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Multiple ratios

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Multiple ratios

by sanaa.rizwan » Sat Nov 10, 2012 4:51 pm
I cant figure out how to solve this :(

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 ratios of soap to alcohol will be doubled while the ratios 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?
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by GMATGuruNY » Sat Nov 10, 2012 5:40 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 cm of alcohol, how many cubic cm of water will it contain?

A. 50

B. 200

C. 400

D. 625

E. 800
Let S = soap, A = alcohol, and W = water.

Original S:A = 2:50.
With the amount of soap doubled, new S:A = 4:50 = 2:25.

Original S:W = 2:100.
With the amount of soap halved, new S:W = 1:100 = 2:200.

Combining the ratios, new S:A:W = 2:25:200.
Since the actual amount of alcohol = 100, and S:A:W = 2:25:200 = 8:100:800, the actual amount of water = 800.

The correct answer is E.
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by GMAT Kolaveri » Sat Nov 10, 2012 6:32 pm
Separate the individual ratios and then combine them again based on the conditions given.
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