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 between p, q, r :
a) $$\frac{1}{r} = \frac{1}{p} + \frac{1}{q}$$
b) $$\frac{1}{r} = \frac{1}{p} – \frac{1}{q}$$
c) $$r{\text{ = }}p{\text{ }} + {\text{ }}q$$
d) $${\text{ }}r{\text{ }} = {\text{ }}p{\text{ }} – {\text{ }}q$$

Answer: b
Explanation:

Net efficiency = q – p (∵ q > p)
Time required
$$\eqalign{ & {\text{r}} = \frac{{pq}}{{q – p}} \cr & or\,\frac{1}{r} = \frac{1}{p} – \frac{1}{q} \cr} $$