A shopkeeper allows a 20% discount on the marked price. What is the marked price of an article whose selling price after discount is Rs. 740?

Introduction / Context:
This percentage problem involves finding the marked price of an article when the discount percentage and the selling price after discount are given. Situations like this are common in shopping and in competitive examinations. Understanding the relationship between marked price, discount percentage, and selling price helps to reverse engineer the original price before discount from the final selling price.

Given Data / Assumptions:
The shopkeeper gives a discount of 20 percent on the marked price (MP).
The selling price (SP) after discount is Rs. 740.
Discount is calculated on the marked price, not on cost price.
We are asked to find the marked price of the article.

Concept / Approach:
A discount of 20 percent means that the customer pays 80 percent of the marked price. In percentage form this is 100% - 20% = 80%. In decimal form, 80 percent is 0.80. Therefore, the selling price can be expressed as SP = 0.80 * MP. Since we know SP, we rearrange this relationship to find MP by dividing the selling price by 0.80. This approach avoids confusion and directly links discount percentage, marked price, and selling price in a simple algebraic equation.

Step-by-Step Solution:
Let the marked price be MP. Discount = 20 percent of MP, so the customer pays 80 percent of MP. Thus, SP = 80 percent of MP = 0.80 * MP. We are given SP = Rs. 740. So, 0.80 * MP = 740. Therefore, MP = 740 / 0.80. Compute MP: 740 / 0.80 = 925. Therefore, the marked price of the article is Rs. 925.

Verification / Alternative check:
We can verify by applying the discount to Rs. 925. Discount amount at 20 percent is 0.20 * 925 = 185. Subtract this from the marked price: 925 - 185 = 740. This matches the given selling price exactly, confirming that our calculated marked price is correct. This forward check is a simple way to ensure that no arithmetic mistake was made while rearranging and solving the equation.

Why Other Options Are Wrong:
If the marked price were Rs. 725, 80 percent of 725 gives 580, not 740, so that option is incorrect. If the marked price were Rs. 875, 20 percent discount leads to a selling price of 700, which again does not match 740. If the marked price were Rs. 1040, then at 20 percent discount the selling price would be 832, not 740. Only the marked price of Rs. 925 correctly produces the given selling price after applying the 20 percent discount.

Common Pitfalls:
Many learners mistakenly subtract 20 percent directly from the selling price instead of from the marked price, which is conceptually wrong. Others divide 740 by 0.20 rather than by 0.80, confusing the discount rate with the payable rate. Another typical mistake is to use 80 instead of 0.80 in the equation, which leads to drastically wrong results. Always remember that selling price after a discount of D percent is (100 - D) percent of the marked price and convert that percentage properly into a decimal factor before calculation.

Final Answer:
The marked price of the article before discount was Rs. 925.