Question
Pipe P can fill a tank by itself
in 16 hours, while pipe R can empty the tank in 36 hours when it is full. Together, pipes P and Q can fill the tank in 9 hours. How long will it take for pipes Q and R, working together, to fill the same tank?Solution
ATQ, Let the capacity of the tank = L.C.M of 16 and 36 = 144 units Then, efficiency of pipe ‘P’ alone = 144 ÷ 16 = 9 units/hour Efficiency of pipe ‘R’ alone = 144 ÷ 36 = 4 units/hour Combined efficiency of pipes ‘P’ and ‘Q’ = 144 ÷ 9 = 16 units/hour So, efficiency of pipe ‘Q’ alone = 16 – 9 = 7 units/hour So, combined efficiency of pipes ‘Q’ and ‘R’ = 7 – 4 = 3 units/hour So, time taken by pipes ‘Q’ and ‘R’ together to ill the tank = 144 ÷ 3 = 48 hours.
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