A retailer offers a discount of 28% on the marked price of goods and thereby ends up selling exactly at cost price. What was the percentage markup of the marked price over the cost price?

Introduction / Context:
This problem combines the ideas of markup and discount. The retailer first increases the price above cost (markup) and then reduces it by giving a discount, finally selling at cost. We must work backward from the information that after discount the selling price equals the cost price. This type of question appears frequently in profit and loss sections of competitive exams.

Given Data / Assumptions:
- Cost price (CP) of an item is some amount, say CP units.
- The retailer marks the price above CP by an unknown percentage m.
- A discount of 28 percent is offered on this marked price (MP).
- After giving this discount, the final selling price equals CP.
- We must find the percentage markup m.

Concept / Approach:
The marked price is related to cost price by MP = CP * (1 + m / 100). The selling price (SP) is related to marked price by SP = MP * (1 - discount / 100). Here, SP is given indirectly as equal to CP. By equating these expressions, we can solve for m. Using CP as a variable makes the solution general, but setting CP = 1 or 100 can simplify mental calculations.

Step-by-Step Solution:
Let CP = 1 unit for simplicity. Let the markup be m percent, so MP = 1 * (1 + m / 100) = 1 + m / 100. Discount offered = 28 percent, so SP = MP * (1 - 28 / 100) = (1 + m / 100) * 0.72. Given that SP equals CP, we have (1 + m / 100) * 0.72 = 1. Therefore, 1 + m / 100 = 1 / 0.72. Compute 1 / 0.72 = 100 / 72 = 25 / 18. So, 1 + m / 100 = 25 / 18. Thus, m / 100 = 25 / 18 - 1 = (25 - 18) / 18 = 7 / 18. Therefore, m = 100 * 7 / 18 = 700 / 18 = 38.88 percent (approximately).

Verification / Alternative check:
Assume CP = Rs. 100 for an easier numeric check. With markup 38.88 percent, MP = 100 + 38.88 = Rs. 138.88. Now apply a 28 percent discount: SP = 138.88 * 0.72. Compute 138.88 * 0.72 which is approximately 100. This shows that the selling price returns to the cost price, confirming that the markup must be about 38.88 percent.

Why Other Options Are Wrong:
18.25 percent and 22 percent: These markups are too low; after a 28 percent discount the selling price would be less than cost, leading to a loss.
28 percent: This corresponds numerically to the discount but not to the required markup to end at cost price.
25 percent: Again, this is insufficient markup to offset a 28 percent discount.

Common Pitfalls:
One common mistake is assuming that a 28 percent markup will cancel a 28 percent discount, which is incorrect because the discount is applied on the marked price, not on cost price. Another error is to try to add or subtract percentages directly without setting up the equations. Always write the relationships between CP, MP, and SP clearly to avoid confusion in such problems.

Final Answer:
The retailer must mark up the goods by approximately 38.88 percent over the cost price to break even after giving a 28 percent discount.