A retailer offers a discount of 20% on the marked price of goods and, as a result, sells them exactly at cost price. What was the percentage mark up of the marked price over the cost price?

Introduction / Context:

This problem relates discount percentage to mark up percentage. The retailer marks the goods above cost price, then gives a discount and still ends up selling at cost price. You are asked to compute how much the goods were marked up initially. This is a classic application of percentage change in pricing.

Given Data / Assumptions:

• Let cost price of the item be C.
• Marked price of the item is some percentage above C.
• A discount of 20% on the marked price is allowed.
• After this discount, the selling price equals the cost price C.
• We need to find the percentage mark up from C to the marked price.

Concept / Approach:

When the retailer gives a discount of 20% on the marked price M, the selling price becomes 80% of M. The question states that this selling price equals the cost price C. So 80% of M is equal to C. From this equation, we can express M in terms of C and then find what percentage M is above C. The mark up percentage is (M − C) / C * 100.

Step-by-Step Solution:

Verification / Alternative check:

Assume a simple cost price, say C = Rs 100. Then marked price M = 1.25 * 100 = Rs 125. With a 20% discount on Rs 125, the reduction is 20% of 125 = 25. Selling price becomes 125 − 25 = Rs 100, which is exactly the cost price. This confirms that a 25% mark up combined with a 20% discount leads to a break-even sale.

Why Other Options Are Wrong:

• 20%: A 20% mark up would make M = 1.20C. After a 20% discount, selling price would be 80% of 1.20C = 0.96C, which is below cost price.
• 30% and 40%: These would lead to M = 1.30C or 1.40C, and after a 20% discount, the selling price would be above cost price, resulting in profit rather than break-even.
• 15%: This mark up is too low and would result in a loss after a 20% discount.

Common Pitfalls:

Some learners confuse the mark up percentage with the discount percentage and assume they must be the same. Others forget that the discount is applied on the marked price, not on the cost price. It is important to carefully define variables, translate the given conditions into equations, and then solve step by step.

Final Answer:

The retailer marked up the goods by 25% over the cost price.