Multiple choice

There are 2 vessels filled with a mixture of milk and water. In the first vessel, the water is 2/3 of the milk and in the second vessel, water is just 40% of the milk. In what ratio are these required to be mixed to make a mixture of 24 litres, in which the ratio of water to milk is 1 : 2?

  1. 4 : 3

  2. 5 : 7

  3. 5 : 2

  4. 7 : 5

  5. 3 : 4
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Vessel 1: Water/Milk = 2/3. Fraction of water = 2/5. Vessel 2: Water/Milk = 40/100 = 2/5. Fraction of water = 2/7. Target: Water/Milk = 1/2. Fraction of water = 1/3. Using alligation: |2/7 - 1/3| : |2/5 - 1/3| = |6/21 - 7/21| : |6/15 - 5/15| = 1/21 : 1/15 = 15:21 = 5:7.

AI explanation

Using the rule of alligation based on the fraction of milk in each solution, the first vessel has a milk fraction of 3/5, the second has a milk fraction of 5/7, and the desired mixture has a milk fraction of 2/3. The ratio of the quantities needed from the first vessel to the second vessel is the difference between the second vessel and the target (5/7 minus 2/3) versus the difference between the target and the first vessel (2/3 minus 3/5). Calculating these differences gives 1/21 and 1/15 respectively, which simplifies to a ratio of 5 to 7.

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