Two varieties of tea cost ₹60 per kg and ₹120 per kg. They are mixed and the mixture is sold at ₹96 per kg.\nIf the seller earns a profit of 20% on the mixture, in what ratio should the ₹60 tea and the ₹120 tea be mixed to form the mixture?

Introduction:
This problem mixes two cost prices and uses selling price with profit to infer the mixture's cost price first. Once the cost price of the mixture is found, we apply alligation between ₹60 and ₹120 to get the required mixing ratio. This is a two-step reasoning question because the mixture CP is not given directly.

Given Data / Assumptions:

• Tea 1 cost = ₹60 per kg
• Tea 2 cost = ₹120 per kg
• Mixture selling price = ₹96 per kg
• Profit = 20% on cost

Concept / Approach:
If profit is 20%, then SP = CP * 1.20. So CP of mixture = SP / 1.20. Then apply alligation:\nRatio (cheaper : dearer) = (dearer - mean) : (mean - cheaper).

Step-by-Step Solution:
Mixture CP = 96 / 1.20Mixture CP = 80Cheaper tea = 60, Dearer tea = 120, Mean (mixture CP) = 80Difference (120 - 80) = 40Difference (80 - 60) = 20Required ratio (₹60 tea : ₹120 tea) = 40 : 20 = 2 : 1

Verification / Alternative Check:
If we mix 2 kg at ₹60 and 1 kg at ₹120, total cost = 2*60 + 1*120 = 240. Total quantity = 3 kg. CP = 240/3 = ₹80 per kg. With 20% profit, SP = 80 * 1.20 = ₹96 per kg, matching the condition.

Why Other Options Are Wrong:
1:2 and 1:3: uses too much ₹120 tea, raising CP above ₹80.3:2: CP becomes closer to ₹60 than ₹80.4:1: CP becomes too low, giving more than 20% profit at ₹96 SP.

Common Pitfalls:
Applying 20% on ₹96 instead of converting ₹96 back to CP.Using alligation directly on ₹96 without first removing profit.Mixing up which difference corresponds to which tea.

Final Answer:
2 : 1