A trader has 6 quintals of wheat. He sells part of it at a profit of 7% and the remainder at a profit of 17%, so that his overall profit percentage is 11%. How many kilograms of wheat does he sell at 17% profit?

Introduction / Context:
This mixture type profit and loss question involves selling different parts of the same commodity at two different profit percentages. The overall gain percentage is given, and you must determine the quantity sold at the higher profit rate. This is a standard weighted average or allegation type problem commonly seen in aptitude exams.

Given Data / Assumptions:

• Total wheat = 6 quintals = 6 * 100 = 600 kg.
• Part of the wheat is sold at 7% profit.
• The rest is sold at 17% profit.
• Overall profit percentage on the entire wheat is 11%.
• We need to find the quantity sold at 17% profit, in kilograms.

Concept / Approach:
Let the quantity sold at 7% profit be x kg, so the quantity at 17% profit is 600 - x kg. If the cost price per kg is the same for all wheat, the effective profit percentage is a weighted average of individual profit percentages, weighted by the respective quantities. Equating the weighted average to 11% allows us to solve for x and then obtain the quantity sold at 17% profit.

Step-by-Step Solution:
Let the cost price per kg be 1 unit (for simplicity). Let quantity at 7% profit be x kg; then quantity at 17% profit is 600 - x kg. Total cost = 600 * 1 = 600 units. Total selling price = 1.07x + 1.17(600 - x). Given overall profit = 11%, so total SP = 1.11 * 600 = 666 units. Thus, 1.07x + 1.17(600 - x) = 666. Simplify: 1.07x + 702 - 1.17x = 666 → -0.10x + 702 = 666 → 0.10x = 36 → x = 360 kg. Hence quantity at 17% profit = 600 - 360 = 240 kg.

Verification / Alternative check:
We can also apply the alligation method on profit rates. Putting 7% and 17% with mean 11% gives ratio of quantities as (17 - 11) : (11 - 7) = 6 : 4 = 3 : 2. So out of total 600 kg, quantity at 7% is (3/5) * 600 = 360 kg and at 17% is (2/5) * 600 = 240 kg, confirming the result.

Why Other Options Are Wrong:
360 kg is the quantity at 7% profit, not at 17%. Quantities 120 kg or 480 kg at 17% are not consistent with the ratio required to obtain an overall 11% gain. Only 240 kg satisfies both the total quantity and the overall profit condition.

Common Pitfalls:
A usual mistake is to assume half the quantity is sold at each rate or to average the percentages arithmetically without considering quantities. Another error is mixing up which quantity corresponds to which profit rate when using the alligation cross differences.

Final Answer:
The trader sells 240 kg of wheat at 17% profit.