Profit and Loss – Equal selling price with opposite percent changes: A dealer sells two TV sets at Rs 3700 each. On one he gains 10% and on the other he loses 10%. What is the overall percentage result (profit or loss) on the combined transaction?

Introduction / Context:
When items are sold at the same selling price and experience equal but opposite percentage changes in profit and loss, the result is always a net loss.

Given Data / Assumptions:

• SP1 = SP2 = Rs 3700
• Gain on first = 10%
• Loss on second = 10%

Concept / Approach:
Compute each cost price. Then total CP vs total SP gives the overall percentage. Alternatively, use the identity: equal SP with +a% and -a% yields net loss = (a^2 / 100)%.

Step-by-Step Solution:
CP1 = 3700 / 1.10 = 3363.636...CP2 = 3700 / 0.90 = 4111.111...Total CP ≈ 7474.747..., Total SP = 7400Loss ≈ 74.747..., Loss% ≈ 74.747 / 7474.747 * 100 ≈ 1%

Verification / Alternative check:
Using formula: a = 10 ⇒ loss% = 10^2 / 100 = 1%.

Why Other Options Are Wrong:
1% gain and no-profit-no-loss contradict the identity. 0.1% and 2% are incorrect magnitudes.

Common Pitfalls:
Averaging +10% and -10% to get 0% instead of using product effects.

Final Answer:
1% loss