Multiple choice

In a 100 litre mixture containing water and milk in equal proportions, 10 litres of mixture is replaced by 10 litres of water in succession, twice. At the end, what is the ratio of milk to water?

  1. 81 : 119

  2. 9 : 11

  3. 40 : 61

  4. 41 : 59

  5. 11 : 9
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A Correct answer
Explanation

Initial: 50L milk, 50L water. Replacing 10L of mixture (5L milk, 5L water) with 10L water. After 1st replacement: Milk = 50 - 5 = 45, Water = 50 - 5 + 10 = 55. After 2nd replacement: Milk = 45 - (10/100)*45 = 45 - 4.5 = 40.5. Water = 100 - 40.5 = 59.5. Ratio = 40.5 : 59.5 = 81 : 119.

AI explanation

Using the replacement formula, the remaining milk after replacing 10 litres of the 100 litre mixture twice with water is 100 multiplied by (0.90) squared, which equals 81 litres. The total volume remains 100 litres, so the final quantity of water is 100 minus 81, which equals 119 litres. The final ratio of milk to water is therefore 81 : 119.

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