Two varieties of wheat cost ₹3.20 per kg and ₹2.90 per kg. In what ratio (cheaper wheat : costlier wheat) should they be mixed so that the resulting mixture is worth exactly ₹3.00 per kg (assume no loss and simple weighted average)?

Introduction / Context:
This is an alligation (weighted average) question. When two items of different prices are mixed, the mean price depends on how much of each is used. The mixing ratio is determined by the differences between each price and the target mean price.

Given Data / Assumptions:

• Cheaper wheat price = ₹2.90 per kg
• Costlier wheat price = ₹3.20 per kg
• Target mixture price = ₹3.00 per kg
• No wastage; mixture value is a weighted average

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

Step-by-Step Solution:

Verification / Alternative check:
Take 2 kg at ₹2.90 and 1 kg at ₹3.20. Total cost = 2*2.90 + 1*3.20 = 5.80 + 3.20 = 9.00. Total kg = 3. Average = 9/3 = ₹3.00. Verified.

Why Other Options Are Wrong:

Common Pitfalls:
People often reverse the ratio by mistake, or ignore that the target mean is closer to the cheaper price, so more cheaper wheat is needed. Another pitfall is rounding or mishandling decimal differences; you can multiply all prices by 10 to make it 32, 29, and 30 to avoid decimals.

Final Answer:
2:1