A store sells a watch at a profit equal to 25% of its cost price. What is the percentage of profit when measured as a percentage of the selling price?

Introduction / Context:
This is a conceptual profit and loss question that checks your understanding of the difference between expressing profit as a percentage of cost price and expressing profit as a percentage of selling price. The numerical value of profit remains the same, but the base for the percentage calculation changes.

Given Data / Assumptions:

• Profit is 25% of cost price (CP).
• We must find profit percentage with respect to selling price (SP).
• The watch is a single item, so we can use one CP and one SP.

Concept / Approach:
If profit is 25% of CP, then profit = 0.25 * CP. Selling price is CP plus profit, SP = CP + 0.25CP = 1.25CP. Profit as a percentage of SP is then (profit / SP) * 100. Since SP is greater than CP, the profit percentage relative to SP will be smaller than 25%.

Step-by-Step Solution:
Let CP = 100 units. Profit = 25% of CP = 25 units. Selling price SP = CP + profit = 100 + 25 = 125 units. Profit as a percentage of SP = (25 / 125) * 100. Simplify: 25 / 125 = 1 / 5. Thus profit percentage relative to SP = (1 / 5) * 100 = 20%.

Verification / Alternative check:
Using algebra, if profit = 0.25CP, then SP = 1.25CP. Profit% on SP = (0.25CP / 1.25CP) * 100 = (0.25 / 1.25) * 100 = (1 / 5) * 100 = 20%. This confirms the use of any assumed CP, such as 100, gives the same result.

Why Other Options Are Wrong:
22%, 18%, and 15% are simply distractors. They do not arise from correct manipulation of profit and selling price. Only 20% satisfies the relationship between a 25% profit on cost price and the equivalent profit percentage on selling price.

Common Pitfalls:
Some learners forget to change the base when switching from profit on cost price to profit on selling price, and they incorrectly answer 25%. Others may incorrectly subtract a fixed number instead of recalculating the ratio. Always remember that percentage is relative to the base value used.

Final Answer:
The profit is 20% when expressed as a percentage of the selling price.