Multiple choice

There is a mixture of water and alcohol of 84 L. When 12 L of water is added to the mixture the ratio of water to alcohol becomes 11 : 5. Find the original ratio of alcohol to water in the mixture.

  1. 6: 11

  2. 9: 5

  3. 5: 9

  4. 11: 6
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let W and A be water and alcohol. W+A = 84. After adding 12L water, W+12 / A = 11/5. Since W = 84-A, (96-A)/A = 11/5. 480 - 5A = 11A, 16A = 480, A = 30. Then W = 54. Original ratio A:W = 30:54 = 5:9.

AI explanation

The total new quantity of the mixture becomes 84 L + 12 L = 96 L. Given the new ratio of water to alcohol is 11 : 5, the new quantity of alcohol is (5 / 16) * 96 = 30 L. Because only water was added, the original mixture also contained 30 L of alcohol, meaning the original water was 84 L - 30 L = 54 L. The original ratio of alcohol to water was 30 : 54, which simplifies to 5 : 9.

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