Question
Pipes X and Y alone can fill a tank in 8 hours and 3 hours respectively. When both pipes along with pipe Z, an outlet pipe, are opened together, 5/12 of the tank gets filled in 60 minutes. Find the time taken by pipe Z to empty a completely filled tank.
Solution
Let the total capacity of the tank be 24 litres.
Efficiency of Pipe 'X' = 24 / 8 = 3 litres/hour
Efficiency of Pipe 'Y' = 24 / 3 = 8 litres/hour
Let pipe 'Z' empties the tank with an efficiency of 'm' litres/hour.
Tank filled in 60 minutes = (5/12) × 24 = 10 litres
ATQ,
(3 + 8 - m) × (60/60) = 10
(11 - m) × 1 = 10
11 - m = 10
m = 1 litres/hour
Time taken by Z to empty the tank = 24 / 1 = 24 hours
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