Question 47

A and B can do a piece of work together in 15 days while A alone can do it in 25 days. They start working together but B leaves 5 days before the completion of the work. For how many days did A and B work together?

Solution

Let the total work be 75 units.

($$\because$$ LCM of 15 and 25 is 75.)

Efficiency of A and B = 75/15 = 5

Efficiency of A = 75/25 = 3

B leaves 5 days before the completion of the work so A works 5 days extra so,

5 days work of A = efficiency $$\times$$ days = 3 $$\times$$ 5 = 15

Remaining work = 75 - 15 = 60 units

60 units work done by A and B so time taken by together = 60/5 = 12 days

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