Multiple choice

Cask I contains wine and water in the respective ratio 6 : 7 and cask II contains wine and water in the respective ratio 9 : 4. In what ratio must the contents of the two casks be mixed to get a mixture of wine and water in the respective ratio 8 : 5?

  1. 2 : 5

  2. 3 : 5

  3. 1 : 5

  4. 1 : 2

  5. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Using alligation: Wine in Cask I = 6/13, Wine in Cask II = 9/13, Mixture = 8/13. (9/13 - 8/13) : (8/13 - 6/13) = 1/13 : 2/13 = 1:2.

AI explanation

Using the rule of alligation on the wine fractions, cask I has a concentration of 6/13 and cask II has a concentration of 9/13. The desired mixture has a wine concentration of 8/13. Calculating the ratio as the difference between the desired and second concentration to the difference between the first and desired concentration gives (8/13 - 9/13) to (6/13 - 8/13), which simplifies to -1/13 to -2/13. Therefore, the required mixing ratio of cask I to cask II is 1 : 2.

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