The cost price of 60 identical articles is equal to the selling price of x articles. If the trader earns a profit of 20%, what is the value of x?

Introduction / Context:
This problem tests your understanding of how profit percentage links cost price and selling price when the number of articles changes. Instead of giving the actual prices of the articles, the question provides a relationship between the cost price of a batch and the selling price of a smaller batch. Your task is to use the profit percentage to connect these quantities and solve for the unknown number of articles x. Such questions appear frequently in aptitude and banking exams because they check ratio and proportion skills in the context of profit and loss.

Given Data / Assumptions:
- Cost price of 60 articles is given in symbolic form. - Selling price of x articles is equal to the cost price of 60 articles. - Profit percentage on each article is 20%. - All articles are identical, so cost price per article is the same. - We need to determine the value of x.

Concept / Approach:
Let the cost price of one article be C. Then the cost price of 60 articles becomes 60 * C. Profit of 20% means the selling price of one article S is given by S = C * (1 + 20 / 100) = 1.2 * C. The key line in the question states that the total selling price of x articles is numerically equal to the cost price of 60 articles. Therefore, x * S = 60 * C. We substitute S = 1.2 * C and solve for x. The cost price C cancels out, showing that we do not need its actual value.

Step-by-Step Solution:
Step 1: Let cost price of one article be C. Step 2: Then cost price of 60 articles = 60 * C. Step 3: Profit is 20%, so selling price of one article S = C * 1.20. Step 4: Given that selling price of x articles = cost price of 60 articles. Step 5: Hence, x * S = 60 * C. Step 6: Substitute S = 1.20 * C to get x * 1.20 * C = 60 * C. Step 7: Cancel C from both sides to obtain 1.20 * x = 60. Step 8: Therefore, x = 60 / 1.20 = 50.

Verification / Alternative check:
Assume a simple cost price to verify. Let C = Rs. 10. Then cost price of 60 articles is 600. Selling price of one article with 20% profit is 12. If x = 50, then selling price of 50 articles is 50 * 12 = 600, which matches the cost price of 60 articles. Hence, x = 50 is consistent. Any other value of x will not match the equality between total selling price and total cost price.

Why Other Options Are Wrong:
If x = 15 or x = 30, the total selling price would be much smaller than the cost price of 60 articles. If x = 80, the total selling price would exceed the cost price by a large margin and would not satisfy the relationship in the question. Only x = 50 fits both the percentage condition and the equality between cost price and selling price.

Common Pitfalls:
A common mistake is to assume some arbitrary cost price and selling price and then forget to apply the correct profit percentage. Another error is to treat 20% as a fraction of the selling price instead of the cost price. Some students also try to plug numbers directly into an equation without clearly defining the variables, which can lead to confusion. Always define cost price per article, convert the profit percentage correctly, and then use the given relationship between the totals.

Final Answer:
The number of articles whose selling price equals the cost price of 60 articles at 20% profit is 50.