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:

The electric pump fills the tank in 6 hours, and due to leakage, it takes $$7\frac{ 1}{3}$$​ hours to fill the tank.
We can assume the pump's rate is the inverse of the time it takes to fill the tank.
Let the leakage rate be L (in tank per hour). Therefore, the effective filling rate is reduced by this leakage rate.

Concept Used: Effective filling rate = $$\frac{1}{6}$$​ - L, and Leakage rate = L. The time to empty the tank will be the inverse of the leakage rate.

Solution:
The electric pump's rate of filling the tank is $$\frac{1}{6}$$​ per hour.
The total time it takes to fill the tank due to leakage is $$7\frac{ 1}{3}$$​ hours, which is equivalent to $$\frac{22}{3}$$​ hours.
The effective rate of filling the tank is $$\frac{3}{22}$$​ per hour.
Therefore, the leakage rate is the difference between the pump's rate and the effective rate:
​$$L = \frac{1}{6} -\frac{ 3}{22}$$​​
Solving for L, we get the leakage rate and the time to empty the tank is 1/L.
The time to empty the tank =$$\frac{1}{L }= 36$$​ hours.

Final Answer: The leakage will take 36 hours to empty the tank.