Multiple choice

There are two containers of equal capacity. The ratio of water to alcohol in the first container is 6:7, and in the second container is 4:5. If they are mixed up, the ratio of water to alcohol in the mixture will be?

  1. 6:4

  2. 64:53

  3. 17:19

  4. 53:64

  5. 11:13
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Container 1: 6/13 water, 7/13 alcohol. Container 2: 4/9 water, 5/9 alcohol. Mix equal volumes: Water = 6/13 + 4/9 = (54+52)/117 = 106/117. Alcohol = 7/13 + 5/9 = (63+65)/117 = 128/117. Ratio = 106:128 = 53:64.

AI explanation

Assume the equal capacity of each container is the least common multiple of the sum of their ratio parts, which is the least common multiple of 13 and 9, giving 117 liters. The first container then holds 117 multiplied by 6 and divided by 13, equaling 54 liters of water, and 63 liters of alcohol. The second container holds 117 multiplied by 4 and divided by 9, equaling 52 liters of water, and 65 liters of alcohol. When mixed, the total water is 54 plus 52, which is 106, and the total alcohol is 63 plus 65, which is 128, giving a final ratio of 53 to 64.

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