Question
A alone can finish a piece of work in 12 days and B
alone in 18 days. They work together for 4 days, then B leaves and C joins A. A and C together finish the remaining work in 3 more days. In how many days can C alone finish the whole work?Solution
Let total work = LCM(12, 18) = 36 units. A’s rate = 36/12 = 3 units/day B’s rate = 36/18 = 2 units/day Together (A + B) rate = 3 + 2 = 5 units/day. Work done in 4 days = 5 × 4 = 20 units. Remaining work = 36 − 20 = 16 units. Now A and C together finish 16 units in 3 days. So (A + C) rate = 16/3 units/day. A’s rate = 3 units/day, so C’s rate = (A + C) − A = 16/3 − 3 = 16/3 − 9/3 = 7/3 units/day. Time taken by C alone = Total work / C’s rate = 36 ÷ (7/3) = 36 × 3/7 = 108/7 days
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