Question
Pipes X and Y can fill a tank in 45 minutes and 60 minutes
respectively. Another pipe Z can empty the tank in 1 hour 30 minutes. If X and Z are opened first and Y is opened after 20 minutes, in how much total time will the tank be filled?Solution
ATQ,
Let tank capacity be 180 litres (LCM of 45, 60, 90)
Efficiency of X = 180 ÷ 45 = 4 litres/minute
Efficiency of Y = 180 ÷ 60 = 3 litres/minute
Efficiency of Z = 180 ÷ 90 = -2 litres/minute
Filled in 20 minutes = (4 - 2) × 20 = 40 litres
Remaining = 180 - 40 = 140 litres
Time for remaining = 140 ÷ (4 + 3 - 2) = 28 minutes
Total time = 20 + 28 = 48 minutes
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