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If a portion of a half water/half alcohol mix is replaced

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Senior Manager
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Re: If a portion of a half water/half alcohol mix is replaced  [#permalink]

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New post 27 Oct 2018, 22:44
zest4mba 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?

A. 3%
B. 20%
C. 66%
D. 75%
E. 80%




Let the volume of solution be 100 ml

Given its a 50% water/505 alcohol solution.

So Alcohol=50ml and water = 50 ml

Now

50-0.50x(removing "x" ml of 50 % alcohol solution) + 0.25x(replacing with 25% alcohol solution) = 30(30%alcohol solution)

X= 80 ml

clearly origininal solution was 100 ml so its 80%

ALTERNATIVE APPROACH

Weighted average

We have 25 - 30 - 50 % alcohol solution

Ratio of 25% alcohol solution to 50% alchohol solution (W1/W2) = 50-30 / 30-25 = 4/1

Therefore we have 4 units of alcohol sulution of of 5 units of net solution
impues 4/5= 80%

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Re: If a portion of a half water/half alcohol mix is replaced  [#permalink]

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New post 25 Dec 2018, 17:57
gmat1011 wrote:
Hi Financier

It will work if you consider it as follows:

50% ---------------- 25%

------------30%---------

5%------------------20%

so ratio is 1:4 in final mixture

Earlier type 1 alcohol was 1

Now it is 1/5 ----> so loss of 4/5 = 80%...


Could someone please explain where 1/5 is coming from towards the end? I have been trying to figure out since past 30 mins but I haven't had any luck. Would immensely appreciate it!
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Re: If a portion of a half water/half alcohol mix is replaced  [#permalink]

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New post 09 Aug 2019, 20:22
Lets test 10 for total weight of solution

5 alcohol 5 water by weight (units are negligible)

x = amount we are replacing
We know that currently if we remove x units of the mix then half of x will be alcohol, the other half water.

This allows us to construct the following

(5-0.5x+0.25x)/10 = 3/10
50-2.5x=30
20=2.5x
x=8
Thus 8/10 = 0.8= 80%
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Re: If a portion of a half water/half alcohol mix is replaced   [#permalink] 09 Aug 2019, 20:22

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