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 taps are opened, the tank is filled in 'r' hours. The relation between P, q and r is?

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

Let the capacity of tank = pq ltr

then,

ATQ,Working together,

Tank will fill in (r hrs.) = \(\frac{pq}{q-p}\)

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