Two varieties of sugar cost ₹18 per kg and ₹24 per kg. In what ratio (cheaper sugar : costlier sugar) should they be mixed so that the resulting mixture costs ₹20 per kg (assuming no loss and simple weighted average pricing)?

Introduction / Context:
This is a standard alligation problem used for mixing two items with different costs to obtain a target average cost. The method ensures the final mixture cost is a weighted average of the two prices. The ratio depends on how far the target price lies from each original price.

Given Data / Assumptions:

• Cheaper sugar price = ₹18 per kg
• Costlier sugar price = ₹24 per kg
• Target mixture price = ₹20 per kg
• No wastage, so mixture price is a weighted average

Concept / Approach:
Alligation rule: cheaper : costlier = (costlier - mean) : (mean - cheaper).

Step-by-Step Solution:

Verification / Alternative check:
If we take 2 kg at ₹18 and 1 kg at ₹24, total cost = 2*18 + 1*24 = 36 + 24 = 60. Total quantity = 3 kg. Average = 60/3 = ₹20 per kg. Verified.

Why Other Options Are Wrong:

Common Pitfalls:
Students sometimes invert the ratio by mistake (using 2:4 instead of 4:2). Another error is taking simple difference of prices (24-18) and guessing the ratio without considering the target mean value.

Final Answer:
2:1