Question

A pump can fill a tank with water in $2$ hours. Because of a leak in the tank, it takes $2\frac{1}{3}$ hours to fill the tank. The leak can empty the filled tank in

• A. $2\frac{1}{3}$ hours
• B. $7$ hours
• C. $8$ hours
• D. $14$ hours

Answer 1

Answer: (D)

$14$ hours

Part of the tank filled by the pump in 1 hour $=\frac{1}{2}$
Total part of the tank filled by the pump and leak in 1 hour $=\frac{1}{\frac{7}{3}}=\frac{3}{7}$

$\therefore$ Part of the tank emptied by the leak in 1 hour $=\frac{1}{2}-\frac{3}{7}=\frac{7-6}{14}=\frac{1}{14}$
$\Rightarrow$ The leak will empty the tank in $14$ hours.