A trader has 12 quintals of wheat in stock. He sells part of the wheat at a profit of 13% and the remaining part at a profit of 23%, so that his overall profit on the entire 12 quintals is 17%. How many kilograms of wheat does he sell at 23% profit?

Introduction / Context:
This question is a classic mixture of profit percentages applied to different parts of the same commodity. The trader sells one part of his wheat stock at a lower profit percentage and another part at a higher profit percentage. We are given the overall profit percentage and must determine how much quantity was sold at the higher rate of profit. It is a standard weighted average profit problem that appears frequently in aptitude exams.

Given Data / Assumptions:

• Total wheat = 12 quintals (1 quintal = 100 kg, so total = 1200 kg).
• Part of the wheat is sold at 13% profit.
• The remaining part is sold at 23% profit.
• Overall profit on the entire stock = 17%.
• The cost price per quintal is assumed to be the same for all wheat.
• We need the quantity sold at 23% profit in kilograms.

Concept / Approach:
We use the idea of weighted average profit. Suppose x quintals are sold at 13% profit and the remaining (12 − x) quintals at 23% profit. The overall profit percentage is then the weighted average of 13% and 23%, weighted by x and (12 − x) respectively. Setting this equal to 17% results in a simple linear equation in x, which we can solve to get the required quantities. Finally, we convert the answer from quintals to kilograms.

Step-by-Step Solution:
Let the cost price per quintal be Rs. 1 (we only need ratios). Let x quintals be sold at 13% profit. Then (12 − x) quintals are sold at 23% profit. Total profit from x quintals = 13x (in profit units). Total profit from (12 − x) quintals = 23(12 − x). Overall profit percentage formula: (13x + 23(12 − x)) / 12 = 17. Compute the numerator: 13x + 276 − 23x = 276 − 10x. So (276 − 10x) / 12 = 17. Multiply both sides by 12: 276 − 10x = 204. Rearrange: 276 − 204 = 10x. 72 = 10x, so x = 7.2 quintals at 13% profit. Quantity at 23% profit = 12 − 7.2 = 4.8 quintals. Convert 4.8 quintals to kilograms: 4.8 * 100 = 480 kg.

Verification / Alternative check:
Check using actual amounts. Assume cost price per quintal is Rs. 100. Then total cost = 12 * 100 = Rs. 1200. Quantity at 13% profit = 7.2 quintals, profit = 7.2 * 13 = Rs. 93.6. Quantity at 23% profit = 4.8 quintals, profit = 4.8 * 23 = Rs. 110.4. Total profit = 93.6 + 110.4 = Rs. 204. Overall profit percentage = (204 / 1200) * 100 = 17%, which matches the given condition. Thus 480 kg is correct.

Why Other Options Are Wrong:
720 kg: Corresponds to 7.2 quintals, but that is the amount at 13% profit, not 23%.
240 kg: Too small a quantity at 23%; the weighted average would be closer to 14–15%, not 17%.
960 kg: Too large at 23%; this would push the overall profit above 17%.
600 kg: Does not satisfy the weighted average equation when checked numerically.

Common Pitfalls:
Many learners confuse which part of the quantity is sold at which profit and sometimes directly average 13% and 23% to get 18%, ignoring the overall 17% condition. Others forget to convert between quintals and kilograms, leading to incorrect unit-based answers. Always write the weighted average profit equation carefully and keep track of units to avoid such errors.

Final Answer:
The trader sells 480 kg of wheat at 23% profit.