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      Question

      Pipe A can fill a tank in 8 hours, while pipe B can

      empty the full tank in 12 hours. Both pipes are opened together. After how many hours should pipe B be closed so that the tank is exactly full in 10 hours?
      A 4 hours Correct Answer Incorrect Answer
      B 2 hours Correct Answer Incorrect Answer
      C 3 hours Correct Answer Incorrect Answer
      D 8 hours Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      Let B be open for x hours. Rates: A = 1/8 per h, B = โˆ’1/12 per h Work done = x(1/8 โˆ’ 1/12) + (10 โˆ’ x)(1/8) = 1 1/8 โˆ’ 1/12 = 1/24 So: x/24 + (10 โˆ’ x)/8 = 1 Multiply 24: x + 3(10 โˆ’ x) = 24 x + 30 โˆ’ 3x = 24 โˆ’2x = โˆ’6 โ†’ x = 3 So B should be closed after 3 hours.

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