Pipe ‘A’ can fill a tank in 60 hours whereas leak

Q: Answer-Pipe ‘A’ can fill a tank in 60 hours whereas leak ‘A’ can empty it in 70 hours. If they both operate...

Let the capacity of the tank be 420 litres LCM 60 and 70 Efficiency of pipe A 420 60 7 litreshour Efficiency of leak A 420 70 6 litreshour Combined efficiency of pipe A and leak A 7 6 1 litrehour Combined efficiency of pipe A, B and leak A 420 35 12 unitshour Efficiency of pipe B 12 1 11 unitshour Time taken by pipe B and leak A to fill the tank 420 11 6 84 hours

‘A’ can empty it in 70 hours. If they both operate along with pipe ‘B’, then the given tank gets filled in 35 hours. How much time is needed to fill the given tank if pipe ‘B’ and leak ‘A’ work together?

A 40 hours Correct Answer Incorrect Answer

B 60 hours Correct Answer Incorrect Answer

C 75 hours Correct Answer Incorrect Answer

D 30 hours Correct Answer Incorrect Answer

E 84 hours Correct Answer Incorrect Answer

Solution

Let the capacity of the tank be 420 litres {LCM (60 and 70)} Efficiency of pipe ‘A’ = 420 ÷ 60 = 7 litres/hour Efficiency of leak ‘A’ = 420 ÷ 70 = 6 litres/hour Combined efficiency of pipe ‘A’ and leak ‘A’ = 7 – 6 = 1 litre/hour Combined efficiency of pipe ‘A’, ‘B’ and leak ‘A’ = 420 ÷ 35 = 12 units/hour Efficiency of pipe ‘B’ = 12 – 1 = 11 units/hour Time taken by pipe ‘B’ and leak ‘A’ to fill the tank = 420 ÷ (11 – 6) = 84 hours

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