When a discount of Rs. 42 is allowed on the marked price of an article, the reduced selling price becomes 86% of the original marked price. What is the marked price of the article?

Introduction / Context:
Questions connecting absolute discounts in rupees with percentage reductions are very standard in profit and loss and percentage chapters. Here, we are given that after allowing a rupee discount, the selling price becomes a certain percentage of the original marked price. The goal is to reverse this information and find the original marked price. This type of question helps strengthen algebraic manipulation skills combined with percentage understanding.

Given Data / Assumptions:

• Let the marked price of the article be P rupees.
• A discount of Rs. 42 is given on this marked price.
• After the discount, the new price becomes 86% of the original marked price.
• We need to find the value of P.

Concept / Approach:
The key idea is to express both the discounted price and the percentage based price in terms of the same unknown marked price P. The discounted price is P minus 42. The percentage based price is 86% of P which is (86 / 100) * P. By equating these two expressions, we obtain a linear equation in P. Solving this equation gives the original marked price. This approach is systematic and avoids guesswork.

Step-by-Step Solution:
Step 1: Let the marked price be P rupees. Step 2: After allowing a discount of Rs. 42, the new price is P - 42. Step 3: According to the question, this discounted price is 86% of the original marked price. So P - 42 = (86 / 100) * P. Step 4: Simplify the equation: P - 42 = 0.86P. Step 5: Bring all P terms to one side: P - 0.86P = 42. Step 6: Compute the difference: 0.14P = 42. Step 7: Solve for P by dividing both sides by 0.14. So P = 42 / 0.14 = 300. Step 8: Therefore, the marked price of the article is Rs. 300.

Verification / Alternative check:
We can verify the result by plugging P = 300 back into the situation. A discount of Rs. 42 gives a selling price of 300 - 42 = Rs. 258. Now, 86% of 300 is (86 / 100) * 300 = 0.86 * 300 = 258. Since both values match, the equation is satisfied and the computed marked price is consistent with the condition given in the question.

Why Other Options Are Wrong:
If P were Rs. 250, then 86% of 250 would be 215, which would not differ from 250 by Rs. 42. Similarly, for P = 350, 86% of 350 equals 301, but 350 minus 42 equals 308, so these do not match. For P = 400, 86% equals 344, while 400 minus 42 equals 358, again inconsistent. Only P = 300 satisfies both the amount discount and the percentage condition.

Common Pitfalls:
A typical mistake is reversing the direction of the percentage, for example treating 86% as the discount instead of the remaining price. Another common error is miscomputing 86% of P. Students sometimes also attempt trial and error with options without understanding the underlying equation, which can be time consuming. Writing down the algebraic expression and solving carefully is the most reliable method.

Final Answer:
The marked price of the article is Rs. 300.