### Introduction

In the context of the time and work, you have to understand the following basic concepts of this chapter:

• If A does a work in ‘a’ day, then in one day A does 1/a of the work.
• If B does a work in b days, then in one day B does 1/b of the work.
• Then, in one day, if A and B work together, then their combined work is (1/a + 1/b) or (a+b)/ab
• In the above case, we take the total work to be done as “1 unit of work”. Hence, the work will be completed when 1 unit of work is completed.

For example, if A can do a work in 10 days and B can do the same work in 12 days, then the work will be completed in how many days.

• One day’s work = 1/10 + 1/12 = (12 + 10)/120

• [Taking LCM of the denominators] = 22/120

• Then the number of days required to complete the work is 120/22.

• Note that this is a reciprocal of the fraction of work done in one day. This is a benefit associated with solving time and work through fractions. It can be stated as—the number of time periods required to complete the full work will be the reciprocal of the fraction of the work done in one time period.

• Formula: (M1D1H1)/W1 = (M2D2H2)/W2.

• Where, M1 and M2 represent the number of “Men”.
• D1 and D2 represent the number of “Days”.
• H1 and H2 represent the number of “Hours”.
• W1 and W2 represent the “Work Done”.

### Practice Questions:

1. A can do work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is:
a. 1/4
b. 1/10
c. 7/15
d. 8/15

2. A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?
a. 12 days
b. 15 days
c. 16 days
d. 18 days

3. A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?
a. Rs. 400
b. Rs. 800
c. Rs. 1600
d. None of these

4. A can do a piece of work in 4 hours; B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it?
a. 10 hours
b. 12 hours
c. 8 hours
d. 24 hours

5. Mr. Ram has a sum of money, which is sufficient to pay Usha's wages for 30 days and Manika's wages for 60 days. If he employs them together, the money is sufficient to pay their wages for how many days?
a) 12 Days
b) 10 Days
c) 30 Days
d) 20 Days
e) 36 Days

6. 24 men and 12 women can do a piece of work in 30 days. In how many days can 12 men and 24 women do the same piece of work? (UPSC 2022)
a. 30 days
b. More than 30 days
c. Less than 30 days or more than 30 days
d. Data is inadequate to draw any conclusion

7. Sudhir can do a work in 10 days and Rahul in 15 days. Mohit, who can finish the same work in 20 days, joins them, then how long will they take to complete the work?
a. 5.12 days
b. 4.62 days
c. 5.67 days
d. 4.82 days

8. Tushar and Ajay together can do a piece of work in 7 days. If Tushar dose twice as much work as Ajay in a given time, how long will Tushar along take to do the work?
a. 6.33 days
b. 10.5 days
c. 11 days
d. 72 days

9. In the previous question in how much time will Alok and Samir finish the whole work together?
a. 6 days
b. 6.66 days
c. 5.33 days
d. 1.66 days

10. A, B, C, and D can do a piece of work in 20 days. If A and B can do it together in 50 days, and C alone in 60 days, find the time in which D alone can do it.
a. 120 days
b. 75 days
c. 150 days
d. 90 days

11. A can do a piece of work in 12 days. B can do this work in 16 days. A started the work alone. After how many days should B join him, so that the work is finished in 9 days?
a. 2 days
b. 3 days
c. 5 days
d. 4 days

12. 45 men can complete a work in 16 days. Six days after they started working, 30 more men joined them. In how many days the total work will be completed ?
a. 12
b. 8
c. 15
d. 14

13. If 9 men working 7.5 hours a day can finish a piece of work in 20 days, then how many days will be taken by 12 men, working 6 hours a day to finish the work? It is being given that 2 men of latter type work as much as 3 men of the former type?
a. 10.5
b. 11
c. 13
d. 12.5

14. A contractor agreeing to finish a work in 150 days, employed 75 men each working 8 hours daily. After 90 days, only 2/7 of the work was completed. Increasing the number of men by ____ and each one is working now for 10 hours daily, the work can be completed in time.
a. 75
b. 225
c. 150
d. 100

15. Twenty women can do a work in sixteen days. Sixteen men can complete the same work in fifteen days. What is the ratio between the capacity of a man and a woman?
a. 3:4
b. 4:3
c. 5:3

16. 10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?
a. 3
b. 5
c. 7
d. Cannot be determined
e. None of these

17. A man complete 7/8 of a job in 21 days. How many more days will it take him to finish the job if quantum of work is further increase by 50 %? (UPSC 2021)
a. 24
b. 21
c. 18
d. 15

18. In a garrison, there was food for 1000 soldiers for one month. After 10 days 1000 more soldiers joined the garrison. How long would the soldiers be able to carry on with the remaining food? (UPSC 2013)
a. 25 days
b. 20 days
c. 10 days
b. 15 days

19. The tank-full of petrol in Arun's motor-cycle lasts for 10 days. If he starts using 25% more every day, how many days will the tank-full of petrol last? (UPSC 2013)
a. 5
b. 6
c. 7
d. 8

20. Ram and Shyam work on a job together for four days and complete 60% of it. Ram takes leaves and then Shyam works for eight more days to complete the job. How long would Ram take to complete the entire job alone? (UPSC 2016)
a. 6 days
b. 8 days
c. 10 days
b. 11 days

21. W can do 25% of a work in 30-day, X can do 1/4 of the work in 10 days, Y can do 40% of work in 40 days and Z can do 1/3 of the work in 13 days. Who will complete the work first?
a. W
b. X
c. Y
b. Z

22. To complete a piece of work, Samir takes 6 days and Tanvir takes 8 days alone respectively. Samir and Tanvir took Rs.2400 to do this work. When Amir joined them, the work was done in 3 days. What amount was paid to Amir?
a. Rs. 300
b. Rs. 400
c. Rs. 800
d. Rs. 500

23. Ram completed the school project in 20 days. How many days will Arun take to complete the same work if he is 25% more efficient than Ram?
a. 10 days
b. 12 days
c. 16 days
d. 15 days

24. A can fabricate a divider in 30 days , while B alone can assemble it in 40 days, If they construct it together and get an instalment of RS. 7000, what B's offer?

a. 2000
b. 3000
c. 4000
d. 6500

25. Kim can do a work in 3 days while David can do the same work in 2 days. Both of them finish the work together and get Rs. 150. What is the share of Kim?

a. Rs. 50
b. Rs. 60
c. Rs. 70
d. Rs. 80

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