Multiple choice

Directions: Solve the following question and mark the best possible option. Bottle 1 contains a mixture of milk and water in 7 : 2 ratio and Bottle 2 contains a mixture of milk and water in 9 : 4 ratio. In what ratio of volumes should the liquids in Bottle land Bottle 2 be combined to obtain a mixture of milk and water in 3 : 1 ratio?

  1. 27 : 14

  2. 27 : 13

  3. 27 : 16

  4. 27 : 18
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B Correct answer
Explanation

The milk fractions are 7/9 and 9/13, while the target milk fraction is 3/4. By alligation, the required volume ratio is (3/4 - 9/13):(7/9 - 3/4) = 3/52:1/36 = 27:13.

AI explanation

Using the rule of alligation on the milk concentrations, the milk fraction in the first bottle is 7/9, in the second bottle is 9/13, and in the desired mixture is 3/4. The required ratio of their volumes is the difference between the second bottle's fraction and the desired fraction, divided by the difference between the desired fraction and the first bottle's fraction. Calculating these differences gives (9/13 minus 3/4) for the first part and (3/4 minus 7/9) for the second part. The calculation results in (36 minus 39)/52 divided by (27 minus 28)/36, which simplifies to 3/52 divided by 1/36, resulting in a 27 to 13 ratio of Bottle 1 to Bottle 2.

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