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1. If A and B together can complete a work in 18 days, A and C together in 12 days, and B and C together in 9 days, then B alone can do the work in:

A. 18 days

B. 24 days

C. 30 days

D. 40 days

Solution:

\begin{aligned} One day's work of \\ (A + B) = \frac{1}{18} . . . . . . . (1) \\ One day's work of \\ (A + C) = \frac{1}{12} . . . . . . . (2) \\ One day's work of \\ (B + C) = \frac{1}{9} . . . . . . . (3) \\ Adding (1), (2) and (3) \\ 2 \times (A + B + C) = \frac{1}{18} + \frac{1}{12} + \frac{1}{9} \\ 2 (A + B + C) = \frac{1}{4} \\ One day's work of \\ A + B + C = \frac{1}{8} \\ B = \frac{1}{8} - (A + C) \\ B = \frac{1}{8} - \frac{1}{12} \\ One day's work of \\ B = \frac{3 - 2}{24} = \frac{1}{24} \\ B need 24 days \end{aligned}

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