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?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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