Question
Pipe βAβ and pipe βBβ, together can fill 20% of
a tank in 5 hours while pipe βCβ takes 37 hours to empty it. Pipe βAβ and pipe βBβ were opened together. After 13 hours, pipe βCβ is also opened. Find the total time taken to fill the empty tank this way.Solution
Time taken by pipe βAβ and pipe βBβ, together to fill the tank = 5/0.20 = 25 hours Let the total capacity of tank = 925 units Efficiency of pipe (A + B) = 925/25 = 37 units/hour Efficiency of pipe βCβ = 925/37 = 25 units/hour Tank filled by pipe (A + B) in 13 hours = 13 Γ 37 = 481 units Time taken by all three pipes to fill the remaining tank = (925 β 481)/(37 β 25) = 37 hrs Total time taken = 13 + 37 = 50 hours
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