Question
Pipes X, Y, and Z can fill a tank in 12 hours, 6 hours,
and 8 hours respectively. If the efficiencies of pipes X and Y are each reduced by 50% of their original efficiency and all three pipes are opened together, find the total time taken to fill the tank.Solution
ATQ, Let the capacity of the tank (LCM of 12, 6, and 8) be 24 liters. Efficiency of pipe X = 24/12 = 2 liters/hour Efficiency of pipe Y = 24/6 = 4 liters/hour Efficiency of pipe Z = 24/8 = 3 liters/hour New efficiency of pipe X = 2 × (50/100) = 1 liter/hour New efficiency of pipe Y = 4 × (50/100) = 2 liters/hour Total efficiency = 1 + 2 + 3 = 6 liters/hour Required time = 24 / 6 = 4 hours
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