Multiple choice

A wine bottle contains 60% alcohol and, the remaining, water. A person takes out some amount of wine from the bottle and replaces it with an equal quantity of another wine containing 30% alcohol. As a result, the bottle now contains 40% alcohol. What fraction of the original wine was taken out from the bottle?

  1. 1 4

  2. 1 3

  3. 2 3

  4. 1 5
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let V be the volume. Using the formula for replacement: Final concentration = Initial * (1 - x/V)^n + Added * (1 - (1 - x/V)^n). Here, 0.40 = 0.60 * (1 - f) + 0.30 * f, where f is the fraction replaced. 0.40 = 0.60 - 0.60f + 0.30f = 0.60 - 0.30f. 0.30f = 0.20, so f = 2/3.

AI explanation

Apply the alligation method to the initial 60% alcohol solution and the replacement liquid containing 30% alcohol to achieve a final concentration of 40%. The ratio of the remaining original liquid to the replacement liquid is (40 - 30):(60 - 40), which equals 10:20 or 1:2. This means the original liquid accounted for 1/3 of the total, proving that 2/3 of it was taken out.

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