Profit and Loss – Equal selling price with +10% and −10% outcomes: A man sells two watches, each for ₹ 495. On one he gains 10% and on the other he loses 10%. What is the overall result (profit or loss percentage) on the entire transaction?

Introduction / Context:
When two items are sold at the same selling price with equal but opposite percentage changes, the net outcome is a loss. This is a well-known effect due to the multiplicative nature of percentage changes.

Given Data / Assumptions:

• Selling prices: ₹ 495 and ₹ 495
• Gains/Losses: +10% and −10%

Concept / Approach:
For equal SP, the overall loss% with +a% and −a% is (a^2 / 100)%. Here a = 10, so loss% = 10^2 / 100 = 1%. Alternatively, compute each cost price and compare total SP vs total CP.

Step-by-Step Solution:
CP of gain watch = 495 / 1.10 = 450CP of loss watch = 495 / 0.90 = 550Total CP = 1000, Total SP = 990 ⇒ Loss = 10Loss% = 10 / 1000 * 100 = 1%

Verification / Alternative check:
Use identity: net loss% = a^2/100 = 1% for a = 10.

Why Other Options Are Wrong:
“Neither gain nor loss” ignores the nonlinearity. 1% gain and 100/99% loss are incorrect magnitudes; 0.1% is too small.

Common Pitfalls:
Averaging +10% and −10% to get 0%.

Final Answer:
1% loss