The marked price of an article is Rs. 5000. Due to a special festive offer a certain percentage discount is allowed, so that a customer buys the article at the reduced price and then sells it at Rs. 5000, making a profit of 11 1/9%. What was the percentage discount allowed on the marked price?

Introduction / Context:
This problem combines discount and profit concepts. The article has a marked price, is purchased at a discounted price, and then sold at the full marked price, generating a given percentage profit for the customer. We need to work backwards from the selling price and profit percentage to find the cost price for the customer, and then compare that cost price with the marked price to determine the discount percentage.

Given Data / Assumptions:

• Marked price of the article = Rs. 5000.
• Customer buys at a discounted price (unknown) and then sells at Rs. 5000.
• The customer makes a profit of 11 1/9% on cost price.
• We assume normal definition of profit: profit = selling price minus cost price.
• We must determine the percentage discount allowed on the marked price.

Concept / Approach:
Let the cost price (discounted price) for the customer be C. The selling price is 5000. Given profit percentage is 11 1/9%, which is 100 / 9 percent, or 1 / 9 in fractional form when expressed relative to cost price. So selling price = C * (1 + 1 / 9) = C * (10 / 9). Using this, we can find C from the known selling price. After obtaining C, we compare it with the original marked price 5000. The discount is the difference between the marked price and C, expressed as a percentage of the marked price.

Step-by-Step Solution:
Step 1: Write the profit percentage as a fraction. Given profit = 11 1/9% = 100 / 9%. As a fraction of cost price, this is 1 / 9. Step 2: Let the customer's cost price (discounted price) = C. Step 3: Selling price SP = C * (1 + 1 / 9) = C * (10 / 9). Step 4: SP is given as Rs. 5000, so C * (10 / 9) = 5000. Step 5: Solve for C: C = 5000 * (9 / 10) = 4500. Step 6: Thus, the discounted price (cost price for the customer) is Rs. 4500. Step 7: Discount amount = marked price - discounted price = 5000 - 4500 = 500. Step 8: Discount percentage = (discount amount / marked price) * 100 = (500 / 5000) * 100 = 10%.

Verification / Alternative check:
Starting from the discounted price C = 4500, compute the profit if the article is sold at 5000. Profit = 5000 - 4500 = 500. Profit percentage on cost = 500 / 4500 * 100 = (1 / 9) * 100 = 11 1/9%. This matches the given profit condition. Also, a discount of 10% on 5000 gives 500 as the discount, making the discounted price 4500, consistent with the calculated cost price. Thus the solution is confirmed.

Why Other Options Are Wrong:
10/3%, 15/2% and 100/9% are much smaller or larger discount percentages and would yield discounted prices on 5000 that do not allow a resale at 5000 with profit exactly equal to 11 1/9%. They would either produce a different profit percentage or fail to match the given relationship between profit and selling price.

Common Pitfalls:
A common mistake is to confuse the profit percentage with the discount percentage and try to set them equal. Another error is misinterpreting the mixed fraction 11 1/9% and incorrectly converting it to an improper fraction or decimal. It is also easy to accidentally divide by the selling price instead of the cost price when computing profit percentage. Always base the percentage profit on cost price and carefully convert mixed percentages to fractions.

Final Answer:
The percentage discount allowed on the marked price was 10%.