If the ratio of the marked price to the selling price of an article is 11 : 10, what is the discount percentage on the marked price?

Introduction / Context:
This question uses a ratio between marked price and selling price to derive the discount percentage. Instead of being given actual rupee values, we work with proportional values. Understanding how to translate ratios into percentages is a key skill in commercial arithmetic, especially in discount and profit loss problems.

Given Data / Assumptions:

• Ratio of marked price (MP) to selling price (SP) = 11 : 10.
• We assume MP and SP are positive amounts in the same units.
• The discount is the difference between MP and SP, taken as a percentage of MP.
• We must find the discount percentage.

Concept / Approach:
If MP : SP = 11 : 10, we can assume a convenient common factor, for example MP = 11 units and SP = 10 units. The discount is then MP minus SP, which is 1 unit. Discount percentage is defined as (discount / MP) * 100. This gives (1 / 11) * 100. The result is a recurring decimal, and we usually round to two decimal places.

Step-by-Step Solution:
Step 1: From the ratio 11 : 10, assume MP = 11 units and SP = 10 units. Step 2: Discount = MP - SP = 11 - 10 = 1 unit. Step 3: Discount percentage = (discount / MP) * 100. Step 4: Substitute values: Discount% = (1 / 11) * 100. Step 5: Compute 100 / 11 ≈ 9.09. Step 6: Therefore, the discount percentage is approximately 9.09%.

Verification / Alternative check:
Consider an actual example with MP = Rs. 110 and SP = Rs. 100 (multiplying both ratio terms by 10). Discount = 110 - 100 = Rs. 10. Discount percentage = (10 / 110) * 100 = 1000 / 11 ≈ 90.91 / 10 = 9.09%. This confirms that the ratio 11 : 10 corresponds to a discount of about 9.09%.

Why Other Options Are Wrong:
11.11%: This would correspond to a ratio more like 9 : 8. Now MP : SP = 9 : 8 implies a discount of 1 / 9 which is about 11.11%, not 1 / 11.
12.5%: This would correspond to a discount of 1 / 8 and a ratio of 8 : 7, unlike the given 11 : 10.
17.28%: This is not consistent with any simple ratio close to 11 : 10.
5%: This would correspond to MP : SP ≈ 100 : 95, which is not 11 : 10.

Common Pitfalls:
One common error is to reverse the ratio and treat SP : MP as 11 : 10, which leads to a completely different calculation. Another mistake is to compute the discount percentage as (1 / 10) * 100 when using the ratio 11 : 10, incorrectly taking SP as the base instead of MP. Always remember that discount percentage is based on the marked price, not the selling price.

Final Answer:
The discount percentage on the marked price is approximately 9.09%.