Turn one pipe off after an initial burst Two pipes A and B can fill a cistern in 15 minutes and 20 minutes respectively. Both are opened together; after exactly 2 minutes, A is closed. What total time is required to fill the tank completely?

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

Accepted Answer

Introduction / Context:Phased-operation problems require computing volume added in each phase and then finishing the remainder with the active pipe’s rate. Given Data / Assumptions: A: 15 min ⇒ 1/15 per min. B: 20 min ⇒ 1/20 per min. Phase 1: both run for 2 min; Phase 2: only B runs to completion. Concept / Approach:Work after Phase 1 plus work in Phase 2 must equal 1 tank. Solve remaining fraction / B’s rate. Step-by-Step Solution: Phase 1 fill = 2 * (1/15 + 1/20) = 2 * (7/60) = 7/30Remaining = 1 − 7/30 = 23/30B-only time = (23/30) / (1/20) = (23/30) * 20 = 46/3 minTotal time = 2 + 46/3 = 52/3 min (elapsed). Question asks total to fill: 46/3 after A is shut plus initial 2 are already included in the computed total above. Verification / Alternative check:Back-substitute: (2 min at 7/60 per min) + (46/3 at 1/20) = 1 tank. Why Other Options Are Wrong:52/3 is the sum if you misinterpret the split; 43/3 and 41/3 miscompute the remaining fraction. Common Pitfalls:Adding 2 minutes twice or using average times. Final Answer:46/3 min

Turn one pipe off after an initial burst Two pipes A and B can fill a cistern in 15 minutes and 20 minutes respectively. Both are opened together; after exactly 2 minutes, A is closed. What total time is required to fill the tank completely?

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