Question
A and B can complete a work in 12 days and 16 days,
respectively. They start working together, but after 4 days, A leaves the work. C joins B, and they complete the remaining work in 6 days. How long would C take to complete the entire work alone?Solution
Work done by A and B together in 4 days = 4 × (1/12 + 1/16) = 4 × (4/48 + 3/48) = 4 × 7/48 = 28/48 = 7/12 of the work. Remaining work = 1 - 7/12 = 5/12. Work done by B and C in 6 days = 6 × (1/16 + 1/C) = 5/12. Simplify: 6 × (1/16 + 1/C) = 5/12. 1/16 + 1/C = (5/12) ÷ 6 = 5/72. 1/C = 5/72 - 1/16 = 5/72 - 9/144 = (10 - 9)/144 = 1/144. C alone can complete the work in 144 days.
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