A dairy mixes cow's milk containing 10% fat with buffalo's milk containing 20% fat.\nAfter mixing, the resulting milk has fat equal to (120/7)%.\nIn what ratio (cow's milk : buffalo's milk) were the two milks mixed to obtain this fat percentage?

Introduction:
This is an alligation problem based on concentration (fat percentage). We mix a lower-fat milk (10%) with a higher-fat milk (20%) to obtain an intermediate fat percentage. The ratio is determined by how far the target lies from each concentration. The target here is (120/7)%, which is approximately 17.142857%.

Given Data / Assumptions:

• Cow's milk fat = 10%
• Buffalo's milk fat = 20%
• Target fat = (120/7)%
• Let cow : buffalo = ?

Concept / Approach:
Using alligation:\nRatio (cow : buffalo) = (buffalo% - target%) : (target% - cow%).\nWork exactly with fractions to avoid rounding errors: target = 120/7.

Step-by-Step Solution:
Cow% = 10, Buffalo% = 20, Target% = 120/7Compute (Buffalo - Target) = 20 - 120/7 = (140/7 - 120/7) = 20/7Compute (Target - Cow) = 120/7 - 10 = (120/7 - 70/7) = 50/7Required ratio (cow : buffalo) = (20/7) : (50/7)Cancel /7: ratio = 20 : 50Simplify ratio = 2 : 5

Verification / Alternative Check:
Mix 2 parts cow and 5 parts buffalo.\nFat contribution = 2*10 + 5*20 = 20 + 100 = 120.\nTotal parts = 7.\nFat% = 120/7, exactly the target. This confirms the ratio without any rounding.

Why Other Options Are Wrong:
1:5: gives fat% closer to 20% than required (too high).2:3 or 3:5: produces fat% lower than 120/7.2:1: produces fat% much closer to 10% than the target.

Common Pitfalls:
Rounding 120/7 too early and getting an inaccurate ratio.Reversing the alligation differences and flipping the ratio.Assuming equal volumes instead of calculating the correct ratio.

Final Answer:
2 : 5