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