GmatKiss 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
Need a generic method (faster) to solve similar problems.
TIA,
GK
OK, so they want to double 2:50 to make the ratio of soap to alcohol in the altered solution to become 4:50 now; and they further want to make half of 2:100 to make the ratio of soap to water in the altered solution to become 1:100 now.
In the altered solution we symbolically have
S:A = 4:50 and S:W = 1:100
And the question cleverly asks us to find A:W first and then answer to the question. See the shortest we can do from here is to divide the two ratios so that the unwanted S cancels out and we have
(S/W)/ (S/A) = A/W
Or A:W in the altered solution = (1/100)/ (4/50) = 1/100 × 50/4 = 1/8 or 1:8.
In other words, in the altered solution, for every 1 cubic centimeters of alcohol, there are 8 cubic centimeters of water contents; likewise for every 100 cubic centimeters of alcohol, there are [spoiler]
800 cubic centimeters[/spoiler] of water contents.
[spoiler]
E[/spoiler]
The mind is everything. What you think you become. -Lord Buddha
Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001
www.manyagroup.com
w = 2:50:100 ----> 1
800
