Question
‘P’ and ‘Q’ can do a piece of work in 12 days
and 18 days, respectively. ‘P’ started working alone and was replaced by ‘Q’ after 4 days. In how many days can ‘Q’ complete the remaining amount of work alone?Solution
Let the total work be 36 units (LCM of 12 and 18) Efficiency of ‘P’ = 36/12 = 3 units/day Efficiency of ‘Q’ = 36/18 = 2 units/day Let the number of days taken by ‘Q’ to finish the remaining amount of work be ‘x’ ATQ, (3 × 4) + 2x = 36 Or, 2x = 36 – 12 Or, 2x = 24 Or, x = 24/2 = 12 Therefore, time taken by ‘Q’ to complete the remaining work alone = 12 days
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