Question

$P$ can do a work in 15 days and $Q$ in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is

Answer 1

Amount of work $P$ and $Q$ can do in 1 day $=\left(\frac{x+y}{xy}\right)=\left(\frac{15+20}{15\times 20}\right)=\left(\frac{35}{15\times 20}\right)=\left(\frac{7}{60}\right)$
Amount of work $P$ and $Q$ can together do in 4 days $=4\times \left(\frac{7}{60}\right)=\frac{7}{15}$
Fraction of work left $=1-\frac{7}{15}=\frac{8}{15}$