Multiple choice

Eight litres are drawn off from a barrel full of milk and then replaced with water. The process is repeated twice. If the final ratio of milk to water in the barrel is 16 : 9, what is volume of the barrel?

  1. 30 litres

  2. 40 litres

  3. 50 litres

  4. 60 litres

  5. 70 litres
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let V be the volume. After 3 operations, milk remaining = V * (1 - 8/V)^3. Ratio of milk to total = 16/25. (1 - 8/V)^3 = 16/25 is not correct; the ratio of milk to water is 16:9, so milk to total is 16/25. (1 - 8/V)^3 = 16/25. (1 - 8/V) = (16/25)^(1/3) = 4/5. 1 - 8/V = 0.8, so 8/V = 0.2, V = 40.

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