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      Question

      An inlet tap alone can fill a tank in 40 minutes.

      However, when both an inlet and an outlet tap are open together, the tank takes 66 (2/3) minutes (or 200/3 minutes) to fill. If 20 inlet taps and 25 identical outlet taps are opened simultaneously, how long will it take to completely fill the tank?
      A 4.5 min Correct Answer Incorrect Answer
      B 2 min Correct Answer Incorrect Answer
      C 4 min Correct Answer Incorrect Answer
      D 10 min Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      Time taken by inlet tap together with outlet tap to fill the tank = (200/3) minutes


      Let the capacity of the tank be 200x units (LCM of 40 and 200)


      Or, efficiency of inlet tap = (200x/40) = 5x units/minute


      Or, efficiency of outlet tap = 5x - {(200x) ÷ (200/3) } = 2x units/minute


      So, combined efficiency of 20 inlet and 25 such outlet pipes:


      = 20 X 5x - 25 X 2x = 50x units/min
      Therefore, required time = (200x/50x) = 4 minutes

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