A tank of capacity 25 litres has an inlet and an outlet tap. If both are opened simultaneously, the tank is filled in 5 minutes. But if the outlet flow rate is doubled and taps are opened, the tank never gets filled up. Which of the following can be the outlet flow rate in liters/min?
Question
A tank of capacity 25 litres has an inlet and an outlet tap. If both are opened simultaneously, the tank is filled in 5 minutes. But if the outlet flow rate is doubled and taps are opened, the tank never gets filled up. Which of the following can be the outlet flow rate in liters/min?
Solution
Let's denote the inlet flow rate as I (liters/min) and the outlet flow rate as O (liters/min).
From the first condition, we know that when both taps are opened, the tank is filled in 5 minutes. This means that the net flow rate (I - O) fills up the tank in 5 minutes. So, we can write the equation:
I - O = 25 litres / 5 min = 5 litres/min. ----(Equation 1)
From the second condition, we know that if the outlet flow rate is doubled and both taps are opened, the tank never gets filled. This means that the inlet flow rate is less than twice the outlet flow rate. So, we can write the equation:
I < 2O. ----(Equation 2)
From Equation 1, we can express I as I = O + 5.
Substitute I in Equation 2:
O + 5 < 2O, which simplifies to O > 5.
So, the outlet flow rate must be more than 5 litres/min.
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