Loss to gain with a ₹12 price change — recover the cost price A man sells an article at a 20% loss. If he had sold it for ₹12 more, he would have made a 10% gain. What is the cost price of the article?

Introduction / Context:Two outcomes on the same article are given: a 20% loss at one selling price and a 10% gain at another price that is ₹12 higher. The gap between these selling prices equals 30% of the cost price, which we can use to find the CP directly.

Given Data / Assumptions:

• SP at −20% = 0.80 * CP.
• SP at +10% = 1.10 * CP.
• Difference between SPs = ₹12.

Concept / Approach:(1.10 * CP) − (0.80 * CP) = 0.30 * CP = ₹12 ⇒ CP = ₹12 / 0.30.

Step-by-Step Solution:0.30 * CP = 12 ⇒ CP = 12 / 0.30 = ₹40.

Verification / Alternative check:At CP = ₹40: SP at −20% = ₹32; SP at +10% = ₹44; difference = ₹12, which matches the condition.

Why Other Options Are Wrong:₹60, ₹30, ₹22, and ₹50 do not satisfy the 30% equals ₹12 relationship.

Common Pitfalls:Applying percentages to SP instead of CP, or forgetting that the 30% gap is of CP.

Final Answer:₹ 40