Alligation (Milk Fat %):\nCow’s milk has 10% fat; buffalo’s milk has 20% fat. A mixture has (120/7)% fat. In what ratio (cow:buffalo) were they mixed?

Introduction / Context:
Alligation quickly finds mixing ratios for target concentrations.

Given Data / Assumptions:

• Cow = 10%, Buffalo = 20%.
• Mixture = 120/7 % ≈ 17.142857%.

Concept / Approach:
Use alligation: ratio (cow:buffalo) = (higher − mean) : (mean − lower).

Step-by-Step Solution:
1) Higher − mean = 20 − (120/7) = (140/7 − 120/7) = 20/7.2) Mean − lower = (120/7) − 10 = (120/7 − 70/7) = 50/7.3) Ratio = (20/7) : (50/7) = 20 : 50 = 2 : 5.

Verification / Alternative check:
Weighted average with 2:5 reproduces 120/7%.

Why Other Options Are Wrong:
Other ratios yield different means (check by weighted average).

Common Pitfalls:
Reversing which difference goes with which component.

Final Answer:
2 : 5