If the selling price of 40 articles is equal to the cost price of 50 articles of the same kind, what is the percentage gain or loss in the transaction?

Introduction / Context:
This is a classic profit and loss question based purely on ratios of quantities. The relationship between the selling price of a certain number of articles and the cost price of a different number of the same articles directly gives the profit or loss percentage, without needing any actual rupee values.

Given Data / Assumptions:

• Selling price of 40 articles (SP40) equals cost price of 50 articles (CP50).
• All articles are identical and have the same cost price per unit.
• We must decide whether there is a gain or loss and then calculate the percentage.

Concept / Approach:
Let the cost price per article be C and the selling price per article be S. Then total cost for 50 articles is 50C, and total selling price for 40 articles is 40S. Given 40S = 50C, we get a direct relationship between S and C. The profit or loss per article is S - C. Expressing this as a percentage of C gives the required profit or gain percentage.

Step-by-Step Solution:
Let CP per article = C and SP per article = S. Given 40S = 50C. Divide both sides by 10 to simplify: 4S = 5C. So S = (5/4) * C = 1.25C. Profit per article = S - C = 1.25C - C = 0.25C. Profit percentage = (0.25C / C) * 100 = 25% gain.

Verification / Alternative check:
Take a simple numeric example. Assume C = Rs 4; then from S = (5/4) * C, we get S = Rs 5. Selling 40 articles at Rs 5 each gives SP40 = 200 rupees. Cost of 50 articles is 50 * 4 = 200 rupees. This satisfies the condition that SP40 equals CP50 and clearly indicates that S is greater than C, implying profit. The percentage profit is (5 - 4)/4 * 100 = 25%.

Why Other Options Are Wrong:
If profit were 20%, then S would be 1.20C which does not satisfy the 40S = 50C relationship. Loss options are incorrect because the selling price is higher than the cost price per unit; hence there is gain, not loss.

Common Pitfalls:
One common error is to reverse the ratio and assume 40C = 50S. Another mistake is to compare 40 and 50 directly and think the percentage is 20% simply from the difference in quantities. Always express SP and CP in terms of the same per unit base variable before computing percentages.

Final Answer:
The trader makes a 25% gain in this transaction.