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alchol and water- mixtures

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by venmic » Mon Sep 05, 2011 4:47 am
If a portion of a half water/half alcohol mix is replaced with 25% alcohol solution, resulting in a 30% alcohol solution, what percentage of the original alcohol was replaced?

[spoiler]
80%[/spoiler]


please explain
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by cans » Mon Sep 05, 2011 4:53 am
initially 50% alcohol solution. (let 100 ml).
we replace x ml with 25% soln.
Thus total alcohol = 50(100-x) + 25x = 5000 - 25x = 3000 (resulting is 30%)
thus x = 80
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by shankar.ashwin » Mon Sep 05, 2011 4:58 am
Using allegations rule, first determine the ratio both the solutions are mixed to produce the 30% solution.

To find the ratio.

Ratio of 25% : Ratio of 50% = (50-30):(30-25) = 4:1. (In general, (Higher - Desired : Desired - Lower)

There the 30% soln has 4 parts of 25% solution and 1 part of 50% solution,

therefore % of 50 solution replaced = % of 30 solution added

So 4/5 * 100 = 80%



venmic wrote:If a portion of a half water/half alcohol mix is replaced with 25% alcohol solution, resulting in a 30% alcohol solution, what percentage of the original alcohol was replaced?

[spoiler]
80%[/spoiler]


please explain
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by GMATGuruNY » Mon Sep 05, 2011 5:57 am
venmic wrote:If a portion of a half water/half alcohol mix is replaced with 25% alcohol solution, resulting in a 30% alcohol solution, what percentage of the original alcohol was replaced?

[spoiler]
80%[/spoiler]
please explain
We can use alligation, which dictates the following:

The proportion of each element in the mixture is equal to the distance between the percentage attributed to the other element in the mixture and the percentage attributed to the mixture.

Proportion of 50% solution = |percentage in 25% solution - percentage in mixture| = |25-30| = 5.
Proportion of 25% solution = |percentage in 50% solution - percentage in mixture| = |50-30| = 20.
Ratio of 50% solution:25% solution = 5:20 = 1:4.

The sum of the values in the ratio = 1+4 = 5.
The proportion of 25% solution in the ratio = 4.
Thus, 4/5 = 80% of the original alcohol was replaced by the 25% solution.
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by saketk » Mon Sep 05, 2011 8:47 am
venmic wrote:If a portion of a half water/half alcohol mix is replaced with 25% alcohol solution, resulting in a 30% alcohol solution, what percentage of the original alcohol was replaced?

[spoiler]
80%[/spoiler]


please explain
Just read the topic on Mixtures and Allegations ... I am sure you wont face much problem after that. :)

Please see the attachment for a 2 step process using a small diagram ..
You do not have the required permissions to view the files attached to this post.
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by venmic » Mon Sep 05, 2011 12:24 pm
Thanks everyone
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