Multiple choice

A 30-litre mixture of milk and water is in the ratio 2 : 1. 15 litres of the mixture is removed and replaced with pure milk. This process is repeated one more time. What is the final ratio of milk to water in the mixture?

  1. 10 : 1

  2. 7 : 5

  3. 8 : 3

  4. 11 : 1

  5. 15 : 7
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D Correct answer
Explanation

Initial: 20L milk, 10L water. Removing 15L (half) leaves 10L milk, 5L water. Adding 15L milk makes it 25L milk, 5L water. Repeating: remove half (12.5L milk, 2.5L water) leaves 12.5L milk, 2.5L water. Adding 15L milk makes it 27.5L milk, 2.5L water. Ratio 27.5 : 2.5 = 11 : 1.

AI explanation

Using the mixture replacement formula for water, the final amount of water is Initial Water * (1 - Replaced Volume / Total Volume)^n. The initial water is 10 litres, so the final water is 10 * (1 - 15/30)^2 = 10 * (1/2)^2 = 2.5 litres. The final milk is 30 - 2.5 = 27.5 litres, making the ratio of milk to water 27.5 to 2.5, which is 11 to 1.

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