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?

 

 

Answer 1

\[\text{ It is given that A and B can finish the work in 20 days }. \]
\[ \therefore \text{ Work done by } \left( A + B \right) \text{ in 1 day }  = \frac{1}{20}\]
\[\text{ Now, A alone can do } \frac{1}{5}\text{ th of the work in 12 days } . \]
\[ \therefore \text { Time taken by A alone to complete the work }  = \left( 5 \times 12 \right) = 60 \text{ days} \]
\[ \Rightarrow \text{ Work done by A in 1 day } = \frac{1}{60}\]
\[\text{ Now, work done by B in 1 day = Work done by }  \left( A + B \right) \text{ in 1 day work - Work done by A in 1 day } \]
\[ = \frac{1}{20} - \frac{1}{60}\]
\[ = \frac{3 - 1}{60} = \frac{2}{60}\]
\[\text{ Thus, B alone can polish the floor in } \frac{60}{2}\text{ days or 30 days }  . \]