The cost price of 20 identical articles is equal to the selling price of x such articles. If the trader makes a profit of 25% on each article, what is the value of x?

Introduction / Context:
This profit and loss question relates total cost and total selling price for different numbers of identical articles. The key idea is that if the cost price of 20 articles equals the selling price of x articles, and there is a 25% profit, then the selling price per article is 25% above cost, which allows us to build a simple equation and solve for x.

Given Data / Assumptions:
- All articles are identical and have the same cost and selling price per unit.
- Cost price of 20 articles = selling price of x articles.
- Profit percentage on each article = 25%.
- We must determine the value of x.

Concept / Approach:
Let the cost price per article be C. Then the selling price per article is C plus 25% of C, which is 1.25C or 5C / 4. Total cost price for 20 articles is 20C, and total selling price for x articles is x * 5C / 4. Since these two totals are equal, we can set up an equation and solve directly for x.

Step-by-Step Solution:
Step 1: Let cost price per article = C rupees.Step 2: Profit is 25%, so selling price per article = C + 0.25C = 1.25C = 5C / 4.Step 3: Total cost price of 20 articles = 20C.Step 4: Total selling price of x articles = x * (5C / 4).Step 5: Given that cost price of 20 articles equals selling price of x articles, set 20C = x * (5C / 4).Step 6: Cancel C on both sides (C ≠ 0): 20 = x * (5 / 4).Step 7: Solve for x: x = 20 * (4 / 5) = 80 / 5 = 16.Step 8: Hence, x = 16.

Verification / Alternative check:
Take a simple value for C to confirm. Suppose C = Rs. 4. Then selling price SP per article = 5C / 4 = 5 rupees. Cost price of 20 articles = 20 * 4 = Rs. 80. We want SP of x articles to also be Rs. 80, so 5x = 80 giving x = 16. This matches our algebraic solution.

Why Other Options Are Wrong:
Values 15, 18, 20, or 25 all fail when substituted into the relation 20C = x * (5C / 4). For example, if x = 20, then SP for 20 articles would be 20 * 5C / 4 = 25C, which is larger than 20C and does not match the given equality. Only x = 16 balances total cost and total selling price under a 25% profit.

Common Pitfalls:
Some learners misinterpret the statement and assume that 20 and x refer to numbers in a ratio rather than equality of money values. Others forget that profit is applied on cost price and not on selling price. Always define an algebraic variable for cost price or selling price and build equations carefully.

Final Answer:
The value of x is 16.