#### Question

*A* and *B* can do a piece of work in 20 days and *B* in 15 days. They work together for 2 days and then *A* goes away. In how many days will *B* finish the remaining work?

#### Solution

\[\text{ It is given that A can finish the work in 20 days and B can finish the same work in 15 days } . \]

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

\[\text{ Work done by B in 1 day } = \frac{1}{15}\]

\[ \therefore \text{ Work done by } \left( A + B \right) \text { in 1 day } = \frac{1}{20} + \frac{1}{15}\]

\[ = \frac{3 + 4}{60} = \frac{7}{60}\]

\[ \therefore \text{ Work done by } \left( A + B \right) \text{ in 2 days } = \frac{14}{60} = \frac{7}{30}\]

\[\text{ Remaining work } = 1 - \frac{7}{30} = \frac{23}{30}\]

\[\text{ It is given that the remaining work is done by B } . \]

\[ \because \text{ Complete work is done by B in 15 days } . \]

\[ \therefore \frac{23}{30} \text{ of the work will be done by B in } \left( 15 \times \frac{23}{30} \right) \text{ days or } \frac{23}{2} \text{ days or } 11\frac{1}{2} \text{ days } . \]

\[\text{ Thus, the remaining work is done by B in 11 } \frac{1}{2} \text{ days .} \]