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1. A can do a certain work in the same time in which B and C together can do it. If A and B together could do it in 10 days and C alone in 50 days, then B alone could do it in:

A. 15 days

B. 20 days

C. 25 days

D. 30 days

Solution:

\begin{aligned} (A + B)'s 1 day's work = \frac{1}{10} \\ C's 1 day's work = \frac{1}{50} \\ (A + B + C)'s 1 day's work \\ = \frac{1}{10} + \frac{1}{50} = \frac{6}{50} = \frac{3}{25} . . . . . . . . (i) \\ A's 1 day's work \\ = (B + C)'s 1 day's work . . . . . . . . (ii) \\ From (i) and (ii),we get : 2 \times (A's 1 day's work) \\ = \frac{3}{25} \\ \Rightarrow A's 1 day's work = \frac{3}{50} \\ ∴ B's 1 day's work (\frac{1}{10} - \frac{3}{50}) \\ = \frac{2}{50} = \frac{1}{25} \\ So, B alone could do the work in 25 days \end{aligned}

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