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Confusing Ratio!!

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Confusing Ratio!!

by sodha.rakesh » Tue Jan 25, 2011 6:59 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 centimeters of alcohol, how many cubic centimeters of water will it contain?

A. 50
B. 200
C. 400
D. 625
E. 800

IMO. E
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by Target2009 » Tue Jan 25, 2011 7:16 am
its E:
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by GMATGuruNY » Tue Jan 25, 2011 7:24 am
sodha.rakesh 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

IMO. E
Original S:A:W = 2:50:100.

Original S:A = 2/50.
To double this ratio, we multiply by 2:
2*(2/50) = 4/50 = 2/25 = 2:25.

So at this point the ratio of S:A:W = 2:25:100.

Original S:W = 2/100.
To halve this ratio, we multiply by 1/2:
(1/2)*(2/100) = 2/200 = 2:200.

So the final ratio of S:A:W = 2:25:200.

Since the actual amount of A = 100, every value in the ratio is multiplied by 4:
S:A:W = 2:25:200 = 8:100:800.
Thus, W = 800.

The correct answer is E.
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