A and B can do a piece of work in 45 days and 40 days respectively They began to do the work togethe...........

Quant (SSC) Time and work

A and B can do a piece of work in 45 days and 40 days respectively. They began to do the work together but A leaves after some days and then B completed the remaining work in 23 days. The number of days after which A left the work was:

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Explanation:

A and B do a piece of work in ‘a’ and ‘b’ days, respectively. Both begin together but after some days, A leaves off and the remaining work is completed by B in ‘x’ days. Then, the time after which A left, is given by
T = (b - x)a /a + b
Given that a = 45 days, b = 40 days, x = 23, T = ?
By the short trick approach, we get
= (40 - 23)45 /45 + 40
= 17 x 45 /85 = 9 days