CAT 2017 Question Paper | Quants Slot 2

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Question 8 : A tank has an inlet pipe and an outlet pipe. If the outlet pipe is closed then the inlet pipe fills the empty tank in 8 hours. If the outlet pipe is open then the inlet pipe fills the empty tank in 10 hours. If only the outlet pipe is open then in how many hours the full tank becomes half-full ?

1. 20
2. 30
3. 40
4. 45

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Video Explanation

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Explanatory Answer

Method of solving this CAT Question from Pipes and Cisterns

Given that the inlet pipe fills the empty tank in 8 hours.
Rate of Inlet pipe = \\frac{1}{8})
If outlet pipe is open then the inlet pipe fills the empty tank in 10 hrs.
Rate of Inlet + Outlet pipe = \\frac{1}{10})
We have to find the time taken for the outlet pipe to empty or half full the full tank.
Rate of Outlet pipe = \\frac{1}{8}) - \\frac{1}{10}) = \\frac{5}{40}) - \\frac{4}{40})
Rate of Outlet pipe = \\frac{1}{40})
For emptying the full tank the outlet pipe takes 40 hours.
Hence for emptying the half tank the outlet pipe takes 20 hours.

The question is "A tank has an inlet pipe and an outlet pipe. If the outlet pipe is closed then the inlet pipe fills the empty tank in 8 hours. If the outlet pipe is open then the inlet pipe fills the empty tank in 10 hours. If only the outlet pipe is open then in how many hours the full tank becomes half-full ?"

Hence, the answer is 20

Choice A is the correct answer