Multiple choice

From a barrel of wine, 4 litres of wine is taken out and it is then filled with water. This process is repeated three more times, and the final mixture in the barrel at the end contains the wine and water in the ratio of 16 : 65. How much wine did the barrel contain initially?

  1. 8 litres

  2. 12 litres

  3. 26 litres

  4. 30 litres

  5. 34 litres
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The ratio of wine to total mixture is 16:81 (since 16:65 is wine:water, total is 16+65=81). The formula for concentration after n replacements is C = C0 * (1 - x/V)^n. Here, (1 - 4/V)^4 = 16/81 = (2/3)^4. Thus, 1 - 4/V = 2/3, so 4/V = 1/3, which means V = 12.

AI explanation

Use the replacement formula where the final amount of wine equals the initial amount multiplied by (1 minus the replaced quantity divided by total volume) raised to the number of operations. Set the initial volume to V, so the final wine quantity is V multiplied by (1 minus 4 divided by V) raised to the power of 4. The final ratio of wine to total mixture is 16 divided by 81, so V multiplied by (1 minus 4 divided by V) raised to 4 equals 16V divided by 81. Taking the fourth root gives (1 minus 4 divided by V) equals 2 divided by 3, which solves to V equals 12 litres.

Keep practicing — related questions