Two vessels A and B contain milk and water in the following ratios: Vessel A: 4:3 (milk:water) Vessel B: 2:3 (milk:water) In what ratio should the liquids from vessels A and B be mixed so that the resulting mixture contains equal parts of milk and water (i.e., 50% milk and 50% water)?

Introduction / Context:
This problem tests mixing two mixtures to achieve a target concentration (here, 50% milk). The correct approach is to use milk fractions (or alligation) and solve for the mixing ratio between the two vessels. Since the vessels have different milk percentages, the final mixture percentage depends on how much is taken from each.

Given Data / Assumptions:

• Vessel A milk:water = 4:3 => total parts 7
• Vessel B milk:water = 2:3 => total parts 5
• Target mixture: 50% milk, 50% water
• Mix quantities in ratio A:B = x:y

Concept / Approach:
Convert each vessel ratio to milk fraction. Set combined milk fraction to 1/2 and solve for x:y.

Step-by-Step Solution:

Verification / Alternative check:
Mix 7 L from A and 5 L from B. Milk = 7*(4/7)=4 plus 5*(2/5)=2 total 6. Total volume = 12, so milk% = 6/12 = 50%. Verified.

Why Other Options Are Wrong:

Common Pitfalls:
People often mix ratios 4:3 and 2:3 directly or take a naive average. Always convert to milk fractions (4/7 and 2/5) first. Another error is mixing up A:B vs B:A.

Final Answer:
7:5