Original gain from a reference sale price — reverse from a loss at 2/3 price An article is sold at some original price P. When sold at (2/3)P, there is a 10% loss. What is the gain percentage at the original price P?

Introduction / Context:This problem gives a reduced selling price that produces a known loss. Use it to connect the unknown cost price (CP) with the original price P, then compute the gain when selling at P instead of (2/3)P.

Given Data / Assumptions:

• Selling at (2/3)P gives a 10% loss ⇒ (2/3)P = 0.90 × CP.
• Find gain% at P: Gain% = (P − CP)/CP × 100.

Concept / Approach:From (2/3)P = 0.90CP, express P in terms of CP and then compute the percentage gain at P relative to CP.

Step-by-Step Solution:(2/3)P = 0.90CP ⇒ P = (0.90 × 3/2)CP = 1.35CP.Gain fraction at P = (1.35CP − CP)/CP = 0.35.Gain% = 0.35 × 100 = 35%.

Verification / Alternative check:Assume CP = 100. Then P = 135; at (2/3)P = 90 there is a 10% loss (since CP 100); at P = 135, gain = 35% (matches).

Why Other Options Are Wrong:33 1/3% and 40% are near but not exact; 20% and 25% are inconsistent with the derived P-to-CP relation.

Common Pitfalls:Adding or subtracting percents on prices without anchoring to CP; always convert to CP to compute true gain or loss.

Final Answer:35%