In what ratio should a mixture having 20% milk strength be mixed with another mixture having 60% milk strength so that the new mixture becomes 25% milk strength? (Assume milk strength means the percentage of milk in the mixture.)

Introduction / Context:This is an alligation (percentage mixing) problem. You are mixing a weaker mixture (20% milk) with a stronger mixture (60% milk) to obtain a target mixture that is only slightly stronger than the weaker one (25% milk). Because the target is close to 20%, you will need much more of the 20% mixture than the 60% mixture. Alligation provides a fast and reliable method using only differences from the mean.

Given Data / Assumptions:

• Mixture 1 milk percentage = 20%
• Mixture 2 milk percentage = 60%
• Target milk percentage = 25%
• Find ratio (20% mixture : 60% mixture)

Concept / Approach:Alligation rule: Required ratio (weaker : stronger) = (stronger - mean) : (mean - weaker). Here weaker = 20, stronger = 60, mean = 25. Compute the two differences and simplify.

Step-by-Step Solution: Weaker = 20, Stronger = 60, Mean = 25 Strong difference = 60 - 25 = 35 Weak difference = 25 - 20 = 5 Ratio (20% : 60%) = 35 : 5 Simplify = 7 : 1

Verification / Alternative check:Take 7 litres of 20% and 1 litre of 60%. Milk = 7*0.20 + 1*0.60 = 1.4 + 0.6 = 2.0 litres. Total = 8 litres. Milk% = 2.0/8 = 25%. Verified exactly.

Why Other Options Are Wrong: 4:1 gives a stronger result than 25% because it uses relatively more 60% mixture. 5:2 and 9:2 shift the weighted average away from 25% when computed. 3:1 makes the mixture much stronger than 25%.

Common Pitfalls:Reversing the ratio order, subtracting differences in the wrong direction, or confusing milk percentage with water percentage.

Final Answer:The required ratio is 7:1 (20% mixture : 60% mixture).