The difference between the selling prices of an article when it is sold at 4% profit and at 3% profit is Rs 3. What is the cost price of the article?

Introduction / Context:
This aptitude question tests the basic concept of profit percentage and how small changes in profit affect the selling price of an article. By comparing selling prices at two slightly different profit percentages, we can work backward to find the unknown cost price. Questions like this are common in competitive exams and are designed to check how comfortably you handle percentage based profit and loss relations.

Given Data / Assumptions:

• The article is sold once at 4% profit.
• The same article is sold once at 3% profit.
• The difference between the two selling prices is Rs 3.
• The cost price of the article is the same in both situations.

Concept / Approach:
The standard relation is: Selling Price (SP) = Cost Price (CP) * (1 + profit_percent / 100). Since only the profit percentage changes, the difference between the two selling prices comes directly from the difference between 4% and 3% profit on the same cost price. That difference is 1% of the cost price. Once we equate that 1% of cost price to Rs 3, we can easily compute the cost price.

Step-by-Step Solution:
Let the cost price of the article be CP.SP at 4% profit = CP * (1 + 4 / 100) = 1.04 * CP.SP at 3% profit = CP * (1 + 3 / 100) = 1.03 * CP.Difference between selling prices = 1.04 * CP - 1.03 * CP = 0.01 * CP.Given that this difference is Rs 3, so 0.01 * CP = 3.Therefore CP = 3 / 0.01 = 300.So, the cost price of the article is Rs 300.

Verification / Alternative check:
If CP = Rs 300, then SP at 4% profit is 300 * 1.04 = Rs 312, and SP at 3% profit is 300 * 1.03 = Rs 309. The difference is 312 - 309 = Rs 3, which matches the data given in the question. Hence the calculated cost price is consistent and correct.

Why Other Options Are Wrong:
Rs 400 would give a 1% difference of Rs 4, not Rs 3, so it does not satisfy the condition. Rs 350 would give a difference of 1% of 350, which is Rs 3.50, again not equal to Rs 3. Rs 100 would give a difference of Rs 1, which is too small. Only Rs 300 gives exactly Rs 3 as 1% of cost price.

Common Pitfalls:
A common mistake is to treat the difference of 1% as 1 rupee directly or to apply percentages incorrectly to the selling price instead of the cost price. Another error is to misinterpret the profit percentages as absolute rupee differences rather than percentage changes. Always remember that profit percentage is always calculated on the cost price unless clearly specified otherwise.

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