Question
Pipe X can fill a tank in 25 minutes, pipe Y can fill it in 50 minutes, while pipe Z can empty it in 20 minutes. Pipe X is opened first, pipe Y after 5 minutes, and pipe Z after 10 minutes. Find the total time taken to fill the tank.
Solution
Let the capacity of the tank be 100 litres. {LCM (25, 50 and 20)}
So, efficiency of inlet pipe X = 100 ÷ 25 = 4 litres/minute
And, efficiency of inlet pipe Y = 100 ÷ 50 = 2 litres/minute
And, efficiency of outlet pipe Z = 100 ÷ 20 = 5 litres/minute
In first 5 minutes, pipe X will fill 5 × 4 = 20 litres
And, pipes X and Y together will fill 5 × (4 + 2) = 30 litres
So, required time = 5 + 5 + {(100 − 20 − 30) ÷ (4 + 2 − 5)} = 60 minutes
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