Multiple choice

Two containers have mixtures of juice and water in the ratios 4 : 3 and 7 : 6, respectively. In what ratio should the contents be mixed so that the ratio of juice to water in the final mixture is 5 : 4?

  1. 14 : 13

  2. 13 : 14

  3. 11 : 14

  4. 14 : 11

  5. None of these
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A Correct answer
Explanation

Use the allegation method. Container 1 has 4/7 juice, Container 2 has 7/13 juice, and the mixture has 5/9 juice. The difference between 4/7 and 5/9 is 1/63. The difference between 7/13 and 5/9 is 2/117. The ratio is (2/117) : (1/63) = 14:13.

AI explanation

Using the rule of alligation, find the fraction of juice in the first container as 4 divided by 7, in the second as 7 divided by 13, and in the final mixture as 5 divided by 9. The required ratio of the first to the second is (7/13 minus 5/9) divided by (5/9 minus 4/7). Calculating this gives (-2/117) divided by (-1/63), which simplifies by cross multiplication to 126 to 117, or 14 to 13.

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