Inlet and Outlet Pipes Tank Filling

CAT 2019 Slot 1 · QA · Easy · Pipes & Cisterns

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A tank is fitted with pipes, some filling it and the rest draining it. All filling pipes fill at the same rate, and all draining pipes drain at the same rate. The empty tank gets completely filled in 6 hours when 6 filling and 5 draining pipes are on, but this time becomes 60 hours when 5 filling and 6 draining pipes are on. In how many hours will the empty tank get completely filled when one draining and two filling pipes are on?

Answer

10

Explanation

Let fill rate per pipe = ff, drain rate per pipe = dd. Capacity C=6(6f−5d)C = 6(6f - 5d). Also C=60(5f−6d)C = 60(5f - 6d). 36f−30d=300f−360d⇒330d=264f⇒5d=4f⇒d=0.8f36f - 30d = 300f - 360d \Rightarrow 330d = 264f \Rightarrow 5d = 4f \Rightarrow d = 0.8f. C=6(6f−5(0.8f))=6(2f)=12fC = 6(6f - 5(0.8f)) = 6(2f) = 12f. Net rate for 2 filling and 1 draining = 2f−d=2f−0.8f=1.2f2f - d = 2f - 0.8f = 1.2f. Time = 12f1.2f=10\frac{12f}{1.2f} = 10 hours.

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