## Time and Work Questions, Tricks, Formulas, Shortcuts and Practice Problems

If a man can do a piece of work in 10 days, he will do 1/10 of the work in 1 day. And conversely, if a man can do 1/10 work in 1 day, he will do the work in 10 days.

If ‘A’ can do a work in ‘a’ days and B can do it in ‘b’ days, then A and B together can do it in

**Examples:**

1. If A can do a work in 4 days and B alone can do it in 6 days. In how many days A and B together can do the work?

Solution:

**Formula:**

2. A and B together can do a work in 30 day s , and A alone can do it 40 days. In how many days B alone do it?

Solution:

3. A and B can do a piece of work in 24 days, B and C in 30 days, C and A in 40 days. How long would all of them take to do the same work?

Solution:

∴ A, B and C together can do the work in 20 days.

4. Ravi car do a work in 20 days, which Sankar can do in 12 days. Sankar worked at It for 9 days and leaves. In how many days can Ravi finish the remaining work?

Solution:

5. A and B can Co a piece of work, in 20 days and 30 days, respectively. They work to gather for 6 days and then B leaves. In how many days the whole work is completed?

Solution:

6. A and B can do a work In 25 days and 20 days respectively. They together under took to do a piece of work for Rs 900 What is the share of B?

Solution:

7. A can do a work in 32 days. B alone can do it in 48 days. They together undertake to do a work for Rs. 1600 with the help of C, they finished the work in 12 days. What is the share of C?

Solution:

8. A and B can do a work in 9 and 12 days respectively. If they work on alternate days, A beginning, on which day will the work be completed?

Solution:

9. Pavan is thrice as good a workman as Praveen. Together they can do a work in 12 days, in how many days Praveen alone can do the work?

Solution:

(Praveen and Pavan) can do the work in 12 days since Pavan = 3 Praveen

(Praveen + 3 praveen) – 12 days.

∴ Praveen can do work in 12 days

Praveen can do work in 12 days 48 days.

10. A is price as fast as B and is therefore finish a work in 40 days less B. In how many days both of them can do the work it they work together?

Solution:

A = 3B

If A can do the work in x days

Difference in time pen is 2x = 40 days

x = 20 days

∴ A alone can do it in 20 days and B alone in 60 days

11. Two taps A and B can fill a tank in 4 hrs. and 5 hrs. respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank?

Solution:

12. Two taps A and B can fill a tank in 20 hrs. and 30 hrs. Third tap C can empty the full tank in 40 hrs. If all the taps are opened together how much time will be taken to fill the tank?

Solution:

13. Two pipes A and B can fill a cistern in 16 hours and 24 hours respectively, while pipe C can empty it in 12 hours. In what time will the cistern be full, if all the pipes are opened together?

Solution:

14. Two pipes A and B can fill a tank In 24 min. and 30 min. respectively. Both are opened together but after 8 min., A is turned off. In how many more minutes, will the tank be filled?

Solution:

15. Three pipes A, B and C can fill a tank in 12 hrs., 4 hrs. and 24 hrs. respectively. Pipe A is opened at 3 A.M., pipe B at 5 A.M. and pipe C is opened at 6 A.M. At what time the tank can be filled?

Solution:

16. A tank can be filled by a tap in 8 hours, but due to a leak in the bottom it takes 2 hrs. longer to fill the tank. If the cisterns is full, in how many hours will the leak empty it?

Solution:

### Time and Work Practice Questions

1. A can do a work in 12 days and B alone can do the same work in 16 days. In how many days A and B together can do the work?

1) 28 2) 24 3) \(6 \frac { 6 } { 7 }\) 4) \(6 \frac { 1 } { 7 }\)

2. A, B and C can do a work in 15, 20 and 12 days respectively. In how many days can they together complete the work ?

1) 10 days 2) 5 days 3) 47 days 4) 12 days

3. Anand and Sanjeev together can finish a work in 8 days. Anand alone can do it in 12 days. How many days will Sanjeev alone take to complete the same work ?

1) 16 2) 24 3) 4 4) None

4. Mohan finished of the work in 10 days. In how many days, will he finish the remaining work ?

1) 50 days 2) 30 days 3) 20 days 4) 40 days

5. A cistern is filled in 9 hours, but takes one hour longer to be filled due to a leak in its bottom. If the cistern is full, in what time will the leak empty it ?

1) 30 hrs. 2) 40 hrs. 3) 45 hrs. 4) 90 hrs.

6. If th part of a cistern is filled with water in one minute, then the time required to fill the remaining, part is

1) 10 sec. 2) 12 sec. 3) 15 sec. 4) 20 sec.

7. A and B can do one work in 6 days. Only A can do the work in 9 days then in how many days B alone can do this work ?

1) 21 days 2) 24 days 3) 18 days 4) 14 days

8. A can do a piece of work in 20 days, B in 15 days and C in 12 days. In how many days can A finish the work if he is assisted by B on one day and by C on the alternate days

1) 14 2) 6 3) 8 4) 10

HINT (A + B) on 1st day, (A + C) on 2nd day, (A + B) on 3rd day, (A + C) on 4th day,…)

9. 10 men, 10 women and 10 children can do a work in 10 days, 20 days and 30 days respectively. Then how many days 5 men, 5 women and 5 children take to complete the same work?

1) 6 2) 8 3) 110/11 4) 10

10) Anand can do a work in 40 days. He worked for 5 days and Bhavani finished the remaining work in 21 days. In how many days can Anand and Bhavani together complete the work ?

1) 64 days 2) 45 days 3) 15 days 4) 20 days

11) A and B can do a work in 18 days and 15 days respectively. They work together for 5 days and B goes away. In how many days will A finish off the remaining work ?

1) 14 days 2) 11 days 3) 100/7 4) 7 days

12. A and B can do a work in 42 and 56 days respectively. They begin the work together, but A left after some days. B completed the remaining work in 42 days. After how many days did A leave ?

1) 6 days 2) 16 days 3) 12 days 4) 10 days

13. Ravi and Ramana can do a work in 25 days and 20 days respectively. They together undertook a piece of work for Rs. 9000. What is the share of Ramana ?

1) Rs. 4000 2) Rs. 5000 3) Rs. 6000 4) Rs. 4500

14. A can do a work in 12 days and B can do the same in 36 days. If they work on alternate days, A beginning, on which day will the work be completed ?

1) 9th day 2) 18th day 3) 27th day 4) 36th day

15. Kavita is twice as good efficient worker as Ramya. Together they can complete a work in 15 days.In how many days Ramya alone complete the work ?

1) 5 days 2) 10 days 3) 15 days 4) 45 days

16. A sum of money is sufficient to pay A’s wages tor 12 days and it is sufficient to pay B’s wages for 36 days. The same sum of money will be sufficient for wages of both for how many days?

1) 48 days 2) 49 days 3) 16 days 4) 24 days

17. Two taps A and B can fill a tank 32 min. and 24 min. respectively. If both the taps are opened simultaneously, after how much time should A be closed so that the tank can be filled in. 18 minutes?

1) 12 min 2) 6 min 3) 8 min. 4) 10 min.

KEY FOR EXERCISE

1. 3 | 9. 3 |

2. 2 | 10. 3 |

3. 2 | 11. 4 |

4. 4 | 12. 1 |

5. 4 | 13. 2 |

6. 3 | 14. 2 |

7. 3 | 15. 4 |

8. 3 | 16. 2 |

17. 3 |

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