A shopkeeper marks an item at Rs. 1250 but finally sells it for Rs. 1000.\nBased on these values of marked price and selling price, what percentage discount is he effectively offering on the marked price?

Introduction / Context:
Discount questions are a core part of percentage based aptitude problems. Here, the shopkeeper has a clearly stated marked price and a lower selling price. The difference between these two values represents the absolute discount, and converting this difference into a percentage of the marked price gives the discount percentage, which is exactly what most competitive exams ask you to calculate.

Given Data / Assumptions:

• Marked price (MP) of the item = Rs. 1250.
• Selling price (SP) of the item = Rs. 1000.
• Discount amount = MP - SP.
• Discount percentage is always calculated on the marked price, not on the selling price.
• All prices are in rupees and represent exact values.

Concept / Approach:
The key idea is that percentage discount = (discount amount / marked price) * 100. So we first compute the discount in rupees by subtracting the selling price from the marked price. Then we divide this discount by the marked price to see what fraction of the original price is being reduced. Finally, we multiply that fraction by 100 to express it as a percentage. This simple three step method works for all direct discount questions.

Step-by-Step Solution:
Step 1: Compute the discount amount: Discount = MP - SP = 1250 - 1000 = Rs. 250. Step 2: Write the formula for discount percentage: Discount% = (Discount / MP) * 100. Step 3: Substitute the values: Discount% = (250 / 1250) * 100. Step 4: Simplify the fraction: 250 / 1250 = 1 / 5. Step 5: Compute: (1 / 5) * 100 = 20. Step 6: Therefore, the discount percentage offered is 20 percent.

Verification / Alternative check:
An alternative way is to think proportionally. If the discount is 20 percent, then the customer pays 80 percent of the marked price. Calculate 80 percent of Rs. 1250: (80 / 100) * 1250 = 0.8 * 1250 = Rs. 1000. This matches the given selling price, confirming that the discount rate we found is correct.

Why Other Options Are Wrong:
25 percent: A 25 percent discount on Rs. 1250 would be 0.25 * 1250 = Rs. 312.50, giving a selling price of Rs. 937.50, not Rs. 1000.
33.3 percent: Around one third off would reduce the price far below Rs. 1000, making it too large a discount.
250 percent: A discount cannot exceed 100 percent in normal situations, so 250 percent is meaningless here.
15 percent: A 15 percent discount would be 0.15 * 1250 = Rs. 187.50, giving a selling price of Rs. 1062.50, not Rs. 1000.

Common Pitfalls:
Common mistakes include dividing the discount by the selling price instead of the marked price, or confusing the absolute discount (in rupees) with the percentage discount. Some learners also reverse the numbers and compute 1000 / 1250 * 100 directly, thinking that gives the discount, whereas it actually gives the percentage of the marked price that is paid. Always remember: discount percentage is based on the marked price.

Final Answer:
The shopkeeper is offering a 20 percent discount on the marked price.