Two bottles contains mixture of milk and water. First bottle contains 64% milk and second bottle contains 26% water. In what ratio these two mixtures are mixed so that new mixture contains 68% milk?

Step 1: Convert percentages to milk content

• First bottle: 64% milk
• Second bottle: 74% milk
• Target mixture: 68% milk

Step 2: Use alligation rule

        First bottle (64%)       Second bottle (74%)
               \                       /
                \                     /
              Target mixture = 68%
                /                     \
               /                       \
       74 - 68 = 6               68 - 64 = 4

Step 3: Write the ratio

Required ratio = 6 : 4 = 3 : 2

Answer: 3 : 2

To get 68% milk in the final mixture, the two mixtures should be mixed in the ratio 3:2 (First bottle : Second bottle).

This problem uses the alligation method, which is especially useful when dealing with mixtures and average values. It's commonly tested in aptitude exams and helps in understanding the efficiency of ratio-based reasoning in real-world problems.