The marked price of a shirt is Rs. 1280. It is being sold for Rs. 900 after a single discount. What is the discount percentage on the shirt?

Introduction / Context:
This problem is a standard marked price and discount percentage question. We are given the marked price, the final selling price and asked to compute the discount percentage. Such questions are frequently used in aptitude tests to verify understanding of percentage decrease and comparison of two monetary values.

Given Data / Assumptions:

• Marked price (MP) of the shirt = Rs. 1280.
• Selling price (SP) after discount = Rs. 900.
• There is a single discount applied on the marked price.
• We must find the discount percentage.

Concept / Approach:
The discount amount is the difference between the marked price and the selling price. The discount percentage is then calculated as (discount amount / marked price) * 100. It is important to divide by the marked price, not the selling price, because discount is defined relative to the original quoted price of the product.

Step-by-Step Solution:
Step 1: Compute the discount amount. Discount = MP - SP = 1280 - 900. Discount = 380. Step 2: Express the discount as a fraction of the marked price. Discount fraction = 380 / 1280. Step 3: Simplify 380 / 1280. 380 / 1280 = 0.296875. Step 4: Convert this fraction into a percentage. Discount percentage = 0.296875 * 100 = 29.6875%. Step 5: Rounded to two decimal places, this is approximately 29.68%.

Verification / Alternative check:
We can reverse-check by applying 29.68% discount to the marked price. A 29.68% discount on 1280 is approximately 0.2968 * 1280 ≈ 380.9. Subtracting this from 1280 gives a selling price near 899.1, which, considering rounding, is consistent with the given selling price of Rs. 900. This confirms that 29.68 is the correct discount percentage among the options.

Why Other Options Are Wrong:
A discount of 31.31% would give a lower selling price than 900. Similarly, 25.57% and 34.36% discounts would produce selling prices that do not match Rs. 900 when applied to 1280. Only around 29.7% discount bridges the gap from 1280 down to 900 accurately.

Common Pitfalls:
A common error is to divide the discount amount by the selling price instead of by the marked price, leading to an incorrect discount percentage. Another error is rounding too early and then using the rounded number to check against the options, which might cause confusion when values are close. Always base the percentage on the marked price and keep enough decimal accuracy until the final step.

Final Answer:
The discount percentage on the shirt is approximately 29.68.