Question

An electric pump can fill a tank in $3$ hours. Because of a leak in the tank, it took $3\frac{1}{2}$ hours to fill the tank. The leak can drain all the water off the tank in

• A. $12$ hours
• B. $10\frac{1}{2}$ hours
• C. $6\frac{1}{2}$ hours
• D. $21$ hours

Answer 1

The correct option is D $21$ hours

Let the leak be able to empty the tank in $x$ hours.
Then, amount filled by the pump in one hour = $\frac{1}{3}$
Amount emptied by the leak = $\frac{1}{x}$
Amount actually filled = $\frac{1}{3.5}$ = $\frac{2}{7}$
i.e $\frac{1}{3}$ - $\frac{1}{x}$ = $\frac{2}{7}$
$\frac{1}{x}$ = $\frac{1}{3}$ - $\frac{2}{7}$
= $\frac{7}{21}$ - $\frac{6}{21}$ = $\frac{1}{21}$
Thus, x = 21 hours