The marked price of an article is 40% more than its cost price, and a discount of 15% is allowed on the marked price. What is the final profit percentage earned by the seller?

Introduction / Context:
This question involves combined concepts of marked price, discount, and profit percentage. It tests your ability to move step by step from cost price to marked price, then to selling price after discount, and finally to calculate overall profit percentage based on cost price. Such questions are common in retail and shopkeeper style word problems in aptitude exams.

Given Data / Assumptions:

• Marked price (MP) is 40% more than cost price (CP).
• Discount of 15% is given on the marked price.
• We must find overall profit percentage based on the original cost price.
• There are no extra costs like transport or taxes.

Concept / Approach:
First, express the marked price in terms of cost price using the 40% increase. Then apply the discount on the marked price to determine the selling price. Finally, compute profit or gain percentage as (SP - CP) / CP * 100. Using a convenient assumed value for CP makes the arithmetic easier without changing the answer.

Step-by-Step Solution:
Assume CP = 100 units. Marked price MP = CP * (1 + 40/100) = 100 * 1.4 = 140 units. Discount = 15% of MP, so discount = 0.15 * 140 = 21 units. Selling price SP = MP - discount = 140 - 21 = 119 units. Profit = SP - CP = 119 - 100 = 19 units. Profit percentage = (19 / 100) * 100 = 19%.

Verification / Alternative check:
We can also treat the combined effect directly: MP = 1.4 * CP and SP = 0.85 * MP = 0.85 * 1.4 * CP = 1.19 * CP. This shows that SP is 1.19 times CP, meaning a 19% profit. Both approaches confirm the same percentage.

Why Other Options Are Wrong:
A 25% profit would require SP = 1.25 * CP which would be 125 units instead of 119. A 15% profit would put SP at 115 units. A 21% profit would require SP = 121 units. None of these match the calculated selling price of 119 units, so 19% is the only correct answer.

Common Pitfalls:
Candidates often subtract discount from cost price instead of marked price, which leads to wrong results. Another error is to forget that profit must always be calculated on cost price, not on marked price or selling price. Careless percentage calculations and skipping the simplification step also cause mistakes.

Final Answer:
The profit percentage earned after a 15% discount on a marked price that is 40% above cost is 19%.