If the cost price of 25 pens is equal to the selling price of 20 pens, what is the profit percentage made when each pen is sold at this selling price?

Introduction / Context:
This is a standard profit percentage question where cost price and selling price are related through numbers of items rather than direct rupee values. It tests the idea that when the total cost of a certain number of items equals the total selling price of a smaller number of items, there is a profit in selling each item at that rate.

Given Data / Assumptions:
- Cost price of 25 pens is equal to selling price of 20 pens. - All pens are identical and sold at the same selling price per pen. - No additional costs such as packaging are involved.

Concept / Approach:
Let cost price per pen be C and selling price per pen be S. The equation from the question is:
25 * C = 20 * S From this, we can express S in terms of C and then use the profit percentage formula:
profit = S - C profit percent = (profit / C) * 100

Step-by-Step Solution:
Step 1: Let cost price per pen = C and selling price per pen = S. Step 2: Given 25C = 20S. Step 3: So S = 25C / 20 = (5/4) * C = 1.25C. Step 4: Profit per pen = S - C = 1.25C - C = 0.25C. Step 5: Profit percent = (0.25C / C) * 100 = 25%.

Verification / Alternative check:
Assume a convenient cost price per pen, say C = Rs 4. Then cost price of 25 pens = 25 * 4 = Rs 100. This must equal the selling price of 20 pens, so S = 100 / 20 = Rs 5 per pen. Profit per pen = 5 - 4 = Rs 1. Profit percent = 1 / 4 * 100 = 25%, confirming the calculation.

Why Other Options Are Wrong:
Option 20% would correspond to a selling price of 1.2C, which does not satisfy 25C = 20S. Option 15% and 5% represent even smaller markups and clearly cannot produce equality between 25C and 20S. Only 25% matches the relationship given in the problem.

Common Pitfalls:
Students sometimes reverse the ratio and assume 20C = 25S or incorrectly treat the numbers of pens as the percentage directly. It is important to set up the equation carefully and then isolate S in terms of C before applying the profit percentage formula.

Final Answer:
The profit made on each pen is 25% of the cost price.