Relating equal loss and profit to compute CP The loss when selling at Rs 270 equals the profit when selling at 10% profit. What is the cost price of the article?

Introduction / Context:
Equal loss and profit comparisons are classic reverse-percentage problems. Express both situations in terms of CP and equate the magnitudes to solve for CP.

Given Data / Assumptions:

• Loss at SP = Rs 270 equals profit at SP corresponding to 10% gain.
• Find CP.

Concept / Approach:
Loss at 270 is CP - 270. Profit at 10% is 0.10 × CP. Set them equal and solve for CP.

Step-by-Step Solution:
CP - 270 = 0.10 CP.0.90 CP = 270.CP = 270 / 0.90 = 300.

Verification / Alternative check:
Loss at 270 = 300 − 270 = 30; 10% profit on 300 = 30 (equal, as stated).

Why Other Options Are Wrong:
90, 110, 363, 330 do not satisfy the equality condition when checked.

Common Pitfalls:
Equating 270 directly to 10% of CP or misinterpreting the statement as equal selling prices rather than equal magnitudes.

Final Answer:
Rs 300