Quote:
Eight litres are drawn off from a vessel full of water and substituted by pure milk. Again eight litres of the mixture are drawn off and substituted by pure milk. If the vessel now contains water and milk in the ratio 9:40, find the capacity of the vessel.
A. 21 liters
B. 22 liters
C. 20 liters
D. 14 liters
E. 28 liters
The way the equation is expressed, it seems to me that the number used for Vf should be the volume of the vessel (this is my understanding of what Vf is supposed to represent). However, that is obviously incorrect. Thus, I am having difficulty conceptualizing what Vf actually represents in the solution you have provided and, further, how you were able to intuitively determine that it should be doubled. I understand that Vi of 3 and Vf of 7 must be doubled in order to ensure that Vf-Vi=8. However, I do not understand why this is permissible within the construct of the concentration equation.
Responding to a pm:
You are correct. In this question Vf is the capacity of the vessel.
What is Vf in replacement questions?
Replacement consists of two steps: - 'withdraw from the vessel' and 'put back into the vessel'.
When you withdraw from the vessel, the volume goes down - This is Vi for the next step.
When you put back, the volume comes up again - this is Vf. In this step, since amount of water stays the same (you are putting in milk), CiVi = CfVf
In this question, vessel is FULL of water and you are substituting part of it by milk. So it will be FULL when you put milk in it in step 2. So Vf is the capacity of the vessel.
Also, we are using ratios here.
Say, you know a/b = 1/2. If a = 10, what is b? It is 20, right?
Similarly, you know a/b = 1/2. If b-a = 4, what is a? Note that on the ratio scale, the difference between b and a is 1 (2 - 1). But actually it is 4 so a must be 4 and b must be 8.
Check out my posts on ratios:
http://www.veritasprep.com/blog/2011/03 ... of-ratios/Since Vi/Vf = 3/7 but Vf - Vi = 8 (twice of what it is on the ratio scale), Vi must be 6 and Vf must be 14.