Question

A tap can fill a tank in 60 min. Tap is turned on to fill the tank. When the tank is half full, it springs a leak at the bottom and the water level falls to 1/4 of the tank in 10 min. The tap is now closed. What is the time taken by the leakage to empty the tank now?

Answer 1

Answer:

Time taken by the tap to fill the tank=60 minute= 1 hour

Let V be the volume of tank .

Now, when the tank is half full, water level falls to $\frac{1}{4}$ of the tank in 10 minute.

In 10 minutes volume is  $\frac{1}{4}$ of half filled tank is $\frac{V}{8}$.

Speed of leak , that is water which passes out through leakage in 1 minute

$=\frac{V}{2}\times \frac{1}{4}\times \frac{1}{10}\\\\=\frac{V}{80}$

Remaining water in tank

$=\frac{V}{2}-\frac{V}{8}\\\\=\frac{3V}{8}$

Let x minutes be taken by leak to completely empty the tank.

$x \times \frac{V}{80}=\frac{3V}{8}\\\\x=\frac{80 \times 3}{8}\\\\x=30$

So, time taken by the leakage to empty the tank now= 30 minutes