A, B and C working together can finish a piece of work in 8 hours. A alone can do it in 20 hours and B alone can do it in 24 hours. In how many hours will C alone do the same work?

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Solution

$A can complete the work in 20 h . Work done per hour by A = \frac{1}{20} B can complete the work in 24 h . Work done per hour by B = \frac{1}{24} It takes 8 h to complete the work if A, B and C work together . Work done together per hour by A, B and C = \frac{1}{8} (Work done per hour by A, B and C) = (work done per hour by A) + (work done per hour by B) + (work done per hour by C) OR (Work done per hour by C) = (work done per hour by A, B and C) - (work done per hour by A) - (work done per hour by B) = \frac{1}{8} - \frac{1}{24} - \frac{1}{20} = \frac{1}{30} ∴ C alone will take 30 h to complete the work .$

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