Question
Pipes ‘A’ and ‘B’ can fill a tank in 6 hours and
4 hours respectively. When both pipes and an outlet pipe ‘C’ are opened together, (2/5)th of the tank is filled in 48 minutes. Find the time required by pipe ‘C’ to empty the full tank.Solution
ATQ; Let the total capacity of the tank be 120 litres. Efficiency of Pipe ‘A’ = (120 / 6) = 20 litres/hour Efficiency of Pipe ‘B’ = (120 / 4) = 30 litres/hour Let pipe ‘C’ empties the tank with an efficiency of ‘m’ litres/hour. Tank filled in 48 minutes = (2/5) × 120 = 48 litres ATQ, (20 + 30 - m) × (48/60) = 48 (50 - m) × 0.8 = 48 40 - 0.8m = 48 0.8m = -8 m = -10 litres/hour (since negative, outlet pipe removes water) Time taken by pipe ‘C’ to empty the tank = (120 / 10) = 12 hours
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