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      Question

      A tank can be filled by pipe A in 6 hours and by pipe B

      in 8 hours. There is also a waste pipe C which can empty the full tank in 12 hours. If all three pipes are opened together when the tank is empty, in how many hours will the tank be filled?
      A 12 hrs Correct Answer Incorrect Answer
      B 5.2 hrs Correct Answer Incorrect Answer
      C 4.8 hrs Correct Answer Incorrect Answer
      D 18 hrs Correct Answer Incorrect Answer

      Solution

      ATQ, Rates of work: A fills 1/6 of tank per hour B fills 1/8 of tank per hour C empties 1/12 of tank per hour Net rate = 1/6 + 1/8 − 1/12 LCM of 6, 8, 12 is 24: 1/6 = 4/24 1/8 = 3/24 1/12 = 2/24 Net = (4 + 3 − 2)/24 = 5/24 of tank per hour Time = 1 ÷ (5/24) = 24/5 = 4.8 hours.

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