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 & Solution

Correct Answer: Option B

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

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A water tap fills a tub in 'p' hours and a...

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 :

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