Worksheet on Time and Work

In worksheet on time and work the questions will be mainly given to calculate the time required to complete the piece of work, to calculate the work done in a given period of time and also the questions will be from pipes and cistern.

1. A can do a piece of work in 24 days while B can do it in 30 days. In how many days can they complete it, if they work together?

2. A can do a piece of work in 15 hours while B can do it in 12 hours. How long will both take to do it, working together?

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?

4. Two motor mechanics, Ron and Sam, working together can overhaul a scooter in 6 hours. Ron alone can do the job in 15 hours. In how many hours, can Sam alone do it?

5. A, B and C can do a piece of work in 8 days, 12 days and 15 days respectively. How long will they take to finish it if they work together?

6. A can do a piece of work in 6 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?

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?

8. A and B can finish a piece of work in 6 days and 4 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.

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 7 days. Then, A was not well and B had to complete the work. In how many days was the work completed?

10. 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?

11. 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?

12. 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?

13. 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?

14. 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?

15. 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?

16. 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?

17. 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?

Hint. Work done by the leak in 1 hour = (¹/₉ – ¹/₁₀) = ¹/₉₀

18. 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 cl?sed. How much time will B take to fill the remaining part of the tank?

Hint. Work done by (A + B) in 1 hour = (¹/₆ + ¹/₈) = ⁷/₂₄

Work done by both in 2 hours = (⁷/₂₄ × 2) = ⁷/₁₂

Remaining part = (1 - ⁷/₁₂) = ⁵/₁₂

Now, ¹/₈ part is filled by B in 1 hour. Find how much time B will take to fill ⁵/₁₂ part.

Below the worksheet on time and work we will find the answers of the given question.

Answers:

1. 13¹/₃ days.

2. 6 hours 40 minutes.

3. 18 days.

4. 10 hours

5. 3⁷/₁₁ days.

6. 48 hours.

7. 30 hours.

8. 3³/₅ days.

9. 10¹/₂ days.

10. 4 days.

11. 16 days.

12. 30 days.

13. 6 hours.

14. 30 hours.

15. 2 hours 40 minutes.

16. 20 minutes.

17. 90 hours.

18. 3¹/₃ hours.