ Work done by both pipe in 1 hour =
Hence, both the tap can filled it in = 