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?

Explanation:-

$$\eqalign{ & {\text{C's}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} \cr & = \frac{1}{3} - \left( {\frac{1}{6} + \frac{1}{8}} \right) = \frac{1}{3} - \frac{7}{{24}} = \frac{1}{{24}} \cr & {\text{A's}}\,{\text{wages:B's}}\,{\text{wages:C's}}\,{\text{wages}} \cr & = \frac{1}{6}:\frac{1}{8}:\frac{1}{{24}} \cr & = 4:3:1 \cr & \therefore {\text{C's}}\,{\text{share}}\,{\text{(for}}\,{\text{3}}\,{\text{days}}\,{\text{)}} \cr & = Rs.\,\left( {3 \times \frac{1}{{24}} \times 3200} \right) \cr & = Rs.\,400 \cr}$$