The marked price of a chair is 40% more than its cost price. After allowing a discount of Rs. 40, the chair is sold for Rs. 520. What is the profit percentage earned on the chair?

Introduction / Context:
This question combines markup (in percentage form) and a fixed discount amount to test your understanding of how to move back to the cost price and then compute profit percentage. The marked price is given as a percentage above cost price, while the actual selling price is the marked price minus a fixed rupee discount. From this information you must recover the cost price and then calculate the profit percentage achieved on the sale of the chair.

Given Data / Assumptions:
- The marked price of the chair is 40% above its cost price. - The discount offered on the marked price is Rs. 40. - The final selling price after discount is Rs. 520. - There are no additional costs or taxes. - We must find the profit percentage on the cost price.

Concept / Approach:
Let the cost price be CP. Then marked price MP = CP * (1 + 40 / 100) = 1.4 * CP. The selling price is given as MP - 40 and is known to be Rs. 520. So we can set up the equation 1.4 * CP - 40 = 520 and solve for CP. Once CP is known, profit is Selling Price - Cost Price, and profit percentage is (Profit / CP) * 100. This structured approach ensures every step is logically consistent and avoids guesswork.

Step-by-Step Solution:
Step 1: Let cost price of the chair be CP. Step 2: Marked price MP = 1.4 * CP. Step 3: After discount of Rs. 40, selling price SP = MP - 40. Step 4: Given SP = 520, so 1.4 * CP - 40 = 520. Step 5: Add 40 to both sides: 1.4 * CP = 560. Step 6: CP = 560 / 1.4 = 400 rupees. Step 7: Profit = SP - CP = 520 - 400 = 120 rupees. Step 8: Profit percentage = (120 / 400) * 100 = 30%.

Verification / Alternative check:
We can verify by reconstructing the marked price. If CP = 400, then MP = 400 * 1.4 = 560. Discount is Rs. 40, so SP = 560 - 40 = 520, which matches the question. The profit is 520 - 400 = 120, and 120 is exactly 30% of 400. Therefore, the computed profit percentage of 30% is fully consistent with all given figures.

Why Other Options Are Wrong:
A 25% profit would give a profit of only 100 on a cost of 400, leading to a selling price of 500, not 520. A 33% profit would produce an approximate selling price of 532, and a 40% profit would result in a selling price of 560, equal to the marked price without discount. None of these match the provided selling price and discount data. Only 30% satisfies the conditions exactly.

Common Pitfalls:
Some students wrongly treat the discount as 40% instead of Rs. 40 because they are used to percent-based discounts. Others forget that profit is computed on cost price, not on marked price. A further mistake is to assume that 40% markup and Rs. 40 discount can be combined directly without setting up an equation. Defining CP, writing expressions for MP and SP, and then solving carefully is the safest route.

Final Answer:
The profit earned on the sale of the chair is 30% of its cost price.