Question
Pipes A and B alone can fill a tank in 6 hours and 4 hours respectively. When both pipes along with pipe C, an outlet pipe, are opened together, 3/8 of the tank gets filled in 90 minutes. Find the time taken by pipe C to empty a completely filled tank.
Solution
Let the total capacity of the tank be 24 litres.
Efficiency of Pipe 'A' = 24 / 6 = 4 litres/hour
Efficiency of Pipe 'B' = 24 / 4 = 6 litres/hour
Let pipe 'C' empties the tank with an efficiency of 'm' litres/hour.
Tank filled in 90 minutes = (3/8) × 24 = 9 litres
ATQ,
(4 + 6 - m) × (90/60) = 9
(10 - m) × 1.5 = 9
15 - 1.5m = 9
1.5m = 6
m = 4 litres/hour
Time taken by C to empty the tank = 24 / 4 = 6 hours
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