Question
Three pipes A, B and C are connected to a reservoir. Pipe A can fill it in 16 minutes, pipe B can fill it in 24 minutes, while pipe C can empty the completely filled reservoir in 48 minutes. Pipe A is opened first, pipe B after 4 minutes, and pipe C after 8 minutes. Find the total time taken to fill the reservoir.
Solution
Let the capacity of the reservoir be 48 litres. {LCM (16, 24 and 48)}
So, efficiency of inlet pipe A = 48 ÷ 16 = 3 litres/minute
And, efficiency of inlet pipe B = 48 ÷ 24 = 2 litres/minute
And, efficiency of outlet pipe C = 48 ÷ 48 = 1 litre/minute
In first 4 minutes, pipe A will fill 4 × 3 = 12 litres
And, pipes A and B together will fill 4 × (3 + 2) = 20 litres
So, required time = 4 + 4 + {(48 − 12 − 20) ÷ (3 + 2 − 1)}
= 8 + (16 ÷ 4) = 12 minutes
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