If the selling price of an item is Rs 9750 after a 25 percent discount, what was the marked price of the item before the discount was applied?

Introduction / Context:
This question is another example of reversing a discount. The selling price after a known percentage discount is given, and the aim is to recover the marked price before the discount. Such problems appear frequently in profit and loss sections where understanding of base value and final value is tested.

Given Data / Assumptions:
Selling price after discount = Rs 9750. Discount rate = 25 percent. Marked price is unknown. No additional charges or hidden costs are involved.

Concept / Approach:
If a store gives a 25 percent discount, the customer pays 75 percent of the marked price. Therefore selling price equals marked price multiplied by 0.75. By dividing the known selling price by 0.75, we can find the original marked price. This is a direct application of the relationship between discount and selling price.

Step-by-Step Solution:
Let marked price be M. Discount = 25 percent, so selling price S = M * (1 - 25/100) = 0.75M. We are given S = 9750. Thus 0.75M = 9750. So M = 9750 / 0.75. Compute 9750 / 0.75 = 13000. Therefore the marked price was Rs 13000.

Verification / Alternative check:
Confirm by applying the discount forward. Take marked price 13000. A 25 percent discount means reduction of 25/100 * 13000 = 3250. Selling price becomes 13000 minus 3250 = 9750. This matches the given selling price exactly, confirming that the marked price is 13000.

Why Other Options Are Wrong:
If marked price were 12187, then 75 percent of this value would not equal 9750. For 14000, 25 percent discount would produce a selling price of 10500. For 13187 or 12500, the resulting selling prices also differ from 9750 when 25 percent discount is applied. Only 13000 satisfies the relationship S = 0.75M with S equal to 9750.

Common Pitfalls:
Students sometimes compute 25 percent of 9750 and add that amount, but discount percentage is always applied to marked price, not to selling price. Another confusion arises when learners subtract 25 rupees instead of 25 percent. It is important to convert the percentage into a decimal multiplier and identify the correct base value each time.

Final Answer:
The marked price of the item before the 25 percent discount was Rs 13000.