GATE ME 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 capacity of the tank be . Since the tank is half-full, the volume of water currently in the tank is , and the volume remaining to be filled is also .
We need to fill the remaining volume in 10 minutes.
1.Calculate the draining rate ():
It takes 30 minutes to empty the half-full tank ().2.Set up the filling equation:
Let be the pumping rate. When pumping and draining occur simultaneously, the net rate of filling is .We need to fill the remaining volume in 10 minutes.
3.Solve for :
Substitute :4.Determine the ratio of to :
Thus, the pumping rate must be 4 times the draining rate. The correct option is (A).Continue learning with Success Tracker
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