Multiple choice

Two vessels A and B contain milk and water mixed in the ratio $8:5$ and $5:2$. The ratio in which these two mixtures be mixed to get a new mixture containing $69\frac { 3 }{ 13 } $% milk, is:

  1. $2:7$
  2. $3:5$
  3. $5:2$
  4. $5:7$
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A Correct answer
Explanation

Milk in A = 8/13, in B = 5/7. Target = 69 3/13% = 900/1300 = 9/13. Using alligation: (5/7 - 9/13) : (9/13 - 8/13) = (65-63)/91 : 1/13 = 2/91 : 7/91 = 2:7.

AI explanation

Convert the target milk percentage of 69 3/13% to the improper fraction 900/1300, which simplifies to the ratio of milk to total mixture as 9/13, making the ratio of milk to water 9 : 4. Using the rule of alligation on the milk concentrations (8/13, 5/13, and 9/13), the ratio is (9/13 - 5/13) : (8/13 - 9/13). This simplifies to 4/13 : 1/13, resulting in a required mixing ratio of 2 : 7.

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