The cost price of 22 articles is equal to the selling price of 18 articles of the same type. What is the percentage profit made by the seller on each article?

Introduction / Context:
This problem involves comparing total cost price and total selling price for different quantities of the same article. It is a standard type of profit percentage question, frequently used to test understanding of proportional reasoning and the relationship between cost price and selling price.

Given Data / Assumptions:

• Cost price of 22 articles together = total CP.
• Selling price of 18 articles together = total SP.
• Given that total CP of 22 articles = total SP of 18 articles.
• All articles are identical and sold at the same rate, and there are no extra costs.

Concept / Approach:
If the cost of 22 articles equals the selling price of only 18 articles, it means that selling one article brings more revenue than its cost price. From this equality we can find the selling price of one article in terms of its cost price. Then the percentage profit is calculated as the difference between selling price and cost price divided by cost price, multiplied by 100.

Step-by-Step Solution:
Let cost price of one article be C. Then total cost price of 22 articles = 22 * C. Let selling price of one article be S. Then total selling price of 18 articles = 18 * S. Given: 22 * C = 18 * S. So S = (22 / 18) * C = (11 / 9) * C. Profit per article = S - C = (11 / 9) * C - C = (2 / 9) * C. Profit percentage = (profit / cost price) * 100. Profit percent = ((2 / 9) * C / C) * 100 = (2 / 9) * 100 ≈ 22.22 percent.

Verification / Alternative check:
Assume C = Rs. 9 for convenience. Then total cost of 22 articles = 22 * 9 = Rs. 198. This equals total selling price of 18 articles, so SP per article S = 198 / 18 = Rs. 11. Profit per article = 11 - 9 = Rs. 2. Profit percent = 2 / 9 * 100 ≈ 22.22 percent. This confirms the result.

Why Other Options Are Wrong:
33.33%: This is larger than the true profit and comes from misinterpreting the ratio 22 : 18 as the direct profit percentage. 11.11% and 1%: These are too small and arise from arithmetic mistakes or incorrect use of ratios. Only 22.22 percent matches the correct calculation.

Common Pitfalls:
A common error is to think that profit percent is based on the difference between 22 and 18 directly. Candidates may also mistakenly treat 22 : 18 as the ratio of selling price to cost price instead of cost price to selling price, or forget that cost price is the base for profit percentage. Always identify which side of the equation represents cost and which represents selling price before computing percentages.

Final Answer:
The seller makes a profit of approximately 22.22% on each article.