Multiple choice

The ratio of water and wine in two different containers is 2 : 3 and 4 : 5 respectively. In what ratio we are required to mix the mixture of two containers in order to get the new mixture in which the ratio of wine and water be 7 : 5 ?

  1. 7 : 3

  2. 5 : 3

  3. 8 : 5

  4. 2 : 7

  5. 3 : 5
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Container 1: Wine = 3/5, Water = 2/5. Container 2: Wine = 5/9, Water = 4/9. Target: Wine = 7/12, Water = 5/12. Using allegation on wine: (5/9 - 7/12) / (7/12 - 3/5) = ((20-21)/36) / ((35-36)/60) = (-1/36) / (-1/60) = 60/36 = 5/3.

AI explanation

In the first container, water is 2/5 of the mixture, and in the second container, water is 4/9 of the mixture. The desired new mixture requires water to be 5/12 of the total. Using the method of alligation on these water fractions, we find the ratio of the first mixture to the second mixture is (4/9 - 5/12) to (5/12 - 2/5). Calculating these fractions gives (16/36 - 15/36) to (25/60 - 24/60), which simplifies to 1/36 to 1/60. Multiplying both sides by 180 yields a ratio of 5 to 3.

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