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Question 31 :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? [TITA]


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Explanatory Answer

Method of solving this CAT Question from Pipes & Cisterns

Given, Tank gets filled in 6 hours when 6 filling and 5 draining pipes are on
Let, F be the rate at which a single filling pipe fills the tanks and D be the rate at which a single draining pipe drains the pipe
6F – 5D = \\frac{1}{6}) th of the tank ---(1)
Also, Tank gets filled in 60 hours when 5 filling and 6 draining pipes are on
5F-6D = \\frac{1}{60}) th of the tank ---(2)

Solving both (1) and (2) we get,
6F - 5D = \\frac{1}{6})
(-) 50 F - 60 D = \\frac{1}{6})
---------------------------
44F = 55D
F:D = 5:4

Replacing values in (1), 6F – 5D = \\frac{1}{6})
15D – 10D = 1/3
D = 1/15 and F = 1/12
When two filling pipes and one draining pipes are on,
2(\\frac{1}{6})) – 1(\\frac{1}{15})) = (\\frac{3}{30})) = \\frac{1}{10})th of the tank

Therefore, they can fill the tank in 10 hours

The question is "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? [TITA]"

Hence, the answer is 10 hours

 

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