A can do a piece of work in 24 hours while B alone can do it in 16 hours. If A, B and C working together can finish it in 8 hours, in how many hours can C alone finish the work?

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Solution

$Time taken by A to complete the piece of work = 24 h Work done per hour by A = \frac{1}{24} Time taken by B to complete the work = 16 h Work done per hour by B = \frac{1}{16} Total time taken when A, B and C work together = 8 h Work done per hour by A, B and C = \frac{1}{8} Work done per hour by A, B and C = (work done per hour by A) + (work done per hour by B) + (work done per hour by C) (Work done per hour by C) = (work done per hour by A, B and C) - (work done per hour by A) - (work done per hour by B) = \frac{1}{8} - \frac{1}{24} - \frac{1}{16} = \frac{6 - 2 - 3}{48} = \frac{1}{48} Thus, C alone will take 48 h to complete the work .$

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