A dealer allows a discount of 15%. A customer pays Rs. 318.75 for an article. At what price is the article listed (what is the marked price)?

Introduction / Context:
This is a straightforward reverse percentage problem involving discount and marked price. We know the discount percentage and the final selling price after discount, and we must find the original marked price before the discount was applied. This type of question is common in commerce and aptitude exams and tests the ability to invert a percentage reduction.

Given Data / Assumptions:
Discount rate = 15 percent on the marked price.
Selling price (SP) after discount = Rs. 318.75.
Marked price (MP) is unknown and must be determined.
Discount is calculated on the marked price, not on some other value.

Concept / Approach:
If the discount is 15 percent, then the customer pays (100 percent - 15 percent) = 85 percent of the marked price. In decimal form, this is 0.85 of MP. Therefore, SP = 0.85 * MP. To find the marked price, we invert this relation and compute MP = SP / 0.85. This direct method avoids confusion and quickly yields the original marked price from the selling price and discount percentage.

Step-by-Step Solution:
Let marked price be MP. Discount = 15 percent, so amount payable is 85 percent of MP. Therefore selling price SP = 0.85 * MP. We are given SP = Rs. 318.75. So 0.85 * MP = 318.75. Hence MP = 318.75 / 0.85. Compute 318.75 / 0.85 = 375. Therefore, the article was listed at Rs. 375.00.

Verification / Alternative check:
Check by computing 15 percent of 375. Discount amount = 0.15 * 375 = 56.25. Subtract from marked price: 375 - 56.25 = 318.75, which matches the given selling price. This confirms that the marked price of Rs. 375 is correct and consistent with a 15 percent discount leading to the final amount paid by the customer.

Why Other Options Are Wrong:
If the marked price were Rs. 366.50, then 15 percent discount would result in a selling price different from 318.75. A marked price of Rs. 350.00 with 15 percent discount would lead to a selling price of 297.50, which is too low. A marked price of Rs. 431.25 with 15 percent discount would produce a selling price much higher than 318.75. Only Rs. 375.00 gives the exact selling price after applying a 15 percent discount.

Common Pitfalls:
Some learners mistakenly compute MP = SP * 0.85 instead of dividing by 0.85, effectively applying the discount twice. Others confuse discount and profit formulas and use the wrong base for percentage calculations. To avoid errors, always write the fundamental relation clearly: SP = MP * (1 - discount percent / 100), and then solve for MP by dividing the selling price by the remaining fraction. This ensures a reliable and systematic solution method.

Final Answer:
The article is listed at a marked price of Rs. 375.00.