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Ratio Problem-Simpler Solution

by [email protected] » Thu Jul 11, 2013 11:08 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?
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by GMATGuruNY » Fri Jul 12, 2013 2:05 am
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 vishugogo » Fri Jul 12, 2013 2:05 am
SOAP ALCOHOL WATER
RATIO ORIGINAL 2 50 100

ALTERED RATIO 2 25
(1ST alteration
soap:alcohol is
doubled)

ALTERED RATIO 1 100
(2ND alteration
soap:water is
halved)

alcohol is 100 cm3

2/25=soap/100

soap=8 cm3

so water is 800cm3
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