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?

Answer 1

\[\text{ It is given that A can finish the work in 20 days and B can finish the same work in 15 days } . \]
\[ \therefore \text{ Work done by A in 1 day } = \frac{1}{20}\]
\[\text{ Work done by B in 1 day } = \frac{1}{15}\]
\[ \therefore \text{ Work done by }  \left( A + B \right) \text { in 1 day } = \frac{1}{20} + \frac{1}{15}\]
\[ = \frac{3 + 4}{60} = \frac{7}{60}\]
\[ \therefore \text{ Work done by }  \left( A + B \right) \text{ in 2 days } = \frac{14}{60} = \frac{7}{30}\]
\[\text{ Remaining work } = 1 - \frac{7}{30} = \frac{23}{30}\]
\[\text{ It is given that the remaining work is done by B }  . \]
\[ \because \text{ Complete work is done by B in 15 days }  . \]
\[ \therefore \frac{23}{30} \text{ of the work will be done by B in }  \left( 15 \times \frac{23}{30} \right) \text{ days or }  \frac{23}{2} \text{ days or  } 11\frac{1}{2} \text{ days } . \]
\[\text{ Thus, the remaining work is done by B in 11 } \frac{1}{2} \text{ days .} \]