A trader mixes 36 kilograms of rice priced at Rs. 20 per kilogram with 14 kilograms of another variety of rice priced at Rs. 36 per kilogram. He sells the mixed rice at Rs. 30 per kilogram. What percentage profit does he make on the overall transaction?

Introduction / Context:
This is a mixture and profit question involving two types of rice with different cost prices. The trader mixes them in given quantities and then sells the mixture at a single uniform price per kilogram. The problem checks whether you can compute the total cost price, total selling price, and then derive the overall percentage profit on the combined quantity.

Given Data / Assumptions:

• First variety of rice: 36 kilograms at Rs. 20 per kilogram.
• Second variety of rice: 14 kilograms at Rs. 36 per kilogram.
• Total mixture is sold at Rs. 30 per kilogram.
• There is no loss of weight during mixing or selling.
• We must find the trader profit percentage on the entire transaction.

Concept / Approach:
The correct method is to compute the total cost of each component and sum them to get the overall cost price of the mixture. Then we compute the total selling price by multiplying the selling rate by the total quantity in kilograms. After that, profit equals total selling price minus total cost price. Finally, percentage profit equals profit divided by total cost price multiplied by 100. There is no need for alligation formula here, though it could also be used as an alternative approach.

Step-by-Step Solution:
Total quantity of rice equals 36 plus 14 which is 50 kilograms.Cost of first variety equals 36 * 20 which is 720 rupees.Cost of second variety equals 14 * 36 which is 504 rupees.Total cost price equals 720 plus 504 which is 1224 rupees.Selling price per kilogram is 30 rupees.Total selling price equals 50 * 30 which is 1500 rupees.Profit equals 1500 minus 1224 which is 276 rupees.Percentage profit equals 276 / 1224 * 100 which is approximately 22.54 percent.

Verification / Alternative check:
We can compute the average cost price per kilogram of the mixture by dividing total cost by total quantity. That gives 1224 divided by 50 which is 24.48 rupees per kilogram approximately. The selling price per kilogram is 30 rupees. The profit per kilogram is therefore 30 minus 24.48 which is 5.52 rupees. The percentage profit per kilogram equals 5.52 / 24.48 * 100 which again gives about 22.54 percent. This confirms that the detailed total calculation is consistent with the average price approach.

Why Other Options Are Wrong:
Option 25 percent would require a higher profit or a lower cost price than actually present in the data. Option 21.14 percent and option 27.32 percent do not match the computed ratio of profit to total cost. They may result from common calculator errors or incorrect use of approximate values. Only 22.54 percent matches the exact calculation derived from the given quantities and prices.

Common Pitfalls:
Some learners mistakenly average the two prices 20 and 36 directly, ignoring the different quantities. Others compute percentage profit based on one component only or mix up per kilogram profit and overall profit. Always remember that when quantities differ, you must use weighted averages or work with full totals for cost and selling price. Careful attention to multiplication and addition avoids most mistakes in such mixture problems.

Final Answer:
The trader makes a profit of approximately 22.54 percent on the mixed rice.