A trader mixes 26 kg of rice priced at Rs. 20 per kg with 30 kg of another variety of rice priced at Rs. 36 per kg and sells the entire 56 kg mixture at Rs. 30 per kg. What is his profit percentage on the whole transaction?

Introduction / Context:
This is a mixture and profit–loss question. A trader mixes two varieties of rice with different cost prices and then sells the mixture at a single uniform selling price per kg. To find the profit percentage, we must first compute the total cost price of the mixture, then the total selling price, and finally express the profit as a percentage of the cost price.

Given Data / Assumptions:
- First variety: 26 kg at Rs. 20 per kg.
- Second variety: 30 kg at Rs. 36 per kg.
- Total mixture quantity = 26 kg + 30 kg = 56 kg.
- Mixture is sold at Rs. 30 per kg.
- All rice is sold, and there are no other expenses or losses.

Concept / Approach:
Total cost price (CP) of the mixture equals the sum of the costs of each variety. Total selling price (SP) is the selling rate per kg multiplied by the total mass of the mixture. Profit = SP - CP. The profit percentage is then calculated using the formula: profit percent = (profit / CP) * 100. We must carry out these steps carefully to avoid arithmetic mistakes.

Step-by-Step Solution:
Step 1: Compute cost of first variety: 26 kg at Rs. 20 per kg gives 26 * 20 = Rs. 520.Step 2: Compute cost of second variety: 30 kg at Rs. 36 per kg gives 30 * 36 = Rs. 1080.Step 3: Total cost price (CP) of the mixture = 520 + 1080 = Rs. 1600.Step 4: Total quantity of mixture = 26 + 30 = 56 kg.Step 5: Total selling price (SP) = 56 kg * Rs. 30 per kg = 56 * 30 = Rs. 1680.Step 6: Profit = SP - CP = 1680 - 1600 = Rs. 80.Step 7: Profit percentage = (profit / CP) * 100 = (80 / 1600) * 100.Step 8: Simplify: 80 / 1600 = 1 / 20, so profit percent = (1 / 20) * 100 = 5%.

Verification / Alternative check:
We can also find the average cost price per kg of the mixture and compare it with the selling price. Average CP per kg = total CP / total quantity = 1600 / 56 = 200 / 7 ≈ Rs. 28.57 per kg. Selling price per kg is Rs. 30. The profit per kg = 30 - 28.57 ≈ Rs. 1.43. Profit percent = (1.43 / 28.57) * 100 ≈ 5%. This confirms our calculation from the direct total CP and SP approach.

Why Other Options Are Wrong:
If it were no profit, no loss, the selling price would have to match the average cost price of about Rs. 28.57 per kg, which it does not. An 8% or 10% profit would require a larger difference between SP and CP than Rs. 80 on Rs. 1600. The 6% option similarly does not match the ratio 80 / 1600. Only 5% accurately reflects the profit.

Common Pitfalls:
Some learners incorrectly average the prices 20 and 36 directly without weighting them by the quantities 26 and 30, which is wrong. Others forget to sum total quantities or miscalculate products like 30 * 36. Always calculate total cost first and then divide by total quantity if you use the average price method.

Final Answer:
The trader makes a profit of 5% on the rice mixture.