Two types of rice are available: Type I costs Rs. 15 per kg and Type II costs Rs. 20 per kg. If the two types are mixed in the ratio 2 : 3 (by weight), what is the price per kilogram of the mixed variety sold at cost?

Introduction / Context:
This is a direct weighted-average (alligation) problem. When two qualities are mixed in a given ratio, the mean price equals the weighted average of the individual prices according to their quantities.

Given Data / Assumptions:

• Type I price = Rs. 15 per kg.
• Type II price = Rs. 20 per kg.
• Mixing ratio (Type I : Type II) = 2 : 3 by weight.
• No wastage or additional costs; mixture is sold at cost.

Concept / Approach:
For prices p1 and p2 mixed in weights w1 and w2, the mixture price p is p = (w1*p1 + w2*p2) / (w1 + w2). Alligation gives the same result here.

Step-by-Step Solution:
Let weights be 2 kg (Type I) and 3 kg (Type II).Total cost = 2*15 + 3*20 = 30 + 60 = Rs. 90.Total weight = 2 + 3 = 5 kg.Mixture price per kg = 90 / 5 = Rs. 18.

Verification / Alternative check:
By alligation: differences are 20 − 18 = 2 and 18 − 15 = 3, giving ratio 3 : 2 (Type I : Type II), which matches the given 2 : 3 after swapping sides, confirming consistency.

Why Other Options Are Wrong:
19.50, 19, and 18.50 are higher than the true weighted average. 17.50 is too low and inconsistent with the ratio favoring the costlier type.

Common Pitfalls:
Taking a simple average (15 and 20) to get 17.5 without using the ratio, or reversing the 2 : 3 weights. Weighted average must honor the given quantities.

Final Answer:
18