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1. A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?

A. Rs. 375

B. Rs. 400

C. Rs. 600

D. Rs. 800

Solution:

\begin{aligned} C's 1 day's work \\ = \frac{1}{3} - (\frac{1}{6} + \frac{1}{8}) \\ = \frac{1}{3} - \frac{7}{24} \\ = \frac{1}{24} \\ A's wages:B's wages:C's wages \\ = \frac{1}{6} : \frac{1}{8} : \frac{1}{24} \\ = 4 : 3 : 1 \\ ∴ C's share (for 3 days) \\ = R s . (3 \times \frac{1}{24} \times 3200) \\ = R s . 400 \end{aligned}

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