Mohan purchases 13 identical articles for Rs. 12 in total and then sells all of them at the rate of 12 articles for Rs. 13. Based on this buying and selling pattern, what is his percentage profit on the cost price?

Introduction / Context:
This is a typical profit and loss question where the trader buys and sells items in unequal number-price combinations, such as “13 for Rs. 12” and “12 for Rs. 13”. These are very common patterns in competitive exams because they test conceptual understanding of unit cost price and unit selling price. The overall profit percentage is found by comparing the cost price per article with the selling price per article. Careful handling of fractions is important to avoid calculation errors and to get the exact profit percentage.

Given Data / Assumptions:
- Mohan buys 13 articles for Rs. 12 (this is the total cost for 13 units). - He sells the articles at the rate of 12 articles for Rs. 13. - All articles are identical with the same cost price and selling price per article. - We must find his profit percentage on the cost price.

Concept / Approach:
To find the profit percentage, we first determine the cost price per article and the selling price per article. Cost price per article is simply total cost divided by number of articles bought in that lot. Similarly, selling price per article is total selling amount divided by the number of articles sold in that selling lot. Once we know CP per unit and SP per unit, we calculate profit per unit as SP - CP and then compute Profit% = (Profit per unit / CP per unit) * 100. Since all articles behave identically, using just one article is enough to understand the entire transaction pattern.

Step-by-Step Solution:
Total cost of 13 articles = Rs. 12. Cost price (CP) per article = 12 / 13 rupees. He sells at 12 articles for Rs. 13. Selling price (SP) per article = 13 / 12 rupees. Profit per article = SP - CP = (13 / 12) - (12 / 13). Compute the difference: (13 / 12) - (12 / 13) = (169 / 156) - (144 / 156) = 25 / 156. Profit per article = 25 / 156 rupees. Profit percentage = (Profit per article / CP per article) * 100. So, Profit% = (25 / 156) / (12 / 13) * 100. Simplify: (25 / 156) * (13 / 12) * 100 = (25 * 13 * 100) / (156 * 12). Compute: 25 * 13 = 325; 156 * 12 = 1,872. Thus Profit% = (325 * 100) / 1,872 ≈ 17.36%.

Verification / Alternative check:
Assume Mohan buys 156 articles in bulk, which is the least common multiple of 12 and 13. For every 13 articles, he pays Rs. 12, so for 156 articles he has 156 / 13 = 12 lots and pays 12 * 12 = Rs. 144. He sells at 12 for Rs. 13, so number of lots for 156 articles is 156 / 12 = 13 lots, and revenue = 13 * 13 = Rs. 169. Profit = 169 - 144 = Rs. 25 on cost price 144, so Profit% = 25 / 144 * 100 ≈ 17.36%, matching the earlier calculation.

Why Other Options Are Wrong:
- 19.47% and 12.5% do not match the correct fraction and arise from approximate or mistaken arithmetic. - 11.11% is a common distractor based on confusion with 9-for-10 or similar patterns. - 15% is a rounded guess and not supported by accurate fraction-based computation.

Common Pitfalls:
Students sometimes incorrectly compare 13 and 12 directly and think profit is simply 1 rupee on 12 rupees, giving 8.33%, which ignores the number of articles. Another mistake is to compute profit percentage based on total selling price or total buying price without normalizing to units. Neglecting to use a convenient common multiple (like 156) can make the arithmetic look harder than it really is.

Final Answer:
Mohan earns a profit of approximately 17.36% on his cost price.