The selling price of an article is Rs 9250 after allowing a discount of 7.5% on the marked price. What is the marked price of the article?

Introduction / Context:
This question reverses the usual discount calculation. Instead of finding the selling price from the marked price and discount, we are given the selling price and discount rate and asked to find the marked price. Such reverse percentage problems are very common in competitive exams, as they test a deeper understanding of how discounts affect prices and require careful algebraic manipulation rather than one step arithmetic.

Given Data / Assumptions:

• Selling price (SP) after discount = Rs 9250.
• Discount rate on marked price (MP) = 7.5%.
• Therefore, the customer pays 100% − 7.5% = 92.5% of the marked price.
• We need to find MP such that SP = 92.5% of MP.

Concept / Approach:
The relationship between selling price and marked price under a discount is SP = MP * (1 − discount/100). Here the discount is 7.5%, so SP = MP * 92.5/100. To find MP, we solve this equation: MP = SP * 100 / 92.5. Recognising that 92.5% is 0.925 in decimal form also helps. This approach is standard for reverse discount and reverse percentage problems.

Step-by-Step Solution:
Step 1: Let marked price be MP. Step 2: Discount rate = 7.5%, so customer pays 92.5% of MP. Step 3: Selling price SP = MP * 92.5/100. Step 4: Given SP = 9250, so 9250 = MP * 92.5/100. Step 5: Rearrange to get MP = 9250 * 100 / 92.5. Step 6: Convert 92.5 to decimal: 92.5 = 92.5. So in decimal form, 92.5/100 = 0.925 and MP = 9250 / 0.925. Step 7: Compute MP: 9250 / 0.925 = 10000.

Verification / Alternative check:
Check the result by forward calculation. If MP = Rs 10000 and discount = 7.5%, discount amount = 10000 * 7.5/100 = 750. Selling price should then be 10000 − 750 = 9250. This matches the given SP in the question, confirming that our computed marked price is correct.

Why Other Options Are Wrong:

• 9000 and 8556.25 are values lower than the selling price or associated with incorrect manipulation of the discount formula.
• 9943.75 is close but still not exact; using it as MP would not yield SP exactly equal to 9250 when a 7.5% discount is applied.

Common Pitfalls:
Some students mistakenly compute MP by subtracting 7.5% from SP, treating SP as if it were the marked price, which leads to a lower and incorrect value. Others misinterpret 7.5% as 0.75 instead of 0.075 or confuse 92.5% with 0.9250 without handling the decimals correctly. To avoid confusion, always write the discount equation clearly and isolate the unknown step by step.

Final Answer:
The marked price of the article is Rs 10000.