A water tap fills a tub in ‘p’ hours and a sink at the bottom empties it in ‘q’ hours. If p < q and both tap and sink are opened the tank is filled in ‘r’ hours, then the relation b/w p, q and r is:

\(\frac{1}{r}=\frac{1}{p}-\frac{1}{q}\)

According to question ,
∵ p < q,

∴ On opening pipe and sink together,

part of the tub filled in 1 hour = \(\frac{1}{p}\) -  \(\frac{1}{q}\)

hence , \(\frac{1}{p}\) -  \(\frac{1}{q}\)  = \(\frac{1}{r}\)