A shopkeeper sold an article for ₹6,750 after giving a 10% discount on the labelled price. If he would have made a 50% profit with no discount, what was the actual percentage of profit earned with the 10% discount?

Introduction / Context:
This is a labelled price and discount problem tied to a target profit without discount. We back-calculate the cost price using the hypothetical 50% profit case, and then compute the actual profit percentage when a 10% discount yields a selling price of ₹6,750.

Given Data / Assumptions:

• Selling price with 10% discount = ₹6,750.
• Let labelled price = L. Then 0.90 * L = 6,750.
• No discount would have given 50% profit on cost.

Concept / Approach:
First find L from the discount relation. The no-discount scenario implies SP_no_disc = L = 1.5 * CP, so CP = L / 1.5. Then compute actual profit% = (6,750 − CP) / CP * 100.

Step-by-Step Solution:
L = 6,750 / 0.90 = ₹7,500CP = 7,500 / 1.5 = ₹5,000Actual profit = 6,750 − 5,000 = ₹1,750Profit% = 1,750 / 5,000 * 100 = 35%

Verification / Alternative check:
If sold at L (no discount), profit would be 7,500 − 5,000 = 2,500 → 50%, consistent with the premise.

Why Other Options Are Wrong:
36%, 40%: Do not match the computed profit over the recovered cost price.

Common Pitfalls:
Confusing profit on SP with profit on CP; forgetting to find CP from the “no-discount 50% profit” clue before evaluating the discounted case.

Final Answer:
35%