Profit and Loss — If the cost price (CP) is 95% of the selling price (SP), determine the profit percentage. Show the conversion from the CP/SP relation to the net gain on CP.

Introduction / Context: Sometimes the relation is given as CP in terms of SP. Converting this to profit% requires comparing the difference (SP − CP) against CP and expressing it as a percentage.

Given Data / Assumptions:

• CP = 95% of SP ⇒ CP = 0.95 * SP

Concept / Approach: Profit% is computed on CP: Profit% = (SP − CP) / CP * 100. Substitute CP = 0.95 * SP and simplify to get a percent independent of absolute amounts.

Step-by-Step Solution:

Verification / Alternative check: Assume a convenient SP, say S = 100. Then CP = 95, Profit = 5. Profit% = 5/95 * 100 ≈ 5.26%, confirming the algebraic result.

Why Other Options Are Wrong: 4%, 4.75%, 5%, and 6% are near but not equal to the exact ratio 0.05/0.95, which yields ≈ 5.26%.

Common Pitfalls: Computing profit% on SP instead of CP, or interpreting “CP is 95% of SP” as “SP is 95% of CP,” which would invert the relationship.

Final Answer: 5.26%