Percentages Question 1 - CAT 2020
Two alcohol solutions, A and B, are mixed in the proportion 1 : 3 by volume. The volume of the mixture is then doubled by adding solution A such that the resulting mixture has 72% alcohol. If solution A has 60% alcohol, then the percentage of alcohol in solution B is
Step-by-Step Explanation
Initially, consider the mixture of A and B as a single solution.
The volume of this mixture is doubled by adding solution A (60% alcohol). Therefore, the original mixture and solution A are mixed in the ratio 1 : 1, resulting in a solution containing 72% alcohol.
Using Alligation,
(72 − 60) / (x − 72) = 1 / 1
where x is the percentage of alcohol in the original mixture.
x = 84%
Now, this original mixture (84% alcohol) was formed by mixing A (60%) and B in the ratio 1 : 3.
Again, using Alligation,
(y − 84) / (84 − 60) = 1 / 3
where y is the percentage of alcohol in solution B.
y = 92%
Hence, the correct answer is Option C.
💡 FundaMakers Tip: In multi-stage mixture questions, solve the problem one stage at a time. First find the concentration of the intermediate mixture, and then apply Alligation again to find the unknown concentration.