A shopkeeper mixes two varieties of rice priced at Rs. 40 per kg and Rs. 60 per kg in the ratio 3 : 2 and sells the mixture at a profit of 10 percent. At what price per kilogram does he sell the mixture?

Introduction / Context:
This is a standard mixture and profit question from quantitative aptitude. A trader mixes two types of rice at different cost prices in a given ratio, finds the average cost of the mixture, and then sells it at a certain profit percent. You need to calculate the selling price per kilogram of the mixture.

Given Data / Assumptions:
Price of cheaper rice = Rs. 40 per kg.
Price of costlier rice = Rs. 60 per kg.
Mixing ratio of the two varieties = 3 : 2 (by weight).
Profit on the mixture = 10 percent on cost price.
We assume perfect mixing and no loss of quantity.

Concept / Approach:
First, find the weighted average cost price of the mixture using the given ratio. When two items are mixed in the ratio a : b, the cost price of the mixture is (a * price1 + b * price2) / (a + b). Once we know the cost price per kilogram, we add 10 percent profit by multiplying by 1.10 to get the selling price per kilogram.

Step-by-Step Solution:
Step 1: Let the quantity of Rs. 40 per kg rice be 3 kg and the quantity of Rs. 60 per kg rice be 2 kg, in line with the ratio 3 : 2. Step 2: Total cost of 3 kg of cheaper rice = 3 * 40 = Rs. 120. Step 3: Total cost of 2 kg of costlier rice = 2 * 60 = Rs. 120. Step 4: Total cost of 5 kg mixture = 120 + 120 = Rs. 240. Step 5: Cost price per kg of mixture = total cost / total weight = 240 / 5 = Rs. 48. Step 6: Profit is 10 percent, so selling price per kg = cost price per kg * (1 + 10/100) = 48 * 1.10 = Rs. 52.8.

Verification / Alternative check:
As a quick check, note that the mixture cost price of Rs. 48 lies between Rs. 40 and Rs. 60, which is reasonable. A 10 percent profit on Rs. 48 must therefore be around Rs. 4.8, giving a selling price of approximately Rs. 52.8. The option Rs. 52.8 matches this estimate, confirming the result.

Why Other Options Are Wrong:
Rs. 56 would correspond to a profit of more than 16 percent on Rs. 48, which is higher than the stated 10 percent.
Rs. 58.8 would represent an even larger profit and is inconsistent with the given data.
Rs. 54 also corresponds to a profit higher than 10 percent on Rs. 48.
Only Rs. 52.8 gives exactly 10 percent profit on the mixture cost price.

Common Pitfalls:
A common mistake is to take the simple average of 40 and 60, which is 50, ignoring the ratio 3 : 2. Another mistake is to add 10 directly to the cost price and write 48 + 10 = 58, which is incorrect because 10 percent of 48 is 4.8, not 10. Always calculate percentage profit on the actual cost price.

Final Answer:
The shopkeeper sells the mixture at Rs. 52.8 per kg.