Question
A alone can complete a piece of work in 18 days and B alone can do it in 24 days. They work together for 6 days, after which A leaves. In how many more days will B finish the remaining work?
Solution
A’s 1-day work = 1/18 B’s 1-day work = 1/24 Together, 1-day work = 1/18 + 1/24 LCM(18, 24) = 72 1/18 = 4/72, 1/24 = 3/72 Together = 7/72 per day Work done in 6 days = 6 × 7/72 = 42/72 = 7/12 Remaining work = 1 − 7/12 = 5/12 B alone does 1/24 per day. Time = (5/12) ÷ (1/24) = (5/12) × 24 = 10 days Answer: B will take 10 more days.
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