Multiple choice

Two glasses contain mixtures of alcohol and water in the ratios 2 : 1 and 1 : 1. The mixtures are poured into a third glass in equal quantities. What is the ratio of alcohol to water in the final mixture?

  1. 5 : 7

  2. 7 : 5

  3. 7 : 6

  4. 6 : 7
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B Correct answer
Explanation

Glass 1 has 2/3 alcohol and 1/3 water. Glass 2 has 1/2 alcohol and 1/2 water. Combining equal parts, the alcohol ratio is (2/3 + 1/2) / 2 = 7/12, and the water ratio is (1/3 + 1/2) / 2 = 5/12. The resulting ratio is 7:5.

AI explanation

Assume 1 liter is taken from each glass. The first glass contributes 2/3 L of alcohol and 1/3 L of water, while the second glass contributes 1/2 L of alcohol and 1/2 L of water. Adding these together gives a total alcohol volume of 2/3 plus 1/2, which is 7/6 L. The total water volume is 1/3 plus 1/2, which is 5/6 L. The final ratio of alcohol to water in the mixture is therefore 7/6 to 5/6, simplifying to 7 to 5.

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