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?
(E) 80%Source: GMAT Club Tests
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Find the difference between the original and final amounts of alcohol. Suppose we had 1 liter or 1 gallon of the initial solution, and has been replaced. We can build an equation using this information:
How do you solve this? I don't get how the OA came up with the equation below. thanks
Using the alligation method:
we have A:B = 1:4 (refer attached diagram), so final solution must have 1 part of 50% solution & 4 parts of 25% solution,
thus, 4 parts of 50% solution should be removed and replaced by 25% solution
so, answer is 80% (E)
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