GATE EC 2014 Set 2 — Question 10
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Question
It takes 30 minutes to empty a half-full tank by draining it at a constant rate. It is decided to simultaneously pump water into the half-full tank while draining it. What is the rate at which water has to be pumped in so that it gets fully filled in 10 minutes?
Correct answer
(A) 4 times the draining rate
Solution
Let the total capacity of the tank be . The volume of a half-full tank is .
1.Calculate the draining rate ():
It takes 30 minutes to empty the half-full tank ().2.Calculate the required net filling rate ():
We want to fill the remaining half of the tank () in 10 minutes.3.Relate rates to find the pumping rate ():
The net rate when pumping and draining occur simultaneously is:Since , we have:Therefore, the pumping rate must be 4 times the draining rate.Continue learning with Success Tracker
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