UGCNET Questions

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.

Pipe A fills 1/10 of the tank per hour, pipe B fills 1/15 per hour, and pipe C empties 1/30 per hour. The net hourly work rate when all three are open is 1/10 + 1/15 − 1/30. Using 30 as the common denominator, this becomes 3/30 + 2/30 − 1/30 = 4/30 = 2/15 of the tank per hour. The time to fill the tank is therefore 1 ÷ (2/15) = 15/2 = 7.5 hours, which matches Option B.

Option A:
Option A, 5 hours, would require a net rate of 1/5 per hour, which is much faster than the computed 2/15 and not achievable with the given pipes.

Option B:
Option B, 7.5 hours, is exactly the reciprocal of the net rate 2/15 and correctly represents the time taken to fill the tank with all three pipes open.

Option C:
Option C, 8 hours, corresponds to a net rate of 1/8 per hour, slower than 2/15, and inconsistent with the detailed rate computation.

Option D:
Option D, 10 hours, duplicates the time taken by pipe A alone and ignores the additional inflow from B and the outflow from C, so it cannot be correct.