A shopkeeper sells an item for Rs 4200, even though the marked price printed on the item is Rs 4800.\nBased on this transaction, what percentage discount on the marked price does the shopkeeper offer?

Introduction / Context:
This question is a standard percentage discount problem from basic profit and loss. The marked price is the printed price on the article, while the selling price is the amount actually paid by the buyer. The goal is to determine how much discount in percentage terms was given relative to the marked price. Such problems appear frequently in entrance exams and daily life situations involving sales and offers in shops or online platforms.

Given Data / Assumptions:

• Marked price of the item = Rs 4800.
• Selling price of the item = Rs 4200.
• Discount is calculated on the marked price, not on the cost price.
• We must find the discount percentage to two decimal places if needed.

Concept / Approach:
The discount amount is the difference between the marked price and the selling price. Once the monetary discount is known, the discount percentage is computed as (discount / marked price) * 100. This formula directly converts the reduction relative to the marked price into a percentage measure. The problem does not require knowledge of the cost price or profit, only the relationship between marked price and selling price.

Step-by-Step Solution:
Step 1: Marked price (MP) = Rs 4800. Step 2: Selling price (SP) = Rs 4200. Step 3: Discount amount = MP - SP = 4800 - 4200 = Rs 600. Step 4: Use the formula for discount percentage: discount percent = (discount amount / MP) * 100. Step 5: Substitute the values: discount percent = (600 / 4800) * 100. Step 6: Simplify the fraction 600 / 4800 = 1 / 8. Step 7: Therefore discount percent = (1 / 8) * 100 = 12.5. Step 8: So the shopkeeper is giving a discount of 12.5 percent on the marked price.

Verification / Alternative check:
We can verify by reversing the calculation. If the discount is 12.5% on Rs 4800, then the discount amount should be (12.5 / 100) * 4800. Now 12.5 / 100 is 0.125 and 0.125 * 4800 = 600. Subtracting 600 from 4800 gives a selling price of Rs 4200, which matches the given selling price exactly. This confirms that our computed discount percentage is consistent with the data in the problem.

Why Other Options Are Wrong:
If the discount were 14.28%, the reduction would be approximately 0.1428 * 4800 which is about 686, not 600. A 10% discount would reduce the price by 480, leading to a selling price of 4320, which is not correct. A 15% discount would reduce the price by 720, giving a selling price of 4080. Since only 12.5% reproduces the exact given selling price of Rs 4200, the other options are incorrect.

Common Pitfalls:
Many learners mistakenly compute the discount percentage using selling price in the denominator instead of marked price, which gives the wrong percentage. Another common error is to round intermediate steps too early or mis-handle decimal values. Working carefully with the formula and keeping track of which price is the base for the percentage avoids these mistakes and leads to the correct 12.5% discount rate.

Final Answer:
The discount offered on the marked price of Rs 4800 is 12.5%.