Question

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. $800$

Answer 1

Answer: (E)

$800$

Step I

Ratio $\frac{\frac{s}{a}}{w}=\frac{\frac{2}{50}}{100}$

Step II

If soap to alcohol is double $=\frac{2s}{a}=\frac{2\times 2}{50}=\frac{4}{50}$

If soap to water is halved $\frac{1}{2}\frac{S}{W}=\frac{1}{2}\frac{2}{100}=\frac{2}{100}or\frac{4}{400}$

$\therefore$ new $\frac{\frac{s}{a}}{w}=\frac{\frac{4}{50}}{400}$, Now if $a=100$ or $2\times 50$

$\therefore S=4\times 2=8$

$w=2\times 400=800$

$\therefore 800{cm}^3$ of water is needed.