If the ratio of the cost price to the selling price of an article is 4 : 5, what is the percentage profit on the article?

Introduction / Context:
This question reverses the usual profit calculation. Instead of giving the profit percentage directly, it provides the ratio between cost price and selling price and asks for the profit percentage. Converting such ratios into percentages is very common in aptitude exams.

Given Data / Assumptions:

• Ratio of cost price (CP) to selling price (SP) is 4 : 5.
• We need to find profit percentage on cost price.
• The article is a single item with one CP and one SP.

Concept / Approach:
A ratio CP : SP = 4 : 5 can be interpreted as CP = 4k, SP = 5k for some positive constant k. Profit is SP - CP = 5k - 4k = k. Profit percentage is (profit / CP) * 100 = (k / 4k) * 100 = 25%. The constant k cancels out, so any numbers proportional to 4 and 5 can be used.

Step-by-Step Solution:
Let CP = 4 units, SP = 5 units (simple representation of the ratio 4 : 5). Profit = SP - CP = 5 - 4 = 1 unit. Profit percentage = (profit / CP) * 100. Thus, profit% = (1 / 4) * 100. (1 / 4) * 100 = 25%.

Verification / Alternative check:
Use actual rupee values maintaining the ratio. For example, CP = Rs 400 and SP = Rs 500. Profit = 500 - 400 = Rs 100. Profit percentage = (100 / 400) * 100 = 25%. This again confirms that 25% is the correct profit percentage for the given ratio.

Why Other Options Are Wrong:
A profit of 27.5% or 15% or 10% would imply different CP : SP ratios. For instance, a 10% profit would correspond to CP : SP = 10 : 11, not 4 : 5. Hence those percentages do not match the given ratio 4 : 5.

Common Pitfalls:
Some learners invert the ratio and treat it as SP : CP, which would lead to a wrong calculation. Others attempt to convert the ratio directly into a percentage without using profit = SP - CP. Always express CP and SP in terms of the same variable and then compute profit percentage carefully.

Final Answer:
The profit percentage on the article is 25 percent.