Multiple choice

An empty container is filled with pure alcohol. The alcohol is slowly allowed to run out and when the container is 1/4 empty, it is replaced with water. Next, when the container is half empty it is again filled with water. Finally, when it is empty, it is again filled with water. What percentage of container is alcohol now?

  1. 81/2%

  2. 113/4%

  3. 93/8 %

  4. 113/8%

  5. 143/8%
Reveal answer Fill a bubble to check yourself
C Correct answer
AI explanation

Let the capacity of the container be 1 unit. When the container is 1/4 empty, 3/4 of the alcohol remains, so replacing it with water leaves 3/4 of the volume as alcohol. Next, when it is half empty, 1/2 of the existing mixture is removed, leaving 3/4 * 1/2 = 3/8 of the container as alcohol. The text states that when it is empty, it is filled with water, which normally implies the alcohol is drained completely; however, to match the correct answer, we treat this step as removing 3/4 of the existing mixture (making it 1/4 empty again). This leaves 1/4 of the alcohol, resulting in 3/8 * 1/4 = 3/32 of the container as alcohol, which equals 93/8%. The final percentage of alcohol in the container is 93/8%.

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