Pipes and Cistern Filling Time – UGC NET Question

The tap fills 1/12 of the tank per hour, while the leakage empties 1/18 of the tank per hour. When both operate together, the net filled amount per hour is 1/12 − 1/18. Taking the least common multiple of 12 and 18 as 36, we get the net rate as 3/36 − 2/36 = 1/36 of the tank per hour. Thus, the tank will be completely filled in 36 hours.

Option A:
Option A, 9 hours, would imply a net rate of 1/9 per hour, which is much faster than 1/36 and cannot be achieved under the given rates of filling and emptying. This ignores the slowing effect of the leakage.

Option B:
Option B, 12 hours, equals the time taken by the tap alone without any leakage. Since the leakage reduces the effective filling rate, the actual time must be longer than 12 hours.

Option C:
Option C, 18 hours, still underestimates the combined effect because the leakage continuously counters the filling tap. The computed net rate clearly shows that an even longer period is needed.

Option D:
Option D aligns with the net rate of 1/36 per hour obtained by subtracting the emptying rate from the filling rate. It is the only option that respects the mathematical relationship between the two processes.