Question

$A$ can do a piece of work in $20$ days and $B$ can do it in $30$ days. How long will they take to do the work together?

Answer 1

Work done by $A$ in $1$ day $=\frac{1}{20}$, Work done by $B$ in $1$ day $=\frac{1}{30}$

Work done by $A$ and $B$ in $1$ day $=\frac{1}{20}+\frac{1}{30}$

$=\frac{3+2}{60}=\frac{5}{60}=\frac{1}{12}$ of the work

Total number of days required to finish the work by $A$ and $B$

$=\frac{1}{\frac{1}{12}}=12days$