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?

Question

Solve this multiple-choice question and choose the correct option.

Accepted Answer

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: Compute r with denominator 2880: 1/32 = 90/2880; 1/36 = 80/2880; 1/20 = 144/2880.r = (90 + 80 − 144)/2880 = 26/2880 = 13/1440 tank/min.t = (1/2) / (13/1440) = (1/2) * (1440/13) = 720/13 ≈ 55.38 minutes. 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)

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?

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