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Time and Work

Points to Remember


1 . If A can finish a piece of work in `n' days, then A's 1 day's work is 1/n .

2 . If the number of men engaged to do a piece of work is changed in the ratio a:b, the time required for the work will be changed in the ratio b:a.

3 . If A is X times as good a workman as B, then A will take 1/x of the time that B takes to do a certain work.

4 . If M1 persons can do `W1' works in D1 days for T1 hours and M2 persons can do `W2' works in D2 days for T2 hours then M1 D1 T1 W2 = M2 D2 T2W1.

If A can finish a work in `x' days and B can finish the same work in `y' days, then time taken by both to finish the work is xy/x+y days.

6 . If A and B together can do a piece of work in x days and A alone can do it in y days then B alone can do it in xy/y-z days.


Solved Examples


1 . 8 boys can arrange all the books of school library in 12 days. In how many days can 6 boys arrange them?
Ans: Ans: M1 D1 = M2 D2
D2= 8x12/6 = 16 days

2 . A can do a piece of work in 12 days and B alone can do it in 15 days. How much time will both take to finish the work?
Ans: A's 1 day's work = 1/12
B's 1 day's work = 1/15
(A+B)'s 1 day's work = 1/12 + 1/15 =3/20
Therefore both together can finish the work in
time and work

3. A and B together can do a piece of work in 12 days. B alone can finish it in 30 days. In how many days can A alone finish the work?
Ans:(A+B)'s 1 day's work = 1/12
B's 1 day's work = 1/30
A's 1 day's work = 1/12 - 1/30 = 1/20
Therefore A alone can finish the work in 20 days.
time and work formula

4 . 16 men can do a piece of work in 10 days. How many men are needed to complete the work in 40 days?
Ans:M1 D1 = M2 D2
M1 = 16, D1 = 10, D2 = 40
16x10 = M2 x 40
M2 = 16 x 10/40 = 4 men.

time and work formula

ANSWERS TO PRACTICE TEST

1 . (1)  2 . (3)

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