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?

  1. A. 12 days ✓
  2. B. 14 days
  3. C. 18 days
  4. D. 16 days

Correct Answer: A. 12 days

Explanation

Work done by A and B in 5 days = 5 \times (\frac{1}{10} + \frac{1}{15}) = 5 \times \frac{5}{30} = \frac{5}{6}. Remaining work = 1 - \frac{5}{6} = \frac{1}{6}. C completes \frac{1}{6} work in 2 days, so C alone takes 2 \times 6 = 12 days to complete the entire work.

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