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
OA is a...
what is the best approach to solving this question. Did you also get 45 as your answer
Problem solving
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Hi Roland2rule,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
OA is a...
what is the best approach to solving this question. Did you also get 45 as your answer
You have been posting many questions. It would be nice if you write the source of questions. Is it a GMAT source?
The correct answer for this one is A, but it involves a lot of calculation which is not expected in the GMAT.
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I agree that this problem is beyond the scope of the GMAT.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
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.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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