Option 2 : 24hours

Given:

Time taken by pipe A to fill the tank alone = 8 hours = 8 × 60 = 480 minutes

Time taken by pipe B to fill the tank alone = 12 hours = 12 × 60 = 720 minutes

Extra time taken, due to the leakage = 72 minutes

Formula Used:

Work = Time taken × Efficiency

Calculation:

Let the capacity of the tank be 24 units (L.C.M of 8, 12)

A's efficiency = 24/8 = 3 units/hr

B's efficiency = 24/12 = 2 units/hr

(A + B)'s time = 24/(3 + 2) = 4 hrs and 48 min = (4 × 60) + 48 = 288 minutes

(A + B + leakage)'s time = 288 + 72 = 360 minutes = 6 hours

(A + B + leakage)'s efficiency = 24/6 = 4 unit/hr

(leakage)'s efficiency = 4 - 5 = -1 unit/hr

Time taken by leakage to empty = 24/1 = 24 hrs

∴ The time in which the leakage can empty the full tank is 24 hours

__Important Points__

The efficiency of leakage or emptying pipe is always negative