A cistern normally takes 10 hours to be filled by a tap. But because of a leak, it takes 2 hours more. In how many hours will the leak empty a full cistern ?

let the capacity of tank be 10 units

time taken to fill the tank = 10 h

therefore a tap fills units per hour = 1 unit

due to leak time taken to fill the tank= 10+2 =12 hrs

in 12 hrs tap would have filled 12 units but, due to leak it filled 10 units [as mentioned in the question]

so therefore due to leak 2 units were lost in 12 hrs

so to empty the tank would lose every 2 units 12 hrs

this means it will take 5*12 = 60 hrs to empty the tank