Tarun receives a 30% discount on the labelled (marked) price of an article and buys it at this reduced price. He then sells the article for Rs. 8750, making a profit of 25% on his purchase price. What was the original labelled price of the article?

Introduction / Context:
This question combines discount and profit concepts. Tarun buys an article after getting a concession on the labelled price and then sells it at a profit over his actual cost. The task is to work backwards from his final selling price and known profit percentage to recover the labelled price. This is a typical exam question involving reverse percentage calculations.

Given Data / Assumptions:

• Labelled price of the article = L rupees (unknown).
• Tarun gets a discount of 30% on L.
• So his purchase price = 70% of L.
• He sells the article for Rs. 8750.
• His profit on the purchase price is 25%.
• We must find the value of L, the original labelled price.

Concept / Approach:
First, we interpret the 25% profit as selling price = 1.25 times the purchase price. Because the purchase price itself is 70% of the labelled price, or 0.7L, the selling price can be expressed in terms of L as 1.25 * 0.7L. This expression is set equal to the actual selling price of Rs. 8750. Solving this equation yields L directly. This approach avoids unnecessary intermediate steps.

Step-by-Step Solution:
Step 1: Purchase price after 30% discount = 70% of L = 0.7L.Step 2: Tarun makes a profit of 25% on this purchase price.Step 3: Therefore, selling price = 1.25 * 0.7L = 0.875L.Step 4: We are told the selling price equals Rs. 8750, so 0.875L = 8750.Step 5: Solve for L: L = 8750 / 0.875.Step 6: Note that 0.875 = 7 / 8, so L = 8750 * 8 / 7 = Rs. 10000.

Verification / Alternative check:
If L = Rs. 10000, the discount of 30% leads to a purchase price of 0.7 * 10000 = Rs. 7000.A 25% profit on Rs. 7000 is 0.25 * 7000 = Rs. 1750.So the selling price becomes 7000 + 1750 = Rs. 8750, exactly matching the given value.

Why Other Options Are Wrong:
Labelled prices such as Rs. 12000, Rs. 13000, or Rs. 14000 would lead to purchase and selling prices different from Rs. 8750 when the same discount and profit percentages are applied. Rs. 9000 also fails the check because 70% of 9000 is 6300 and 25% profit on that would not reach 8750. Only Rs. 10000 satisfies all conditions.

Common Pitfalls:
Students often apply the 25% profit directly to the labelled price instead of to the discounted price, which is incorrect. Others may mis-handle the division by 0.875, or convert percentages incorrectly. Writing the relationships clearly as equations and reducing fractions like 0.875 to 7 / 8 helps to avoid computational mistakes.

Final Answer:
The original labelled price of the article was Rs. 10000.