If a shopkeeper sells an item for 4,400 rupees when its marked price is 5,000 rupees, then what percentage discount is he offering?

Introduction / Context:
This standard profit and loss question asks you to calculate the discount percentage when both marked price and selling price are known. Such problems help you practice the basic relationship between marked price, discount amount, and discount rate, which is essential for commercial arithmetic.

Given Data / Assumptions:
- Marked price (MP) = 5,000 rupees.
- Selling price (SP) = 4,400 rupees.
- Discount amount = MP - SP.
- Discount percentage = (Discount amount / MP) * 100 percent.

Concept / Approach:
The discount amount is the reduction from the marked price. Once we compute the rupee discount, we express that amount as a fraction of the marked price and then convert it into a percentage by multiplying by 100. It is important to remember that the base for discount percentage is always the marked price, not the selling price or cost price.

Step-by-Step Solution:
Step 1: Compute the discount amount: Discount = MP - SP = 5,000 - 4,400.Step 2: Discount amount = 600 rupees.Step 3: Use the formula: Discount percentage = (Discount / MP) * 100.Step 4: Substitute values: Discount percentage = (600 / 5,000) * 100.Step 5: Simplify 600 / 5,000 = 0.12.Step 6: So discount percentage = 0.12 * 100 = 12 percent.

Verification / Alternative check:
Another way is to see that 10 percent of 5,000 is 500 rupees. The discount here is 600 rupees, which is 100 rupees more than 10 percent, and 100 rupees is 2 percent of 5,000. Therefore the total discount of 600 rupees is 12 percent of the marked price (10 percent plus 2 percent), confirming the result.

Why Other Options Are Wrong:
- 20 percent and 15 percent represent larger discounts than 600 rupees on a 5,000 rupee item; 20 percent would be 1,000 rupees off and 15 percent would be 750 rupees off.
- 10 percent corresponds to a 500 rupee discount, which is smaller than the actual discount of 600 rupees.

Common Pitfalls:
One common mistake is to use the selling price as the base when computing the discount percentage, which would give (600 / 4,400) * 100 and an incorrect value. Always use the marked price as the denominator when dealing with discount percentages. Another error is subtracting percentages instead of actual rupee amounts, which does not apply here because only one discount is given.

Final Answer:
The discount offered by the shopkeeper is 12 percent.