Multiple choice

A 20-litre mixture contains milk and water in the respective ratio of 3 : 2. Then 10 litres of the mixture is removed and replaced with pure milk, and the operation is repeated once more. At the end of the two removals and replacements, what will be the ratio of milk and water in the resultant mixture respectively?

  1. 17 : 3

  2. 9 : 1

  3. 4 : 17

  4. 5 : 3

  5. 3 : 14
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Initial: 12L milk, 8L water. After removing 10L (6L milk, 4L water) and adding 10L milk: 16L milk, 4L water. After repeating: remove 10L (8L milk, 2L water), add 10L milk: 18L milk, 2L water. Ratio = 18:2 = 9:1.

AI explanation

Using the successive replacement formula, the amount of water remaining after the operations is calculated as Initial Water times ((Total Volume - Replaced Volume) / Total Volume)^n. The initial mixture has 8 litres of water, and replacing 10 litres out of 20 litres twice leaves 8 times (10/20)^2, resulting in 2 litres of water. The total mixture is still 20 litres, so the final amount of milk is 20 - 2 = 18 litres. The final ratio of milk to water is 18:2, which simplifies to 9:1.

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