The percentage profit earned by selling an article for Rs. 1920 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to earn a profit of 25% on its cost price?

Introduction / Context:
This profit and loss question uses a symmetric condition where the percentage profit at one selling price equals the percentage loss at another selling price. From this condition we can determine the cost price and then compute a new selling price that yields a specified profit percentage. It tests both algebraic manipulation and understanding of the relationship between cost, selling price, profit and loss.

Given Data / Assumptions:

• Selling price 1 (with profit) = Rs. 1920.
• Selling price 2 (with loss) = Rs. 1280.
• The percentage profit at Rs. 1920 equals the percentage loss at Rs. 1280.
• The cost price of the article is the same in both cases.
• We must find the selling price that gives a 25% profit.

Concept / Approach:
Let the cost price be C. Profit percentage at Rs. 1920 is (1920 - C) / C * 100, and loss percentage at Rs. 1280 is (C - 1280) / C * 100. These percentages are equal, so the numerators must be equal: 1920 - C = C - 1280. Solving this equation gives C. Once C is known, a 25% profit means new selling price = C * 1.25. This approach neatly uses symmetry around cost price.

Step-by-Step Solution:
Step 1: Let C be the cost price of the article.Step 2: Profit at Rs. 1920: profit amount = 1920 - C.Step 3: Loss at Rs. 1280: loss amount = C - 1280.Step 4: Given that profit percentage equals loss percentage, we set 1920 - C = C - 1280.Step 5: Solve: 1920 + 1280 = 2C which gives 3200 = 2C, so C = 1600.Step 6: For a 25% profit, required selling price = C * 1.25 = 1600 * 1.25 = Rs. 2000.

Verification / Alternative check:
Check profit at Rs. 1920: profit = 1920 - 1600 = 320, so profit percentage = 320 / 1600 * 100 = 20%.Check loss at Rs. 1280: loss = 1600 - 1280 = 320, so loss percentage = 320 / 1600 * 100 = 20%.Thus the given condition is satisfied. A 25% profit on cost price 1600 is 400, so selling price 1600 + 400 = Rs. 2000, matching the calculation.

Why Other Options Are Wrong:
Rs. 2200 and Rs. 2400 correspond to profit percentages larger than 25% on a cost of Rs. 1600. The option “Data inadequate” is incorrect because the symmetric condition uniquely determines the cost price. Rs. 2600 would represent a much higher profit percentage and is not asked for in the question.

Common Pitfalls:
Learners sometimes mistakenly equate profit percentage to loss amount or mix up the formula for percentage. Others forget that equality of percentages implies equality of profit and loss amounts only because the denominator (cost price) is the same in both cases. Writing the expressions explicitly and simplifying step by step avoids such confusion.

Final Answer:
To earn a 25% profit, the article should be sold for Rs. 2000.