If the cost price of an article is 25% of its selling price, what is the profit percentage made on the article?

Introduction / Context:
This problem checks understanding of the relationship between cost price, selling price and profit percentage when the cost price is given as a percentage of the selling price. Instead of the usual situation where selling price is expressed as a percentage above cost, here the direction is reversed, which can confuse learners who do not carefully interpret the statement.

Given Data / Assumptions:

• Cost price (CP) is 25% of selling price (SP).
• All transactions involve a single article.
• We must find profit percentage based on cost price.

Concept / Approach:
If CP is 25% of SP, then CP = 0.25 * SP, or equivalently SP = 4 * CP. Profit is defined as SP - CP, and profit percentage is (Profit / CP) * 100. Once we express SP in terms of CP, we can find the ratio SP / CP and therefore the profit percentage. Working in terms of a symbolic cost price CP keeps the steps simple.

Step-by-Step Solution:
Step 1: Let cost price be CP and selling price be SP.Step 2: Given that CP is 25% of SP, so CP = 0.25 * SP.Step 3: Rearranging, SP = CP / 0.25 = 4 * CP.Step 4: Profit = SP - CP = 4CP - CP = 3CP.Step 5: Profit percentage = (Profit / CP) * 100 = (3CP / CP) * 100 = 300%.

Verification / Alternative check:
Assume CP = Rs. 100 for convenience.Then CP = 25% of SP implies 100 = 0.25 * SP, giving SP = 400 rupees.Profit = 400 - 100 = 300 rupees, and profit percentage = 300 / 100 * 100 = 300%, confirming the formula-based solution.

Why Other Options Are Wrong:
Profit percentages such as 150%, 200% or 250% would correspond to SP values of 2.5CP, 3CP or 3.5CP respectively, none of which matches the exact relationship CP = 0.25 * SP. A profit of 350% would be even larger and not consistent with SP = 4CP. Only 300% is aligned with SP being four times CP.

Common Pitfalls:
Many learners mistakenly interpret “cost price is 25% of selling price” as “selling price is 25% above cost price,” which would be a much smaller increase. Others incorrectly use (SP / CP) * 100 as profit percentage and forget to subtract one before converting to a percentage. Being careful about which quantity is a percentage of which prevents these misreadings.

Final Answer:
The profit percentage made on the article is 300%.