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      Question

      Pipe A can fill a tank in 10 minutes, and Pipe B can

      fill the same tank in 15 minutes. Pipe C can empty the full tank in 30 minutes. All three pipes are opened together when the tank is empty. In how much time will the tank be completely filled?
      A 7.5 mins Correct Answer Incorrect Answer
      B 5 mins Correct Answer Incorrect Answer
      C 10 mins Correct Answer Incorrect Answer
      D 1.8 mins Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      ATQ, Rates (tank/minute): Pipe A: 1/10 Pipe B: 1/15 Pipe C (emptying): −1/30 Net rate when all three are open: = 1/10 + 1/15 − 1/30 LCM of 10,15,30 = 30 = 3/30 + 2/30 − 1/30 = (3 + 2 − 1)/30 = 4/30 = 2/15 tank per minute Time to fill 1 tank = 1 ÷ (2/15) = 15/2 = 7.5 minutes.

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