A shopkeeper sells 5 identical items and earns a profit equal to the selling price of 1 item. What is his profit percentage on the cost price?

Introduction / Context:
This problem uses a simple relationship between total profit and selling price to test your algebraic thinking. The shopkeeper sells 5 items and is told that the total profit he earns is equal to the selling price of one item. By translating this statement into an equation, you can determine the profit percentage on the cost price. Questions of this kind are common in competitive exams because they combine basic profit concepts with a short algebraic step.

Given Data / Assumptions:
- The shopkeeper sells 5 identical items. - Total profit on the sale of these 5 items equals the selling price of 1 item. - All items have the same cost price and selling price. - We need the profit percentage on the cost price. - No additional costs or discounts are involved.

Concept / Approach:
Let cost price of each item be C and selling price of each item be S. Then, for 5 items, total cost is 5 * C and total selling price is 5 * S. Profit = Total Selling Price - Total Cost Price = 5S - 5C. The question states that this profit is equal to the selling price of 1 item, i.e., 5S - 5C = S. We solve this equation to find the ratio S / C, and then use that ratio to compute the profit percentage as ((S - C) / C) * 100.

Step-by-Step Solution:
Step 1: Let cost price per item be C and selling price per item be S. Step 2: Total cost for 5 items = 5 * C. Step 3: Total selling price for 5 items = 5 * S. Step 4: Profit = Total selling price - Total cost price = 5S - 5C. Step 5: Given that profit = selling price of 1 item = S. Step 6: So, 5S - 5C = S. Step 7: Rearrange: 5S - S = 5C, so 4S = 5C. Step 8: Therefore, S = (5 / 4) * C. Step 9: Profit per item = S - C = (5 / 4) * C - C = (1 / 4) * C. Step 10: Profit percentage = (Profit per item / C) * 100 = (C / 4) / C * 100 = 25%.

Verification / Alternative check:
Assume a convenient cost price, say C = Rs. 4. Then S = (5 / 4) * 4 = Rs. 5. For 5 items, total cost = 5 * 4 = Rs. 20 and total selling price = 5 * 5 = Rs. 25. Profit = 25 - 20 = Rs. 5, which is exactly equal to the selling price of 1 item. Profit percentage = (1 / 4) * 100 = 25%. This numerical example confirms the algebraic result.

Why Other Options Are Wrong:
A 20% profit would correspond to S = 1.2 * C and would not satisfy the equation 5S - 5C = S. Similarly, profit percentages of 16% or 22.5% give different S to C ratios, none of which make the total profit equal to S for 5 items. Only 25% profit gives a neat and exact equality as described in the problem statement.

Common Pitfalls:
Students sometimes misinterpret the statement and think that profit on each item equals selling price of one item, which is incorrect. The profit equality mentioned in the problem is about total profit on 5 items. Another mistake is not creating an algebraic equation and instead trying to guess the percentage. Systematically defining variables and writing the relationship avoids these errors.

Final Answer:
The shopkeeper earns a 25% profit on the cost price of each item.