An electric pump can fill a tank in 6 hours. Due to a leakage in the tank, it takes 7 $$\frac{1}{5}$$ hours to fill the tank.
How much time will this leak take to empty the full tank if water does not get in or out of the tank through any other point during this period?

Correct option is C

Given:

An electric pump fills the tank in 6 hours.

Due to a leakage, it now takes 7$$\frac{1}{5} = \frac{36}{5}$$​ hours to fill the tank.

Solution:

Let capacity of tank = 1 unit.

Filling rate of pump = $$\frac{1}{6}$$​ tank/hour

Net rate (with leakage) = $$\frac{5}{36}$$​ tank/hour

Leakage rate = $$\frac{1}{6} - \frac{5}{36} = \frac{6 - 5}{36} = \frac{1}{36}$$​​

So, leak empties $$\frac{1}{36}$$​ tank per hour => it will empty the tank alone in 36 hours

Alternate Solution: 

Let the capacity of the tank = LCM of 6 and $$\frac{36}{5}$$​ = 36 units

Pump fills 36 units in 6 hours => 6 units/hour

Net filling time = $$\frac{36}{\frac{36}{5}}$$​ = 5 units/hour

Leakage rate = 6 – 5 = 1 unit/hour (i.e., leak removes 1 unit per hour)

So, time taken by leak alone to empty 36 units =$$\frac{36}{1}$$​ = 36 hours