Anmol sells two items for Rs. 1,000 each. On the first item he gains 10%, and on the second item he loses 10%. What is his overall gain or loss percentage on the entire transaction?

Introduction / Context:
This question illustrates a classic conceptual trap in profit and loss. Many people incorrectly assume that a gain of 10% on one item and a loss of 10% on another item of the same selling price will cancel each other out, resulting in no profit or loss. However, because the percentages apply to different cost prices, the net result is actually a loss. This problem is important for building conceptual clarity about percentage gain and loss.

Given Data / Assumptions:

• Two items are sold, each for a selling price of Rs. 1,000.
• On the first item, Anmol gains 10% over its cost price.
• On the second item, Anmol loses 10% over its cost price.
• We need to determine overall profit or loss percentage over the combined cost price of both items.

Concept / Approach:
Profit or loss percentage must always be calculated as (Net profit or loss) divided by (Total cost price) multiplied by 100. A 10% gain and a 10% loss do not cancel out because the base for calculation (the cost price) is different in each case. Therefore, we calculate the individual cost prices from the given selling prices and gains or losses, then compute total cost, total selling price, and finally find the net result as a percentage.

Step-by-Step Solution:
Let the first item have cost price C1 and selling price S1 = Rs. 1,000 with a 10% gain.So, S1 = 1.10 * C1 ⇒ 1000 = 1.10 * C1 ⇒ C1 = 1000 / 1.10 = Rs. 909.09 (approximately).Let the second item have cost price C2 and selling price S2 = Rs. 1,000 with a 10% loss.So, S2 = 0.90 * C2 ⇒ 1000 = 0.90 * C2 ⇒ C2 = 1000 / 0.90 = Rs. 1,111.11 (approximately).Total cost price = C1 + C2 ≈ 909.09 + 1111.11 = Rs. 2,020.20.Total selling price = S1 + S2 = 1000 + 1000 = Rs. 2,000.Net loss = Total cost price − Total selling price ≈ 2020.20 − 2000 = Rs. 20.20.Loss percentage ≈ (20.20 / 2020.20) * 100 ≈ 1%.

Verification / Alternative check:
Using exact fractions: 1000 / 1.1 = 10000 / 11 and 1000 / 0.9 = 10000 / 9.Total cost price = 10000/11 + 10000/9 = (90000 + 110000)/99 = 200000/99 ≈ 2020.20.Net loss = 200000/99 − 2000 = (200000 − 198000)/99 = 2000/99.Loss percentage = (2000/99) / (200000/99) * 100 = (1/100) * 100 = 1%.

Why Other Options Are Wrong:
A profit of 0.95% arises from incorrect approximate algebra.A profit of 10% or a loss of 10% both misunderstand how gains and losses are applied to different cost prices.The correct net effect is a small loss of 1%, not zero profit.

Common Pitfalls:
The most common misconception is to assume that equal percentage gain and loss cancel each other out.Another error is to average the percentages arithmeticly without considering the different cost bases.Students also sometimes confuse which value is cost price and which is selling price when setting up the equations.

Final Answer:
Anmol makes an overall loss of 1% on the entire transaction.