Question
Pipe ‘A’ can fill a tank in 30 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 20 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 90 litres {LCM (30 and 45)} Efficiency of pipe ‘A’ = 90 ÷ 30 = 3 litres/hour Efficiency of leak ‘A’ = 90 ÷ 45 = 2 litres/hour Combined efficiency of pipe ‘A’ and leak ‘A’ = 3 – 2 = 1 litre/hour Combined efficiency of pipe ‘A’, ‘B’ and leak ‘A’ = 90 ÷ 20 = 4.5 units/hour Efficiency of pipe ‘B’ = 4.5 – 1 = 3.5 units/hour Time taken by pipe ‘B’ and leak ‘A’ to fill the tank = 90 ÷ (3.5 – 2) = 60 hours
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