Three pipes act on a tank: Pipe A fills it in 32 minutes, Pipe B fills it in 36 minutes, and Pipe C empties it in 20 minutes. If all three pipes are opened simultaneously, in how many minutes will exactly half of the tank be filled?

Introduction / Context:
We combine the two inlet rates and subtract the outlet rate to obtain the net rate. Since the target is half the tank, we set (net rate) * time = 1/2 and solve for time. If that value does not match any provided option, “None of these” is appropriate.

Given Data / Assumptions:

• A = 1/32 tank/min.
• B = 1/36 tank/min.
• C = −1/20 tank/min.
• Goal: reach 1/2 tank from empty.

Concept / Approach:
Net rate r = 1/32 + 1/36 − 1/20. Then time t satisfies r * t = 1/2 ⇒ t = (1/2) / r.

Step-by-Step Solution:

Verification / Alternative check:
Multiply r by 720/13: (13/1440) * (720/13) = 1/2, confirming correctness.

Why Other Options Are Wrong:
16/24/48 min do not match 720/13; hence the correct choice is “None of these.”

Common Pitfalls:
Dropping the outlet term or using rounded intermediate values. Keep exact fractions until the final step.

Final Answer:
None of these (exact time = 720/13 minutes ≈ 55.38 min)