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1. A can finish a work in 24 days, B in 9 days and C in 12 days. B and C start the work but are forced to leave after 3 days. The remaining work was done by A in:

A. 5 days

B. 6 days

C. 10 days

D. $10 \frac{1}{2}$ days

Solution:

\begin{aligned} (B + C)'s 1 day's work \\ = \frac{1}{9} + \frac{1}{12} = \frac{7}{36} \\ Work done by B and C in 3 days \\ = \frac{7}{36} \times 3 = \frac{7}{12} \\ Remaining work \\ = 1 - \frac{7}{12} = \frac{5}{12} \\ Now, \frac{1}{24} work is done by A in 1 day \\ So, \frac{5}{12} work is done by A in \\ 24 \times \frac{5}{12} = 10 days \end{aligned}

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