Class 8 RD Sharma Solutions – Chapter 11 Time And Work – Exercise 11.1 | Set 2

Chapter 11 Time And Work – Exercise 11.1 | Set 1

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.

Solution:

Given:

A can do a piece of work in = 6 days

A’s 1 day work = 1/6

B can do a piece of work in = 4 days

In 2 days the work completed by A = 2 × 1/6 = 1/3 part of work

Remaining work = 1 – 1/3

= (3-1)/3

= 2/3

A and B can finish the remaining work in = (2/3)/(1/6 + 1/4)

= (2/3)/(5/12)

= (2×12)/(3×5)

= 8/5 days

Therefore,

Total time taken to complete the work by A and B = 2 + 8/5

= (10+8)/5 = 18/5

= 3 3  days.
      5

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?

Solution:

Given:

6 men can complete the job in = 7 days

1 man can complete the job in = 6 × 7 = 42 days

Therefore,

21 men can complete the job in = 42/21 = 2 days

Question 17. 8 men can do a piece of work in 9 days. In how many days will 6 men do it?

Solution:

Given:

8 men can do a piece of work = 9 days

1 man can complete a piece of work in = 8 × 9 = 72 days

Therefore,

6 men can complete the work in = 72/6 = 12 days

Question 18. Reema weaves 35 baskets in 25 days. In how many days will she weave 55 baskets?

Solution:

Given:

Reema weaves 35 baskets in = 25 days

Time taken by Reema to weave 1 basket = 25/35

Therefore,

Time taken by Reema to weave 55 baskets = 25/35 × 55

= 5/7 × 55

= 275/7

= 39 2 days.
        7

Question 19. Neha types 75 pages in 14 hours. How many pages will she type in 20 hours?

Solution:

Given:

Number of pages Neha can type in 14 hours = 75 pages

Number of pages Neha can type in 1 hour = 75/14

Therefore,

Number of pages Neha can type in 20 hours = 20 × 75/14

= 750/7

= 107 1  pages.
          7

Question 20. If 12 boys earn Rs 840 in 7 days, what will 15 boys earn in 6 days?

Solution:

Given:

Earning of 12 boys in 7 days = Rs 840

Earning of 12 boys in 1 day = Rs 840/7

= Rs 120

Earning of 1 boy in 1 day = 120/12 = Rs 10

Earning of 1 boy in 6 days = 10 × 6 = Rs 60

Therefore

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?

Solution:

Given:

In 10 days 25 men can earn = Rs.1000

In 1 day 25 men can earn = 1000/10 = Rs 100

In 1 day 1 man can earn = 100/25 = Rs 4

In 15 days 1 man can earn = 15 × 4 = Rs 60

Therefore, 

In 15 days 15 men can earn = 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?

Solution:

Given:

Working 8 hours a day, Ashu can complete a work in = 18 days

Working 1 hour a day, Ashu can complete the work in = 18 × 8 = 144 days

Therefore,

Number of hours Ashu should work to complete the work in 12 days = 144/12 = 12 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?

Solution:

Given:

In 3 hours, 9 Girls can prepare = 135 garlands

In 1 hour, 9 girls can prepare = 135/3 = 45 garlands

In 1 hour, 1 girl can prepare = 45/9 = 5 garlands

Therefore,

In 1 hour, Number of girls required to prepare 270 garlands = 270/5 = 54 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?

Solution:

Given:

A cistern can be filled by one tap in = 8 hours

A cistern filled by one tap in 1 hour = 1/8

Another cistern can be filled in = 4 hours

Cistern filled by another tap in 1 hour = 1/4

Total cistern filled in 1 hour = 1/4 + 1/8

= (2+1)/8

= 3/8

Therefore,

Cistern can be filled when both the taps are opened together in = 8/3 = 223 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?

Solution:

Given:

Tap A can fill the tank in = 10 hours

Tap A can fill the tank in 1 hour = 1/10

Tap B can fill the tank in = 15 hours

Tap B can fill the tank in 1 hour = 1/15

Both taps together can fill the tank in 1 hour = 1/10 + 1/15

= (3+2)/30 = 5/30

= 1/6

Both taps together can fill the tank in 4 hours = 4 × 1/6 = 2/3

Remaining tank to be filled = 1 – 2/3

= (3-2)/3

= 1/3

Therefore,

Time taken by A to fill the remaining tank = (1/3)/(1/10)

= 10/3

= 3 1  hours.
      3

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?

Solution:

Given:

When there is no leakage A pipe can fill the cistern in = 10 hours

In 1 hour without leakage A pipe can fill the cistern in = 1/10 hours

When there is leakage cistern gets filled in = 12 hours

In 1 hour, when there is leakage cistern gets filled in = 1/12 hours

In 1 hour, due to leakage cistern gets filled to = 1/10 – 1/12

= (12-10)/120

= 2/120

= 1/60 part

Therefore,

Due to leakage the cistern gets emptied in = 1/(1/60) = 60 hours.

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?

Solution:

Given:

Inlet A can fill the cistern in = 12 hours

Inlet A can fill the cistern in 1 hour = 1/12

Inlet B can fill the cistern in = 15 hours

Inlet B can fill the cistern in 1 hour = 1/15

Outlet pipe can empty the cistern in = 10 hours

Outlet pipe can empty the cistern in 1 hour = 1/10

So we have, (1/12 + 1/15) – 1/10

= (9/60) – 1/10

= (9-6)/60

= 3/60

= 1/20 part

Therefore,

When all 3 pipes are opened together to empty the cistern, time taken to fill the cistern completely = 1/(1/20) = 20 hours

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?

Solution:

Given:

Inlet tap can fill a cistern in = 4 hours

Inlet tap can fill a cistern in 1 hour = 1/4

Outlet tap can empty the cistern in = 6 hours

Outlet tap can empty the cistern in 1 hour = 1/6

Work done by both pipe in 1 hour = (1/4 – 1/6)

= (3-2)/12

= 1/12

Therefore,

When both tap and pipe are opened together the cistern can be filled in = 1/(1/12) = 12 hours.