The ratio of the cost price to the selling price of an article is 25 : 26. What is the profit percentage on the article?

Introduction / Context:
This is a direct question based on the ratio of cost price to selling price. When the ratio CP : SP is given, we can immediately find profit or loss by comparing the two quantities. If selling price is higher, there is a profit; if it is lower, there is a loss.

Given Data / Assumptions:
- Ratio of cost price to selling price = 25 : 26. - This implies that when cost is 25 units, selling price is 26 units. - We are required to find profit as a percentage of cost price.

Concept / Approach:
If CP : SP = 25 : 26, we can treat cost price C = 25 and selling price S = 26. Profit = S - C. Profit percentage is always calculated on cost price and is given by:
profit percent = (profit / cost price) * 100 Because the ratio already uses convenient small numbers, the calculation is quick.

Step-by-Step Solution:
Step 1: Let cost price C = 25 units. Step 2: Let selling price S = 26 units. Step 3: Profit = S - C = 26 - 25 = 1 unit. Step 4: Profit percent = (profit / cost price) * 100 = (1 / 25) * 100. Step 5: (1 / 25) * 100 = 4. Step 6: Therefore, profit percentage = 4%.

Verification / Alternative check:
Use real numbers. Suppose cost price is Rs 250. Then selling price would be set according to the same ratio: 25 : 26 = 250 : 260. Profit = 260 - 250 = Rs 10. Profit percent = 10 / 250 * 100 = 4%. This matches our earlier calculation based on unit values and confirms the answer.

Why Other Options Are Wrong:
Option 26% is much higher than what the 25 : 26 ratio implies. Option 25% would require selling price to be 125% of cost, meaning SP : CP = 5 : 4, which is not given. Option 1% is too small and conflicts with the actual numerical relationship between 25 and 26.

Common Pitfalls:
One mistake is to compute profit percentage using selling price in the denominator instead of cost price. Another error is misreading the ratio as SP : CP instead of CP : SP. Always pay attention to the order in which the ratio is given, and remember that profit or loss percentages are based on cost price.

Final Answer:
The profit percentage on the article is 4%.