Multiple choice

Two equal containers are filled with a mixture of water and alcohol. One of them contains three times as much alcohol as the other. The mixtures in the two containers are then mixed and it is found that the ratio of water to alcohol is 3 : 2. Find the ratio of water to alcohol in each of the original containers.

  1. 2 : 1, 3 : 4

  2. 1 : 3, 1 : 2

  3. 2 : 3, 4 : 1

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the containers have total volume V. Container 1 has alcohol A1 and water W1. Container 2 has alcohol A2 and water W2. Given A2 = 3A1. After mixing, total water/total alcohol = 3/2. Solving the ratios leads to the original compositions.

AI explanation

Testing the values for option C, assume each container holds 5 units. The first container has 2 units of water and 3 units of alcohol, while the second has 4 units of water and 1 unit of alcohol. Mixing them gives 6 units of water and 4 units of alcohol. This resulting mixture has a water to alcohol ratio of 6 to 4, which simplifies to 3 to 2, matching the condition given in the problem. The required ratios are 2 to 3 and 4 to 1.

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