Roland2rule 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:37.5
B:37
C:45
D:25
E:35
I agree that this problem is beyond the scope of the GMAT.
That said, here's an efficient approach:
Use the formula for REPEATED FRACTIONAL CHANGE.
If amount
x DECREASES by fraction
a/b exactly
n times:
Final amount = x * (1 - a/b)^n.
In the problem at hand:
Original amount:
Let the capacity of the container = x.
Since the container is full of A, the original amount of A = x.
Final amount:
After two replacements, A:B = 9:16.
Since 9+16 = 25, A will constitute 9/25 of the container.
Thus, the final amount of A = (9/25)x.
Fractional decrease:
Since 15 liters of x are removed with each replacement, the fractional decrease = 15/x.
Since the volume decreases TWICE, n = 2.
Plugging these values into the formula, we get:
(9/25)x = x * (1 - 15/x)²
9/25 = (1 - 15/x)²
3/5 = 1 - 15/x
15/x = 2/5
2x = 75
x = 37.5.
Note that if amount
x INCREASES by fraction
a/b exactly
n times, the formula is as follows:
Final amount = x * (1 + a/b)^n.Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
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