Aptitude Discussion

Q. |
Pipe $A$ usually fills a tank in 2 hours. On account of a leak at the bottom of the tank, it takes pipe $A$ 30 more minutes to fill the tank. How long will the leak take to empty a full tank if pipe $A$ is shut? |

✖ A. |
2 hours 30 minutes |

✖ B. |
5 hours |

✖ C. |
4 hours |

✔ D. |
10 hours |

**Solution:**

Option(**D**) is correct

Pipe $A$ fills the tank normally in 2 hours. Therefore, it will fill \(\dfrac{1}{2}\) of the tank in an hour.

Let the leak take $x$ hours to empty a full tank when pipe $A$ is shut.

Therefore, the leak will empty \(\dfrac{1}{4}\) of the tank in an hour.

The net amount of water that gets filled in the tank in an hour when pipe $A$ is open and when there is a leak

= \(\dfrac{1}{2}-\dfrac{1}{x}\)of the tank. ------- (1)

When there is a leak, the problem states that Pipe $A$ takes two and a half hours to fill the tank. i.e. \(\dfrac{5}{2}\) hours.

Therefore, in an hour, \(\left(\dfrac{5}{2}\right)^{th}\) of the tank gets filled. --------- (2)

Equating (1) and (2), we get \(\dfrac{1}{2}-\dfrac{1}{x}=\dfrac{2}{5}\)

\(\dfrac{1}{x}=\dfrac{1}{2}-\dfrac{2}{5}=\dfrac{1}{10}\)

\(\Rightarrow x=10\) hours

The problem **can also be done mentally** as follows.

Pipe $A$ takes 2 hours to fill the tank. Therefore, it fills half the tank in an hour or $50\%$ of the tank in an hour.

When there is a leak it takes 2 hours 30 minutes for the tank to fill. i.e \(\dfrac{5}{2}\) hours to fill the tank or \(\left(\dfrac{2}{5}\right)^{th}\) or $40\%$ of the tank gets filled.

On account of the leak, $(50−40)\%=10\%$ of the water gets wasted every hour.

Therefore, the leak will take **10 hours** to drain a full tank.

**Herat Patel**

*()
*

**Zoha Amjad**

*()
*

convert hours into mins before solving.

$\dfrac{1}{120} - \dfrac{1}{L} = \dfrac{1}{150}$

$L= 600\text{ mins}$

Which is $\textbf{10 hours}$

suppose A is fill tap and B is Leakage

A 2hrs 5 ltr/hr Lets Tank Size = LCM(2 , 2.5) = 10

B ? -1 ltr/hr

------------------------------------

A+B 2.5 hrs 4 ltr/hr

Now we know 1ltr/hr is leak from the tank

so 10/1

Ans = 10hrs