Question

Two persons $A$ and $B$ are engaged in a work. $A$ can do a piece of work in $12$ days and $B$ can do the same work in $20$ days. They work together for $3$ days and then $A$ goes away. In how many days will $B$ finish the work?

Answer 1

Work done by $A$ in $1$ day $=\frac{1}{12}$
Work done by $B$ in $1$ day $=\frac{1}{20}$
Work done by $A$ and $B$ together in $1$ day $=\frac{1}{12}+\frac{1}{20}$
$=\frac{5+3}{60}=\frac{8}{60}=\frac{2}{15}$
Work done by $A$ and $B$ together in $3$ days $=\frac{2}{15}\times 3=\frac{2}{5}$
Remaining Work $=1-\frac{2}{5}=\frac{3}{5}$
Number of days taken by $B$ to finish the remaining work $=\frac{\frac{3}{5}}{\frac{1}{20}}=\frac{3}{5}\times \frac{20}{1}$
$=12$ days.