Multiple choice

9 litres of milk is drawn from a cask full of milk and replaced with water. Again, 9 litres of the mixture is drawn from the cask and replaced with water. As a result, the ratio of milk to water in the resulting mixture becomes 16 : 9. Find the capacity of the cask.

  1. 65 litres

  2. 63 litres

  3. 46 litres

  4. 45 litres
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let capacity be C. After 2 operations, milk remaining = C * (1 - 9/C)^2. Ratio of milk to total = 16/25. (1 - 9/C)^2 = 16/25. 1 - 9/C = 4/5. 9/C = 1/5. C = 45.

AI explanation

Use the replacement formula, which states that the final quantity of milk divided by the total volume equals (1 minus the replacement volume divided by the total volume) raised to the number of replacements. The final ratio of milk to the total mixture is 16 divided by the sum of 16 and 9, which simplifies to 16/25. This gives the equation (1 minus 9/V) squared equals 16/25, so taking the square root of both sides results in 1 minus 9/V equaling 4/5. Solving this gives 9/V equaling 1/5, which means the capacity V is 45 litres.

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