Question

$A$ can do $\frac{2}{3}$ of a certain work in $16$ days and $B$ can do $\frac{1}{4}$ of the same work in $3$ days. In how many days can both finish the work. working together?

Answer 1

$A$ does $\frac{2}{3}$ work in $16$ $days.$

Therefore, $A$ can do whole work in $16\times \frac{3}{2}=24$ $days$

$B$ does $\frac{1}{4}$ work in $3$ days.

Therefore, $B$ can do whole work in $12$ $days$.

$1$ day's work of $A$ and $B$ together $=\frac{1}{24}+\frac{1}{12}=\frac{1}{8}$

Therefore, $A$ and $B$ can together finish the work in $8$ $days$.