Multiple choice

A milk trader has two containers of milk. The first contains 25% water and the rest is milk. The second contains 50% water. How much milk should he mix from each of the containers so as to get 14 litres of mixture such that the ratio of water to milk is 3 : 4?

  1. 4 and 10

  2. 6 and 8

  3. 7 and 7

  4. 8 and 6

  5. None of these
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A Correct answer
Explanation

Container 1: 25% water (ratio 1:3). Container 2: 50% water (ratio 1:1). Target: 3:4 water to milk (ratio 3:4). Using alligation on water fraction: 1/4 and 1/2, target 3/7. (1/2 - 3/7) : (3/7 - 1/4) = (1/14) : (5/28) = 2 : 5. Total 7 parts = 14 litres, so 1 part = 2 litres. Amounts are 4 and 10.

AI explanation

The desired 14 litres of mixture has a water to milk ratio of 3 : 4, meaning it contains 6 litres of water and 8 litres of milk, so the water percentage is 6/14 or 3/7. Using the rule of alligation with the water percentages of 1/4 for the first container and 1/2 for the second, the ratio of their quantities is (1/2 - 3/7) : (3/7 - 1/4), which is 1/14 : 5/28 or 2 : 5. Dividing the 14 litres into 2 : 5 gives 4 litres from the first container and 10 litres from the second. The required amounts are 4 litres and 10 litres.

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