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. In how much time can the leak drain all the water of the tank?

• A. $21$ hours
• B. $29$ hours
• C. $20$ hours
• D. $11$ hours

Answer 1

The correct option is A $21$ hours

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

$\therefore$ Part of the tank emptied by the leak in 1 hour $=\frac{1}{3}-\frac{2}{7}=\frac{1}{21}$
$\therefore$ The tank will be emptied by the leak in $21$ hours.