venmic wrote:If a portion of a half water/half alcohol mix is replaced with 25% alcohol solution, resulting in a 30% alcohol solution, what percentage of the original alcohol was replaced?
[spoiler]
80%[/spoiler]
please explain
We can use
alligation, which dictates the following:
The proportion of each element in the mixture is equal to the distance between the percentage attributed to the other element in the mixture and the percentage attributed to the mixture.
Proportion of 50% solution = |percentage in 25% solution - percentage in mixture| = |25-30| = 5.
Proportion of 25% solution = |percentage in 50% solution - percentage in mixture| = |50-30| = 20.
Ratio of 50% solution:25% solution = 5:20 = 1:4.
The sum of the values in the ratio = 1+4 = 5.
The proportion of 25% solution in the ratio = 4.
Thus, 4/5 = 80% of the original alcohol was replaced by the 25% solution.
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