The marked price of a chair is 40% more than its cost price. If the chair is sold for Rs 520 after giving a discount of Rs 40 on the marked price, what is the profit percentage earned on the sale?

Introduction / Context:
This problem combines the ideas of marked price, discount, and profit. Many real life shopkeeping situations involve marking goods above cost, then offering a discount, and still earning profit. The learner must be able to move from marked price back to cost price and then compare cost and selling price to compute profit percentage.

Given Data / Assumptions:
- Marked price is 40% more than cost price. - The final selling price is Rs 520. - A discount of Rs 40 is given on the marked price. - Only one item is considered, and there are no taxes or extra costs.

Concept / Approach:
We use these relations:
marked price = cost price * 1.4 selling price = marked price - discount profit = selling price - cost price profit percent = (profit / cost price) * 100 First we find the marked price using the selling price and discount, then find the cost price, and finally compute the profit percentage.

Step-by-Step Solution:
Step 1: Selling price S = Rs 520. Step 2: Discount = Rs 40, so marked price M = S + discount = 520 + 40 = Rs 560. Step 3: Marked price is 40% above cost price, so M = 1.4 * cost price. Step 4: Therefore cost price C = 560 / 1.4 = Rs 400. Step 5: Profit = S - C = 520 - 400 = Rs 120. Step 6: Profit percent = 120 / 400 * 100 = 30%.

Verification / Alternative check:
We can also compute directly from cost price. If cost is Rs 400, then 40% of 400 is 160, so marked price should be 560. After allowing a flat discount of 40, we again reach 520 as selling price. The profit of 120 on a cost of 400 is clearly 30%, so the result is confirmed by two consistent checks.

Why Other Options Are Wrong:
Option 33 would require a profit of about Rs 132, which does not match the given numbers. Option 40 would be correct only if the selling price were higher for the same cost. Option 25 comes from mixing up marked price and cost price or using 520 as the base in the denominator, which is incorrect for profit percentage.

Common Pitfalls:
Learners sometimes treat marked price as cost price or calculate profit on marked price instead of on cost price. Another common error is forgetting that discount reduces marked price, not cost price. Careful identification of each price level avoids these mistakes.

Final Answer:
The profit percentage earned on the sale of the chair is 30%.