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1. A takes twice as much time as B or thrice as much time as C to finish a piece of work. Working together, they can finish the work in 2 days. B can do the work alone in:

A. 4 days

B. 6 days

C. 8 days

D. 12 days

Solution:

\begin{aligned} Suppose A, B and C take \\ x, \frac{x}{2}, \frac{x}{3} days respectively to finish the work \\ Then, \frac{1}{x} + \frac{2}{x} + \frac{3}{x} = \frac{1}{2} \\ \Rightarrow \frac{6}{x} = \frac{1}{2} \\ \Rightarrow x = 12 \\ So, B takes \frac{12}{2} \\ = 6 days to finish the work \end{aligned}

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