Two inlets P and Q can fill a cistern in 12 minutes and 15 minutes, respectively. Both are opened together, but after exactly 3 minutes, P is turned off and only Q continues. How much longer (beyond the first 3 minutes) will it take to fill the.

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

Accepted Answer

Introduction / Context:We find the fraction filled in the first 3 minutes with both inlets, then compute the remaining time with only Q running at its solo rate. Given Data / Assumptions: P = 1/12 tank/min. Q = 1/15 tank/min. Both on for 3 minutes; after that only Q continues. Concept / Approach:Phase 1 fill = 3 * (1/12 + 1/15). Remainder / (1/15) gives the additional minutes needed. Step-by-Step Solution: Phase 1 fill = 3 * ((5 + 4)/60) = 3 * (9/60) = 27/60 = 9/20.Remaining = 1 − 9/20 = 11/20.Extra time = (11/20) / (1/15) = 11 * (15/20) = 165/20 = 8.25 minutes = 8 1/4 minutes. Verification / Alternative check:In 8.25 min, Q adds 8.25/15 = 11/20; total reaches 1. Why Other Options Are Wrong:Other times do not correspond to the exact remainder at Q’s rate. Common Pitfalls:Arithmetic with common denominators; avoid rounding until the end. Final Answer:8 1/4 minutes

Two inlets P and Q can fill a cistern in 12 minutes and 15 minutes, respectively. Both are opened together, but after exactly 3 minutes, P is turned off and only Q continues. How much longer (beyond the first 3 minutes) will it take to fill the cistern completely?

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