Question
Pipe ‘A’ can fill a tank in 15 hours whereas leak
‘A’ can empty it in 45 hours. If they both operate along with pipe ‘B’, then the given tank gets filled in 9 hours. How much time is needed to fill the given tank if pipe ‘B’ and leak ‘A’ work together?Solution
Let the capacity of the tank be 45 litres {LCM (15 and 45)} Efficiency of pipe ‘A’ = 45 ÷ 15 = 3 litres/hour Efficiency of leak ‘A’ = 45 ÷ 45 = 1 litres/hour Combined efficiency of pipe ‘A’ and leak ‘A’ = 3 – 1 = 2 litre/hour Combined efficiency of pipe ‘A’, ‘B’ and leak ‘A’ = 45 ÷ 9 = 5 units/hour Efficiency of pipe ‘B’ = 5 – 2 = 3 units/hour Time taken by pipe ‘B’ and leak ‘A’ to fill the tank = 45 ÷ (3 – 1) = 22.5 hours
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