The cost price of an item is two-thirds of its selling price. What is the gain (or loss) percentage?

Introduction / Context:When CP and SP are linked by a fixed ratio, profit percentage is found by comparing SP − CP to CP. Here, CP = (2/3)SP implies a straightforward fraction for profit relative to CP.

Given Data / Assumptions:

• CP = (2/3)SP.
• Profit% = (SP − CP)/CP * 100.

Concept / Approach:Let SP = S. Then CP = (2/3)S. Profit = S − (2/3)S = (1/3)S. Profit% on CP = [(1/3)S] / [(2/3)S] * 100 = (1/2) * 100 = 50%.

Step-by-Step Solution:Profit% = ( (1/3)S / (2/3)S ) * 100 = (1/2) * 100 = 50

Verification / Alternative check:Take S = 300; CP = 200; Profit = 100; Profit% = 100/200 * 100 = 50.

Why Other Options Are Wrong:45/35/54 do not match the fixed ratio implied by CP = two-thirds of SP.

Common Pitfalls:Using SP as the base for profit%; accidentally computing loss instead of profit.

Final Answer:50