Question

$A$ and $B$ working separately can do a piece of work in 10 and 15 days respectively. If they work on alternate days beginning with $A$, in how many days will the work be completed?

Answer 1

Work done by $A$ in 1 day $=\frac{1}{10}$
Work done by $B$ in 1 day $=\frac{1}{15}$
Work done by $A$ and $B$ in 2 days $=\frac{1}{10}+\frac{1}{15}=\frac{3+2}{30}=\frac{5}{30}=\frac{1}{6}$
$\because \frac{1}{6}$ work is done in 2 days
1 work will be done in $2\times 6=12$ days.