A tap takes 42 hours extra to fill a tank due to leakage equivalent to half of its inflow. The inlet pipe alone can fill the tank in how many hours?

Let the inlet pipe's rate be 1 unit per hour, so it fills the tank in x hours (tank capacity = x units). The leak drains at half the inflow rate = 0.5 units per hour. Net fill rate with leak = 1 - 0.5 = 0.5 units per hour. Time with leak = tank capacity / net rate = x / 0.5 = 2x hours. Given: 2x - x = 42 hours (the extra time due to leak). So x = 42 hours. The inlet pipe alone takes 42 hours. This matches option A.