Question

A water tap fills a tank in p hours and the tap of the bottom of the tank empties it in q hours. If p is less than q and when both the taps are open, the tank is filled in r hours. Then

• A. $\frac{1}{r}=\frac{1}{p}+\frac{1}{q}$
• B. $\frac{1}{r}=\frac{1}{p}-\frac{1}{q}$
• C. $r=p+q$
• D. $r=p-q$

Answer 1

The correct option is B $\frac{1}{r}=\frac{1}{p}-\frac{1}{q}$

If a water tap fills a tank in $p$ hours, then

part filled in $1$ hour $\frac{1}{p}$.

If tap empty a tank in $q$ hours, then

part emptied in $1$ hour $\frac{1}{q}$.

When both the taps are open, the net part filled in $1$ hour

$\frac{1}{r}=\frac{1}{p}-\frac{1}{q}$

Hence, this is the answer.