subhakam wrote:GMATGuruNY wrote:diebeatsthegmat wrote:15 lts are taken of from a container full of liquid A and replaced with Liquid B. Again 15 more lts of the mixture is taken and replaced with liquid B. After this process, if the container contains Liquid A and B in the ratio 9:16,What is the capacity of the container?
A:45
B:25
C:37.5
D:36
E:42
Sorry GMAT Guru - I still do not get it
Can you show it algebraically? I really get confused on the second mixing.
Let the capacity of the container = x.
Every time 15 liters are removed, the volume of liquid inside the container decreases by 15/x.
To illustrate:
If x=30, removing 15 liters from the container -- 1/2 of the volume -- is equivalent to reducing the volume by 15/x = 15/30 = 1/2.
If x=45, removing 15 liters from the container -- 1/3 of the volume -- is equivalent to reducing the volume by 15/x = 15/45 = 1/3.
Thus, every time 15 liters are removed, the volume of A inside the container decreases by 15/x.
At the start, the container is full of A.
Thus, the original amount of A = x.
When 15 liters are removed, the decrease in A = (15/x)x = 15.
Remaining amount of A = x-15.
When 15 more liters are removed, the decrease in A = (15/x)(x-15).
Remaining amount of A = (x-15) - (15/x)(x-15) = (x-15)*(1 - 15/x) =
(x-15)*(x-15)/x.
At the end of the process, A:B = 9:16.
Since 9+16 = 25, liquid A constitutes 9 of every 25 liters inside the container, implying that A =
(9/25)x.
Since both expressions in red above represent the amount of A at the end of the process, we get:
(x-15)*(x-15)/x = (9/25)x
(x-15)² = (9/25)x²
x-15 = (3/5)x
5x - 75 = 3x
2x = 75
x = 37.5.
