# Moderate Time and Work Solved QuestionAptitude Discussion

 Q. Pipe $A$ can fill a tank in '$a$' hours. On account of a leak at the bottom of the tank it takes thrice as long to fill the tank. How long will the leak at the bottom of the tank take to empty a full tank, when pipe $A$ is kept closed?
 ✔ A. $\dfrac{3a}{2}$ hours ✖ B. $\dfrac{2a}{3}$ hours ✖ C. $\dfrac{4a}{3}$ hours ✖ D. $\dfrac{3a}{4}$ hours

Solution:
Option(A) is correct

Pipe $A$ fills the tank in '$a$' hours.

Therefore, $\dfrac{1}{a}$ of the tank gets filled in an hour.

On account of the leak it takes $3a$ hours to fill the tank.

Therefore, $\dfrac{1}{3a}$of the tank gets filled in an hour.
Let the leak at the bottom of the tank take '$x$' hours to empty the tank.

Hence, $\dfrac{1}{x}$of the tank gets emptied every hour.

$\dfrac{1}{a}-\dfrac{1}{x}=\dfrac{1}{3a}$

$\dfrac{1}{x}=\dfrac{1}{a}=\dfrac{1}{3a}=\dfrac{2}{3a}$

Hence, $x = \dfrac{3a}{2}$