Multiple choice

Bottle 1 contains a mixture of milk andwater in 7: 2 ratio and Bottle 2 contains amixture of milk and water in 9: 4 ratio. Inwhat ratio of volumes should the liquids inBottle 1 and Bottle 2 be combined toobtain a mixture of milk and water in 3:1ratio?

  1. 24:13

  2. 27:13

  3. 27:16

  4. 23:18

  5. 27:14
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B Correct answer
Explanation

Using alligation on milk: Bottle 1 has 7/9 milk, Bottle 2 has 9/13 milk, target is 3/4. (3/4 - 9/13) / (7/9 - 3/4) = (39-36)/52 / (28-27)/36 = (3/52) / (1/36) = 108/52 = 27/13.

AI explanation

Using the rule of alligation, find the fraction of milk in the first bottle as 7/9, in the second as 9/13, and in the desired mixture as 3/4. The ratio of the volume of bottle 1 to bottle 2 is calculated as (3/4 minus 9/13) divided by (7/9 minus 3/4). This calculation gives (3/52) divided by (1/36), which simplifies by cross multiplication to 108 to 52, or 27 to 13.

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