The selling price of an item is Rs 728 after the shopkeeper offers a 9% discount on its marked price. What was the original marked price of the item in rupees?

Introduction / Context:
This question focuses on reversing a percentage discount to recover the marked price of an item. Such problems are very common in profit and loss or percentage chapters and test the ability to correctly handle percentage reduction in reverse.

Given Data / Assumptions:

• Selling price after discount = Rs 728.
• Discount on marked price = 9 percent.
• Marked price of the item = unknown (let it be M).
• No taxes or additional discounts are involved beyond the given 9 percent discount.

Concept / Approach:
If a discount of d percent is given on the marked price, then: Selling price = Marked price * (1 - d/100). Here, d = 9, so factor = 1 - 9/100 = 0.91. We know the selling price and need to find the marked price M using: M = Selling price / 0.91.

Step-by-Step Solution:
Step 1: Let the marked price be M. Step 2: A 9 percent discount means selling price = M * 0.91. Step 3: Given selling price = Rs 728, so M * 0.91 = 728. Step 4: Solve for M: M = 728 / 0.91. Step 5: Compute the division to get M = 800.

Verification / Alternative check:
Take M = Rs 800 and apply the discount again to verify. Discount at 9 percent = 800 * 9/100 = Rs 72. Selling price = 800 - 72 = Rs 728. This matches the given selling price exactly, confirming that the marked price is correct.

Why Other Options Are Wrong:
Rs 667 and Rs 662.48: These values are too low. After a 9 percent discount, they would give a selling price much less than Rs 728. Rs 793.52: This is close but not exact; applying 9 percent discount to it does not give exactly Rs 728. Rs 760: This also leads to a selling price below Rs 728 after a 9 percent reduction.

Common Pitfalls:
A frequent mistake is to subtract 9 percent of the selling price from 728 instead of reversing the operation on the marked price. Another error is to treat the discount as 728 * (1 + 9/100) which is completely incorrect. Remember that when the discounted price is known, you must divide by (1 - discount percent) rather than subtracting or adding percentages blindly.

Final Answer:
The original marked price of the item is Rs 800.