Question
Two pipes X and Y can fill a tank in 90 minutes and 60
minutes respectively. A third pipe Z can empty the tank in 2 hours 30 minutes. X is kept closed. Y and Z are opened together. After 40 minutes, Y is closed and X is opened. How much total time will it take to fill the tank?Solution
ATQ,
Let the tank capacity be 900 litres (LCM of 90, 60 and 150) Efficiency of 'X' = 900 ÷ 90 = 10 litres/minute Efficiency of 'Y' = 900 ÷ 60 = 15 litres/minute Efficiency of 'Z' = 900 ÷ 150 = -6 litres/minute Water filled in 40 minutes = (15 - 6) × 40 = 360 litres Remaining = 900 - 360 = 540 litres Time to fill remaining = 540 ÷ (10 - 6) = 135 minutes Total time = 40 + 135 = 175 minutes
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