Multiple choice

A boy mixes milk and sugar in the ratio 2:3 in container 1 and milk and sugar in the ratio 4:1 in container 2. Find the ratio of milk to sugar of both container's mixtures are mixed in the ratio 2:1 ?

  1. 8:7

  2. 7:8

  3. 5:3

  4. 3:5

  5. None
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A Correct answer
Explanation

Container 1: Milk = 2/5, Sugar = 3/5. Container 2: Milk = 4/5, Sugar = 1/5. Mixed in 2:1 ratio: Milk = (2 * 2/5 + 1 * 4/5) / 3 = (4/5 + 4/5) / 3 = 8/15. Sugar = (2 * 3/5 + 1 * 1/5) / 3 = (6/5 + 1/5) / 3 = 7/15. Ratio = 8:7.

AI explanation

Let the total amount of the new mixture be 3 units, comprising 2 units from container 1 and 1 unit from container 2. The amount of milk is (2/5)*2 + (4/5)*1 = 8/5 units, and the amount of sugar is (3/5)*2 + (1/5)*1 = 7/5 units. The resulting ratio of milk to sugar is (8/5) to (7/5), which simplifies to 8 to 7.

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