Question
Pipe ‘A’ can fill a tank in 16 hours whereas leak
‘A’ can empty it in 20 hours. If they both operate along with pipe ‘B’, then the given tank gets filled in 8 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 80 litres {LCM (16 and 20)} Efficiency of pipe ‘A’ = 80 ÷ 16 = 5 litres/hour Efficiency of leak ‘A’ = 80 ÷ 20 = 4 litres/hour Combined efficiency of pipe ‘A’ and leak ‘A’ = 5 – 4 = 1 litre/hour Combined efficiency of pipe ‘A’, ‘B’ and leak ‘A’ = 80 ÷ 8 = 10 units/hour Efficiency of pipe ‘B’ = 10 – 1 = 9 units/hour Time taken by pipe ‘B’ and leak ‘A’ to fill the tank = 80 ÷ (9 – 4) = 16 hours
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