A retailer buys goods from a shopkeeper at a discount of 40% on the list (marked) price and sells them to customers at a discount of 25% on the same list price. What is the retailer's profit percentage?

Introduction / Context:
This question deals with successive discounts on the same marked price, one from the wholesaler to the retailer and another from the retailer to the final customer. The retailer purchases goods below the marked price and sells them at a higher price, but still below the marked price. The task is to compute the profit percentage made by the retailer relative to his cost price. This is a standard application of percentages in trade and commerce.

Given Data / Assumptions:

• Marked price (list price) of the goods = M (assume M rupees).
• Retailer buys goods at 40% discount from M.
• Retailer sells the goods at 25% discount from M to customers.
• We ignore transport or other overhead costs; only purchase and sale discounts matter.
• We must find profit percentage on the retailer's cost price.

Concept / Approach:
The retailer's cost price is the price at which he buys the goods from the shopkeeper. A 40% discount on M means he pays 60% of M, or 0.60M. The retailer's selling price to customers is 75% of M, or 0.75M, since he offers a 25% discount on the marked price. Profit percentage is computed as (SP - CP) / CP * 100, where CP is the retailer's purchase price and SP is the retailer's selling price.

Step-by-Step Solution:
Step 1: Let marked price be M rupees. Step 2: Retailer buys at 40% discount, so his cost price CP = M * (1 - 40/100) = 0.60M. Step 3: Retailer sells at 25% discount, so his selling price SP = M * (1 - 25/100) = 0.75M. Step 4: Profit made by retailer = SP - CP = 0.75M - 0.60M = 0.15M. Step 5: Profit percentage on CP = (Profit / CP) * 100 = (0.15M / 0.60M) * 100. Step 6: Simplify fraction: 0.15M / 0.60M = 0.25 = 1/4. Step 7: Profit percentage = 0.25 * 100 = 25%.

Verification / Alternative check:
Assume a simple marked price, for example M = Rs. 100. Retailer's cost price at 40% discount = Rs. 60. Retailer's selling price at 25% discount = Rs. 75. Profit = 75 - 60 = Rs. 15. Profit percentage on CP = (15 / 60) * 100 = 25%. This numerical example confirms the symbolic calculation with M and shows clearly how the profit arises in practice.

Why Other Options Are Wrong:
Profit percentages of 10%, 15% or 20% would require different relative positions of CP and SP than the ones arising from 40% and 25% discounts on the same marked price. A profit of 5% is far too small for the difference between Rs. 60 and Rs. 75. Only 25% matches the actual comparison between CP and SP.

Common Pitfalls:
Some learners mistakenly subtract the discount percentages (40% - 25% = 15%) and assume 15% is the profit. Others confuse discount on marked price with profit on cost price, which are based on different denominators. Always convert each discount to an actual price, then compute profit relative to the cost price to obtain the correct profit percentage.

Final Answer:
The retailer earns a profit of 25% on his cost price.