#### Question

*A* and *B* can finish a work in 20 days. A alone can do \[\frac{1}{5}\] th of the work in 12 days. In how many days can *B* alone do it?

#### Solution

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

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

\[\text{ Now, A alone can do } \frac{1}{5}\text{ th of the work in 12 days } . \]

\[ \therefore \text { Time taken by A alone to complete the work } = \left( 5 \times 12 \right) = 60 \text{ days} \]

\[ \Rightarrow \text{ Work done by A in 1 day } = \frac{1}{60}\]

\[\text{ Now, work done by B in 1 day = Work done by } \left( A + B \right) \text{ in 1 day work - Work done by A in 1 day } \]

\[ = \frac{1}{20} - \frac{1}{60}\]

\[ = \frac{3 - 1}{60} = \frac{2}{60}\]

\[\text{ Thus, B alone can polish the floor in } \frac{60}{2}\text{ days or 30 days } . \]