A pipe can fill an empty cistern with water in 5 hours. Due to leakage in its bottom, it takes 6 hours to fill the cistern. When the cistern is full, the time (in hours) in which it is emptied due to leakage is

Let us call the Pipe A.

Pipe A fills the cistern in 5hrs

so in one hr Pipe A fills 1/5th of the cistern.

However with the leak it takes 6hrs for Pipe A to fill the cistern.

Hence in one hour the cistern will have 1/6th left in.

So the difference between not leaking and leaking is 1/5 - 1/6= 1/30th of the cistern

this is amount of leak per hour.

Hence it will take 30 hours to fully empty the cistern.

A is correct choice.