A can complete a piece of work in 10 days, and B can do the same work in 15 days. They work together for 5 days, and then C finishes the remaining work in 2 days. How long would C alone take to complete the entire work?
12 days
One day's work of A = \(\frac{1}{10}\) and of B = \(\frac{1}{15}\); together = \(\frac{1}{10} + \frac{1}{15} = \frac{5}{30} = \frac{1}{6}\).
Work done by A and B in 5 days = \(5 \times \frac{1}{6} = \frac{5}{6}\), so remaining work = \(\frac{1}{6}\).
C does \(\frac{1}{6}\) of the work in 2 days, so C alone does the whole work in \(2 \times 6 = 12\) days.
Hence, the answer is 12 days.
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