Two inlets A and B can fill a cistern in 12 minutes and 14 minutes, respectively, while an outlet C can empty it in 8 minutes. If all three taps are opened simultaneously on an empty cistern, what fraction of the cistern remains unfilled at the end.

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

Accepted Answer

Introduction / Context:Compute the net rate with all three taps, multiply by 7 minutes to get the filled fraction, then subtract from 1 to get the unfilled fraction. Given Data / Assumptions: A = 1/12 tank/min. B = 1/14 tank/min. C = −1/8 tank/min. Concept / Approach:Net rate r = 1/12 + 1/14 − 1/8. Filled in 7 minutes = 7r. Unfilled = 1 − 7r. Step-by-Step Solution: LCM 168 ⇒ r = (14 + 12 − 21)/168 = 5/168 tank/min.Filled in 7 min = 7 * 5/168 = 35/168 = 5/24.Unfilled = 1 − 5/24 = 19/24. Verification / Alternative check:Converting to decimals yields the same result; 19/24 ≈ 0.7917 unfilled, consistent. Why Other Options Are Wrong:5/24 is the filled fraction, not the unfilled; 7/24 and 17/24 do not match the exact arithmetic. Common Pitfalls:Confusing “remaining unfilled” with “filled.” Always subtract from 1. Final Answer:19/24

Two inlets A and B can fill a cistern in 12 minutes and 14 minutes, respectively, while an outlet C can empty it in 8 minutes. If all three taps are opened simultaneously on an empty cistern, what fraction of the cistern remains unfilled at the end of 7 minutes?

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