Multiple choice

From a cask of milk containing 12 litres milk, 3 litres is drawn out and replaced with water. The same process is repeated for the resultant mixture. Find the ratio of milk to water in the cask?

  1. 9 : 7

  2. 1 : 1

  3. 2 : 1

  4. 4 : 3
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A Correct answer
Explanation

Initial milk = 12. Draw 3 (1/4 of total). Milk remaining = 12 * (3/4) * (3/4) = 12 * 9/16 = 6.75. Water = 12 - 6.75 = 5.25. Ratio = 6.75 / 5.25 = 675 / 525 = 9 / 7.

AI explanation

By applying the formula for the remaining pure milk after repeated replacement, the final quantity of milk is 12 multiplied by (1 minus 3 divided by 12) squared. This calculates to 12 multiplied by 0.75 squared, resulting in 12 multiplied by 0.5625, which gives 6.75 litres of milk. The total volume remains 12 litres, so the water is 5.25 litres, making the ratio of milk to water 6.75 to 5.25, which simplifies to 9 to 7.

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