Sugar at Rs. 15/kg is mixed with sugar at Rs. 20/kg in the ratio 2 : 3. Find the price per kilogram of the resulting mixture (weighted average price).

Introduction / Context:
Alligation and mixture questions often reduce to computing a weighted average when proportions and individual prices are known. Here, two types of sugar are mixed in a stated ratio; we must compute the average price per kilogram of the mixture.

Given Data / Assumptions:

• Sugar A price = Rs. 15/kg.
• Sugar B price = Rs. 20/kg.
• Mixing ratio A : B = 2 : 3.

Concept / Approach:
Weighted average price = (sum of price * quantity) / total quantity. With a ratio, use the ratio numbers as proxy quantities to keep arithmetic simple and exact.

Step-by-Step Solution:
Let quantities be 2 kg (at Rs. 15) and 3 kg (at Rs. 20). Total cost = 2*15 + 3*20 = 30 + 60 = Rs. 90. Total quantity = 2 + 3 = 5 kg. Mixture price = 90 / 5 = Rs. 18 per kg.

Verification / Alternative check:
The result lies between Rs. 15 and Rs. 20 and is closer to 20 (because more of Rs. 20 sugar is used), which matches Rs. 18 being nearer to 20 than 15.

Why Other Options Are Wrong:
Rs. 16 and Rs. 17 are too low; Rs. 19 is too high relative to the 2 : 3 weighting.

Common Pitfalls:
Averaging the prices directly (i.e., taking (15 + 20)/2) ignores the ratio and gives a wrong value. Always weight by quantities.

Final Answer:
Rs. 18