Profit and Loss – Loss at one price vs profit at another, with “double” relation: An article sold for Rs 75 results in a loss. If it were sold for Rs 96, the gain would be double the former loss. What is the cost price?

Introduction / Context:
We are given a linear relationship between two absolute profit/loss amounts at two selling prices. Set the loss at Rs 75 equal to half the gain at Rs 96 (since gain is double the loss) and solve for cost price.

Given Data / Assumptions:

• Selling price 1 = Rs 75 ⇒ Loss = CP − 75
• Selling price 2 = Rs 96 ⇒ Gain = 96 − CP
• Gain = 2 * Loss

Concept / Approach:
Set 96 − CP = 2(CP − 75) and solve. This produces a single linear equation in CP with a unique solution.

Step-by-Step Solution:
96 − CP = 2CP − 15096 + 150 = 3CP246 = 3CP ⇒ CP = 82

Verification / Alternative check:
Loss at 75 = 82 − 75 = 7; gain at 96 = 96 − 82 = 14, which is indeed double.

Why Other Options Are Wrong:
81, 83, 85.5, and 80 do not satisfy the doubled-gain condition.

Common Pitfalls:
Equating percentage loss to percentage gain; the relationship is between absolute rupee amounts.

Final Answer:
Rs 82