The cost price of 28 articles is equal to the selling price of 21 articles of the same kind. What is the percentage of profit made by the seller?

Introduction / Context:
This question is about comparing total cost and total selling price for different quantities of the same article. The condition that the cost of a larger number of articles equals the sales revenue of a smaller number indicates a profit on each article. The goal is to compute the profit percentage per article, which is a standard type in profit and loss topics using ratio and proportion concepts.

Given Data / Assumptions:

• Cost price of 28 articles equals selling price of 21 articles.
• All articles are identical in cost and selling price behavior.
• Let cost price per article be C and selling price per article be S.
• We need to find profit percentage on cost price.

Concept / Approach:
Since the articles are identical, we can express total cost and total selling price in terms of per article prices and number of articles. Then use the equality between total cost of 28 and total selling price of 21 to find the ratio of S to C. Once this ratio is known, profit per article is S - C and the profit percentage is (S - C) / C * 100. This approach avoids needing any actual currency values and relies purely on ratios.

Step-by-Step Solution:
Step 1: Let cost price per article = C.Step 2: Let selling price per article = S.Step 3: Total cost of 28 articles = 28C.Step 4: Total selling price of 21 articles = 21S.Step 5: Given that 28C = 21S.Step 6: Divide both sides by 7: 4C = 3S.Step 7: Therefore S = (4/3) * C.Step 8: Profit per article = S - C = (4/3)C - C = (1/3)C.Step 9: Profit percentage = [(1/3)C / C] * 100 = (1/3) * 100 = 33 1/3 %.

Verification / Alternative check:
We can use notional values to confirm. Suppose C = Rs 3. Then S = (4/3) * 3 = Rs 4. Cost of 28 articles = 28 * 3 = Rs 84. Selling price of 21 articles = 21 * 4 = Rs 84, which satisfies the given condition. Profit per article is Rs 1 on a cost of Rs 3. Profit percentage is 1 / 3 * 100 = 33 1/3 %, confirming the earlier ratio based calculation.

Why Other Options Are Wrong:
Option A (12%), option C (20%) and option D (22%) are all smaller than the correct profit percentage and do not match the ratio S = 4C/3 implied by the equality 28C = 21S. Only option B, 33 1⁄3 %, exactly arises from the fraction (1/3)C and matches the derived profit percentage.

Common Pitfalls:
Students sometimes misinterpret the statement and reverse the relationship, such as equating cost of 21 items with selling price of 28 items, leading to a loss instead of a profit. Others may divide 28 by 21 or vice versa without linking correctly to per unit prices. Writing down the symbolic expressions for total cost and total selling price and then solving for S in terms of C is the safest way to handle such comparisons.

Final Answer:
The profit percentage made by the seller is 33 1⁄3 %.