A shopkeeper sells 21 identical items and finds that his total profit is exactly equal to the selling price of 1 item. What is his percentage profit on each item?

Introduction / Context:
This problem deals with the basic relationship between cost price, selling price, and profit percentage when multiple identical items are sold. Instead of giving direct numerical prices, the question uses a clever condition based on total profit and the selling price of one item. Such questions appear often in aptitude exams to test algebraic thinking and the ability to form equations from verbal statements.

Given Data / Assumptions:

• All 21 items are identical.
• Total profit earned by selling 21 items equals the selling price of 1 item.
• We assume each item has the same cost price and selling price.
• We need to find the profit percentage on each item.

Concept / Approach:
We use the following ideas:

• Let cost price of one item be C and selling price be S.
• Total profit for 21 items is 21(S - C).
• Given that total profit = S.
• This condition leads to an equation that relates S and C.
• Once S in terms of C is known, profit percent = ((S - C) / C) * 100.

Step-by-Step Solution:
Let cost price of one item be C and selling price be S. Total profit for 21 items = 21(S - C). Given: 21(S - C) = S. Rearrange: 21S - 21C = S, so 20S = 21C. Thus S / C = 21 / 20. Profit on one item = S - C = (21/20)C - C = (1/20)C. Profit percent = ((S - C) / C) * 100 = (1/20) * 100 = 5%.

Verification / Alternative check:
Assume an easy cost price to verify, for example C = 20. Then S = (21/20) * 20 = 21. Profit per item is 1. For 21 items, total profit is 21 * 1 = 21. This is exactly equal to the selling price of 1 item, which is also 21. The condition in the question is satisfied, and the calculated profit percent is (1 / 20) * 100 = 5%. This confirms that our algebraic solution is correct.

Why Other Options Are Wrong:
If profit were 2% or 2.5%, S / C would be close to 1.02 or 1.025, which would not satisfy 21(S - C) = S. Similarly, 4% or 6% would yield different ratios that do not lead to total profit equalling the selling price of 1 item. Only a 5% profit ensures that total profit becomes exactly the price of one item.

Common Pitfalls:
Students often try random trial and error with percentages instead of forming the equation. Another mistake is misinterpreting the statement and equating profit per item to the selling price of one item instead of total profit to one selling price. Always translate the language of the problem into algebra calmly and then solve step by step.

Final Answer:
The shopkeeper makes a profit of 5% on each item.