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PS | Mixtures | OG 12

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PS | Mixtures | OG 12

by [email protected] » Sat Oct 06, 2012 1:42 pm
The ratio, by volume, of soap to alcohol to water in a
certain solution is 2:50:100. The solution will be
altered so that the ratio of soap to alcohol is doubled
while the ratio of soap to water is halved. If the altered
solution will contain 100 cubic centimeters of alcohol,
how many cubic centimeters of water will it contain?

(A) 50
(B) 200
(C) 400
(D) 625
(E) 800

Would be helpful, if I can have the explanation in a chart form. Makes it easier.
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by anuprajan5 » Sat Oct 06, 2012 2:10 pm
The answer should be E

Soap:Alc: Water = 2:50:100

Soap:Alc = 2:50

When doubled, that changes to 4:50

Soap: Water: 2:100

When halved, that changes to 2:200 or 4:400

New ratios,Soap:Alc:Water = 4:50:400

If alcohol is 100, then by that ratio water should be 800

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by Anurag@Gurome » Sun Oct 07, 2012 8:30 pm
[email protected] wrote:The ratio, by volume, of soap to alcohol to water in a
certain solution is 2:50:100. The solution will be
altered so that the ratio of soap to alcohol is doubled
while the ratio of soap to water is halved. If the altered
solution will contain 100 cubic centimeters of alcohol,
how many cubic centimeters of water will it contain?

(A) 50
(B) 200
(C) 400
(D) 625
(E) 800

Would be helpful, if I can have the explanation in a chart form. Makes it easier.
Given: S : A : W = 2 : 50 : 100
The ratio of soap to alcohol is doubled implies S : A = 2 * (2/50) = 4/50
The ratio of soap to water is halved implies S : W = (1/2) * (2/100) = 1/100 or 4/400

Therefore, new ratio of S : A : W = 4 : 50 : 400 implies A : W = 50 : 400
If A = 2 * 50 = 100, then W = 2 * 400 = 800

The correct answer is E.
Anurag Mairal, Ph.D., MBA
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