#### Question

*A*,* B* and *C* working together can do a piece of work in 8 hours. *A* alone can do it in 20 hours and *B* alone can do it in 24 hours. In how many hours will *C* alone do the same work?

#### Solution

\[\text{ Time taken by A to do the work = 20 hours } \]

\[\text{ Time taken by B to do the work = 24 hours} \]

\[\text{ Time taken by } \left( A + B + C \right) \text{ to do the work = 8 hours } \]

\[\text{ Now, } \]

\[ \text{ Work done by A } = \frac{1}{20}\]

\[ \text{ Work done by B } = \frac{1}{24}\]

\[ \text{ Work done by } \left( A + B + C \right) = \frac{1}{8}\]

\[ \therefore \text{ Work done by C } = \frac{1}{8} - \left( \frac{1}{20} + \frac{1}{24} \right)\]

\[ = \frac{1}{8} - \left( \frac{6}{120} + \frac{5}{120} \right) = \frac{1}{8} - \left( \frac{11}{120} \right)\]

\[ = \frac{15 - 11}{120} = \frac{4}{120} = \frac{1}{30}\]

\[\text{ Thus, C can do the work in 30 hours .} \]