Time and Work Problems

Basics:
1.     If A can do a piece of work in n days then A’s 1 day’s work=1/n.
2.     If A’s 1 day’s work=1/n, then A can finish the work in n days.
3.     If A is twice as good a workman as B, then
Ratio of work done by A and B = 2 : 1.
Ratio of times taken by A and B to finish a work= 1 : 2.
4.     If A can do a piece of work in x days and B can do it in y days then A and B working together will do the same work in xy/x+y days.
5.     If M1 persons can do W1 work in D1 days by working H1 hours and M2 persons can do W2 work in D2 days by working H2 hours then we have a very general formula in the relationship of
M1D1H1/W1=M2D2H2/W2.

Time and Work Problems






Problems:
1.     A can do a piece of work in 10 days B in 15 days in how many days they together can complete that work.

2.     A can do a piece of work in 10 days B in 20 days C in 30 days in how many days A,B and C can complete that work working together.

3.     A and B together can do a piece of work in 20 days. A alone can do that work in 30 days in how many days B alone can complete that work.

4.     A and B can do a piece of work in 12days B and C in 15days C and A in 20 days in how many days all of them can complete working together.

5.     A can do a job in 5 days B in 4 days and A, B and C together in 2 days in what time C can do it alone.

6.     A can do a piece of work in 10 days B in 15 days. A started the work and worked for 4 days then A left B alone can complete the remaining work in how many days.

7.     A can do a piece of work in 10 days B in 15 days they together worked for 4 days and then B left in how many days A alone can complete the remaining work.

8.     A can do a piece of work in 10 days B in 15 days. A worked for 4 days and then B is joined. In how many days they together can complete the remaining work.

9.     X and Y can do a piece of work in 30 days and 40 days respectively they began the work together but Y left after some days X complete the remaining work in 9 days. after how many days did Y leave.

10. A and B can do a piece of work in 15 days and 20 days respectively. In how many days they complete the work if they are working on alternate days started by A.

11. A is 40% more efficient then Band he can complete a piece of work in 20days in how many days B alone can complete that work.

12.           X is thrice as efficient as Y and they together can complete that work in 12 days.In  
      how many days Y alone can complete that work.

13.  A can do a piece of work in 10 days B in 15 days they under to do a piece of work        for Rs. 250. Find the wage of A if they completed the work together.

14. A and B can finish a work in 10 days and 15 days respectively. They worked together for two days and A left the remaining work was completed by B. If they together earned Rs.250 what is the share of

15. 12 men can do a piece of work in 20days 15 men can complete that work in how many days.

16. A certain no.of men complete a piece of work in 60 days. If there were 8 more men the work could be finished in 10 days less. How many men were there originally.

17. 20 men complete a work in 30 days. When should 5 men leave so that it may be completed in 35 days.

18. 10 men or 12 women can do a piece of work in 44 days. In how many days 5 men and 6 women can complete that work.

19. A is 50% as efficient as B. C does half of the work done by A and B together. IfC alone does the work in 40 days, then A, B and C together can do the work in

20. If 4 men and 3 women can do a piece of work in 8 days 6 men and 9 women can do it in 4 days. In how many days 20 men and 6 women do the same work.

Answers
1
6
2
5  5/11
3
60
4
10
5
20
6
9
7
3 1/3
8
3 3/5
9
12
10
17
11
28
12
48
13
150
14
50
15
16
16
40
17
15
18
44
19
13 1/3
20
2

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