Three pipes can fill a tank in 3 hours, 4 hours and 6 hours. However, there is a leak in the tank at a height of 1/3 of the tank from the bottom which can drain the rest of the tank in 9 hours. What will be the time taken to fill the tank?

The three filling pipes together fill at rate 1/3 + 1/4 + 1/6 = 4/12 + 3/12 + 2/12 = 9/12 = 3/4 tank per hour. The leak affects only the top 2/3 of the tank. For the first 1/3, only filling pipes work: time = (1/3) / (3/4) = 4/9 hours. For the remaining 2/3, effective rate = 3/4 - 1/9 = (27-4)/36 = 23/36 tank per hour. Time = (2/3) / (23/36) = 24/23 hours. Total = 4/9 + 24/23 = (92+216)/207 = 308/207 hours = 1.488 hours = 89.28 minutes.