Question
A alone can complete a work in 18 days, and B alone can
complete the same work in 24 days. They start working together, but A leaves after 4 days. In how many more days will B finish the remaining work alone?Solution
ATQ, A’s 1-day work = 1/18 B’s 1-day work = 1/24 Work done together in 1 day = 1/18 + 1/24 LCM of 18 and 24 is 72. 1/18 = 4/72, 1/24 = 3/72 So together = 7/72 per day. Work done in first 4 days = 4 × 7/72 = 28/72 = 7/18 Remaining work = 1 − 7/18 = 11/18 Now B alone works at 1/24 per day. Time to finish remaining work = (11/18) ÷ (1/24) = (11/18) × 24 = 11 × (4/3) = 44/3 = 14⅔ days.
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