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      Question

      Three pipes A, B and C are connected to a tank. Pipe A

      can fill the tank in 12 minutes, pipe B can fill it in 15 minutes, and pipe C can empty the full tank in x minutes. If all three pipes are opened together and the tank gets filled in exactly 10 minutes, what is the value of x?
      A 18 mins Correct Answer Incorrect Answer
      B 20 mins Correct Answer Incorrect Answer
      C 24 mins Correct Answer Incorrect Answer
      D 32 mins Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      ATQ, Let the capacity of the tank = 1 unit. Rates: Pipe A fills = 1/12 per minute Pipe B fills = 1/15 per minute Pipe C empties = 1/x per minute (i.e., тИТ1/x in net work) When all three are open, net rate = 1/10 (since tank fills in 10 minutes): 1/12 + 1/15 тИТ 1/x = 1/10 Compute 1/12 + 1/15: LCM(12,15) = 60 1/12 = 5/60 1/15 = 4/60 Sum = 9/60 = 3/20 So: 3/20 тИТ 1/x = 1/10 тЗТ 3/20 тИТ 1/10 = 1/x 1/10 = 2/20 So: 3/20 тИТ 2/20 = 1/20 = 1/x тЗТ x = 20 minutes

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