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1. A and B can do a piece of work in 30 days, while B and C can do the same work in 24 days and C and A in 20 days. They all work together for 10 days when B and C leave. How many days more will A take to finish the work?

A. 18 days

B. 24 days

C. 30 days

D. 36 days

Solution:

\begin{aligned} 2(A + B + C)'s 1 day's work \\ = \frac{1}{30} + \frac{1}{24} + \frac{1}{20} \\ = \frac{15}{120} = \frac{1}{8} \\ ∴ (A + B + C)'s 1 day's work \\ = \frac{1}{2 \times 8} = \frac{1}{16} \\ Work done by A, B, C in 10 days \\ = \frac{10}{16} = \frac{5}{8} \\ Remaining work \\ = 1 - \frac{5}{8} = \frac{3}{8} \\ A's 1 day's work \\ = \frac{1}{16} - \frac{1}{24} = \frac{1}{48} \\ Now, \frac{1}{48} work isdone by A in 1 day \\ So, \frac{3}{8} work will be done by A in \\ 48 \times \frac{3}{8} = 18 days \end{aligned}

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