A pipe can fill a tank in 24hrs. Due to a leakage in the botom, it is filled in 36 hrs. If the tank is half full, how much time will the leak take to take to empty the tank?

Let the volume of the tank = V

Time required for the pipe to fill the tank = 24hrs

$$=$$>  Volume filled by the tank in 1 hour = $$\frac{V}{24}$$

Let the time required for leak to empty the tank = $$x$$ hrs

$$=$$>  Volume emptied by the leak in 1 hour = $$\frac{V}{x}$$

Time required to fill the tank when both the pipe and leak are working = 36hrs

$$=$$> Volume filled in 1 hour when both the pipe and leak are working = $$\frac{V}{36}$$

$$=$$>  $$\frac{V}{24}-\frac{V}{x}=\frac{V}{36}$$

$$=$$>  $$\frac{V}{x}=\frac{V}{24}-\frac{V}{36}$$

$$=$$>  $$\frac{1}{x}=\frac{3-2}{72}$$

$$=$$>  $$\frac{1}{x}=\frac{1}{72}$$

$$=$$>  $$x=72$$ hours

$$\therefore\ $$Time required for the leak to empty the tank = 72 hours

$$=$$>  Time required for the leak to empty half of the tank = $$\frac{72}{2}$$ = 36 hours

Hence, the correct answer is Option C