A shopkeeper sells an item for Rs. 1600, while its marked price is Rs. 2000.\nWhat percentage discount is the shopkeeper offering on the marked price?

Introduction / Context:
This question focuses on calculating discount percentage based on marked price and selling price. Understanding how to compute discount percentages is essential for both everyday shopping situations and exam style profit and loss problems. The marked price is the listed price, and the discount is the reduction from this marked price to the selling price.

Given Data / Assumptions:

• Marked price (listed price) of the item = Rs. 2000.
• Selling price after discount = Rs. 1600.
• We need to find the discount percentage with respect to the marked price.
• There are no additional taxes or extra charges mentioned.

Concept / Approach:
Discount is defined as the difference between marked price and selling price. Discount percentage is calculated as (discount / marked price) * 100. Since all figures are given directly, we only need to compute the difference and express it as a percentage of the marked price. This is a direct application of a basic percentage formula.

Step-by-Step Solution:
Step 1: Compute the discount amount: discount = marked price - selling price.Step 2: Substitute the values: discount = 2000 - 1600 = 400 rupees.Step 3: Compute the discount percentage using the formula discount percent = (discount / marked price) * 100.Step 4: Substitute the numbers: discount percent = (400 / 2000) * 100.Step 5: Simplify: 400 / 2000 = 0.2, so discount percent = 0.2 * 100 = 20%.

Verification / Alternative check:
We can also reason mentally. A 10% discount on Rs. 2000 is Rs. 200, so a 20% discount would be twice that, which is Rs. 400. Subtracting Rs. 400 from Rs. 2000 gives Rs. 1600. This matches the given selling price, so a 20% discount is consistent with the information in the question.

Why Other Options Are Wrong:
25% discount on Rs. 2000 would be Rs. 500, leading to a selling price of Rs. 1500, not Rs. 1600.
30% discount would be Rs. 600, giving a selling price of Rs. 1400.
10% discount would be only Rs. 200, giving a selling price of Rs. 1800.
15% discount would give Rs. 300 off and a selling price of Rs. 1700. None of these match the given selling price.

Common Pitfalls:
One frequent mistake is to divide the discount amount by the selling price instead of the marked price. Discount percentages are always calculated on the original or marked price unless explicitly stated otherwise. Another error is misreading the numbers or incorrectly subtracting selling price from marked price. Writing down the formula and substituting values step by step helps avoid these mistakes.

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