Question
Pipe ‘X’ and pipe ‘Y’ can fill a tank in 30
hours and 45 hours respectively. Pipe ‘Z’ is 20% more efficient than pipe ‘X’. If pipe ‘Y’ and pipe ‘Z’ are turned on together for 10 hours, how long will pipe ‘X’ take to fill the rest of the tank alone?Solution
ATQ,
Let total capacity of the tank be 180 units {LCM of (30 and 45)} Efficiency of pipe ‘X’ = 180 ÷ 30 = 6 units/hour Efficiency of pipe ‘Y’ = 180 ÷ 45 = 4 units/hour Efficiency of pipe ‘Z’ = 1.20 × 6 = 7.2 units/hour Water filled by pipe ‘Y’ and pipe ‘Z’ in 10 hours = (4 + 7.2) × 10 = 112 units Remaining water to be filled = 180 – 112 = 68 units Time taken by pipe ‘X’ to fill remaining tank = 68 ÷ 6 = 11.33 hours
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