Multiple choice

Nine litres of liquid is drawn from a cask full of wine and it is then filled with water. This operation is done twice. The ratio of quantity of wine now left in the cask to that of the water in it is 16 : 9. How much can the cask hold (in litres)?

  1. 25 litres

  2. 30 litres

  3. 35 litres

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

Let capacity be x. After 2 operations, wine remaining = x * (1 - 9/x)^2. The ratio of wine to water is 16:9, so wine is 16/25 of the total. x * (1 - 9/x)^2 = 16/25 * x. (1 - 9/x)^2 = 16/25. 1 - 9/x = 4/5. 9/x = 1/5, so x = 45.

AI explanation

Apply the replacement formula where the final wine quantity equals the total capacity multiplied by (1 minus 9 divided by V) raised to the power of 2. The final ratio of wine to total mixture is 16 divided by 25, so V multiplied by (1 minus 9 divided by V) raised to 2 equals 16V divided by 25. Taking the square root gives (1 minus 9 divided by V) equals 4 divided by 5, so 9 divided by V equals 1 divided by 5, solving to V equals 45 litres.

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