Question
‘X’ and ‘Y’ can do a piece of work in 10 days
and 25 days, respectively. ‘X’ started working alone and was replaced by ‘Y’ after 5 days. In how many days can ‘Y’ complete the remaining amount of work alone?Solution
Let the total work be 200 units (LCM of 10 and 25) Efficiency of ‘X’ = 200/10 = 20 units/day Efficiency of ‘Y’ = 200/25 = 8 units/day Let the number of days taken by ‘Y’ to finish the remaining amount of work be ‘x’ ATQ, (20 × 5) + 8x = 200 Or, 8x = 200 – 100 Or, 8x = 100 Or, x = 100/8 = 12.5 Therefore, time taken by ‘Y’ to complete the remaining work alone = 12.5 days
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