Profit and Loss – Current gain vs hypothetical cheaper buy and lower SP: A man sells an article at a 15% gain. If he had bought it 10% cheaper and sold it for Rs 4 less than the actual selling price, he would have gained 25%. What is the cost price of the article?

Introduction / Context:
Here we compare the actual transaction with a “what-if” scenario. We relate both to the original cost price, then equate the two selling prices based on the given rupee difference to solve for the unknown cost price.

Given Data / Assumptions:

• Actual SP = 1.15 * CP
• Hypothetical CP = 0.90 * CP
• Hypothetical SP = 1.25 * (0.90 * CP) = 1.125 * CP
• Given: hypothetical SP = actual SP − Rs 4

Concept / Approach:
Set 1.125 * CP = 1.15 * CP − 4 and solve for CP. This is a linear equation in CP with a small difference (2.5% of CP equals Rs 4).

Step-by-Step Solution:
1.15 * CP − 1.125 * CP = 40.025 * CP = 4CP = 4 / 0.025 = 160

Verification / Alternative check:
Actual SP = 1.15 * 160 = 184. Hypothetical SP = 1.125 * 160 = 180, which is Rs 4 less than 184, as required.

Why Other Options Are Wrong:
140, 150, 180, and 200 do not satisfy the 2.5% of CP equals Rs 4 relation.

Common Pitfalls:
Applying 10% cheaper to the selling price instead of the cost price, or mixing percentage bases.

Final Answer:
Rs 160