Multiple choice

A vessel contains a mixture of milk and water in the ratio of 5 : 3, respectively. How much of the mixture must be siphoned off and replaced with water, so that the mixture may be half milk and half water?

  1. 1/3

  2. 1/4

  3. 1/7

  4. 1/5
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the initial mixture be 8 liters (5 milk, 3 water). We want the final ratio to be 1:1. Let x be the fraction replaced. The amount of milk remaining is 5(1-x). The amount of water becomes 3(1-x) + 8x. Setting 5(1-x) = 3(1-x) + 8x, we get 2(1-x) = 8x, 2 - 2x = 8x, 10x = 2, x = 1/5.

AI explanation

Let the total mixture be 8 units, so it contains 5 units of milk and 3 units of water. If you remove 1/5 of the mixture and replace it with water, the 6.4 units of remaining mixture contains 4 units of milk. Adding 1.6 units of water makes the total 8 units with an equal 4 units of milk and 4 units of water.

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