Two inlet pipes J and K can fill a tank in 24 minutes and 36 minutes respectively, while an outlet pipe L can empty the full tank in 18 minutes. If in the 1st minute only J and K operate, in the 2nd minute J, K and L operate together, and this 2-minute cycle continues until the tank is 50% filled, after that only pipe J is kept open. Find the total time to fill the tank completely.

ATQ, Total capacity of tank = 72 litres (LCM of 24, 36 and 18) Efficiency of J, K, and L = 3 l/min, 2 l/min and -4 l/min respectively Now, for first minute J and K work = 3 + 2 = 5 litres For second minute J, K and L work = 3 + 2 - 4 = 1 litre So, in 2 mins tank filled = 5 + 1 = 6 litres Then, 50% of tank filled = 72/2 = 36 litres Time to fill 36 litres = 36/6 * 2 = 6 * 2 = 12 minutes Now, remaining 50% of tank = 36 litres filled by J only Time = 36/3 = 12 minutes Thus, the required time taken = 12 + 12 = 24 minutes Hence, the required answer = 24 minutes