# Moderate Time and Work Solved QuestionAptitude 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.

## (2) Comment(s)

Herat Patel
()

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

$\dfrac{1}{120} - \dfrac{1}{L} = \dfrac{1}{150}$
$L= 600\text{ mins}$
Which is $\textbf{10 hours}$