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

Introduction / Context:
This is a simple question where the ratio of cost price to selling price is given directly. From this ratio, we must compute the profit percentage. Such problems are fundamental in the profit and loss section and help reinforce the understanding of how to transform a ratio into an actual profit percentage without needing explicit rupee values.

Given Data / Assumptions:

• Ratio of cost price (CP) to selling price (SP) = 4 : 5.
• This means CP : SP = 4 : 5.
• We assume CP and SP are positive and correspond to the same article.
• We need to calculate profit percentage on the basis of cost price.

Concept / Approach:
When a ratio CP : SP = 4 : 5 is given, it is convenient to assume CP = 4 units and SP = 5 units. Then profit = SP − CP in the same units. The profit percentage is then (Profit / CP) * 100. Because the ratio is scale-invariant, these unit values directly give the correct profit percentage even without rupee amounts.

Step-by-Step Solution:
Assume CP = 4 units.Then SP = 5 units, following the given ratio 4 : 5.Profit = SP − CP = 5 − 4 = 1 unit.Profit percentage = (Profit / CP) * 100 = (1 / 4) * 100.Compute: (1 / 4) * 100 = 25%.Thus, the profit percentage is 25.

Verification / Alternative check:
Take an example with real rupee values: let CP = Rs. 400 (scaling by 100).Then SP must be Rs. 500 to maintain the 4 : 5 ratio.Profit = 500 − 400 = Rs. 100.Profit percentage = (100 / 400) * 100 = 25%.This confirms that the ratio-based calculation is correct.

Why Other Options Are Wrong:
A profit percentage of 20 or 10 would require different CP : SP ratios, such as 5 : 6 or 10 : 11.0.1 is not a reasonable profit percentage in this context and clearly does not match the 4 : 5 ratio.Only 25 is compatible with a CP : SP ratio of 4 : 5.

Common Pitfalls:
Students may invert the ratio and mistakenly treat it as SP : CP = 4 : 5, leading to a completely different percentage.Another mistake is to forget that profit percentage is based on cost price and accidentally use SP in the denominator.Some candidates also misinterpret the options as ratios instead of percentages.

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