Equal profit–loss from two selling prices Selling at Rs 425 gives the same profit as the loss when selling at Rs 355. What is the cost price?

Introduction / Context:
When profit from one selling price equals loss from another, the cost price lies exactly midway between those selling prices. We can also show this algebraically.

Given Data / Assumptions:

• Profit at SP1 = Rs 425 equals loss at SP2 = Rs 355.
• Find cost price (CP).

Concept / Approach:
If 425 - CP = CP - 355, then CP is the average of 425 and 355. Solve directly or via averages.

Step-by-Step Solution:
Set 425 - CP = CP - 355.2 × CP = 425 + 355 = 780.CP = 780 / 2 = 390.

Verification / Alternative check:
Profit at 425: 425 - 390 = 35. Loss at 355: 390 - 355 = 35. Equal as given.

Why Other Options Are Wrong:
385 or 395 breaks the equality; 400 and 405 give unequal profit and loss.

Common Pitfalls:
Adding instead of averaging, or mixing up which side is profit or loss.

Final Answer:
Rs 390