Inlet Pipe A can fill a tank in 30 minutes, and outlet pipes B and C can empty the tank in 2 hours each. If all 3 pipes operate together, the tank will be filled in:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 1 hour
Capacity of tank = 1 unit
Work rate of pipe A (inlet): $\frac{1}{30}$ per minute
Work rate of pipe B (outlet): $\frac{1}{120}$ per minute
Work rate of pipe C (outlet): $\frac{1}{120}$ per minute
Net work rate = $\frac{1}{30} - \frac{1}{120} - \frac{1}{120}$
= $\frac{4 - 1 - 1}{120} = \frac{2}{120} = \frac{1}{60}$ per minute
Therefore, time to fill the tank = $\frac{1}{\frac{1}{60}} = 60$ minutes