A dealer sells two cattle for Rs. 500 each, making a loss of 10% on one animal and a gain of 10% on the other; what is his overall percentage gain or loss on the entire transaction?

Introduction / Context:
This profit and loss question illustrates an important concept: equal percentage gain and percentage loss on equal selling prices do not cancel out. Even though one item is sold at a 10% profit and the other at a 10% loss, the dealer does not break even. The overall result is a small net loss. Understanding why this happens is crucial for aptitude exams and real life business decisions.

Given Data / Assumptions:

• The dealer sells two cattle.
• Selling price of each animal = Rs. 500.
• On one animal, there is a 10% loss.
• On the other animal, there is a 10% profit.
• We need to find the net percentage gain or loss on the combined transaction.

Concept / Approach:
Profit and loss percentages are calculated on cost price, not on selling price. If selling prices are equal but cost prices are different, equal percentages of profit and loss do not cancel each other. The usual approach is to compute the separate cost prices of both cattle using the known selling price and percentages, then sum these cost prices to find the total cost. Compare total cost with total selling price to find total profit or loss, and then compute the net percentage effect.

Step-by-Step Solution:
Step 1: Let the first animal be sold at a loss of 10%.Step 2: Selling price of the first animal = Rs. 500.Step 3: If loss is 10%, then selling price = 90% of cost price.Step 4: So cost price of first animal = 500 / 0.90 = Rs. 555.56 approximately.Step 5: For the second animal, there is a profit of 10%.Step 6: Selling price of the second animal = Rs. 500.Step 7: If profit is 10%, then selling price = 110% of cost price.Step 8: So cost price of second animal = 500 / 1.10 = Rs. 454.55 approximately.Step 9: Total cost price = 555.56 + 454.55 ≈ Rs. 1010.11.Step 10: Total selling price = 500 + 500 = Rs. 1000.Step 11: Net loss = Total cost price minus Total selling price ≈ 1010.11 - 1000 = Rs. 10.11 (approximately).Step 12: Loss percentage = (Net loss / Total cost price) * 100 ≈ (10.11 / 1010.11) * 100 ≈ 1% loss.

Verification / Alternative check:
A known result in aptitude is that if a trader gains x% on one sale and loses x% on another sale of equal cost price, the net effect is a loss of x^2 / 100 percent. However in this question the selling prices are equal, not the cost prices. Still, computing numerically as done above clearly shows a small loss. If we take exact fractions (500 / 0.9 and 500 / 1.1) and simplify using algebra, the percentage loss tends to approximately 1%. This reconfirms that the trader loses around 1% overall.

Why Other Options Are Wrong:

• 10% loss: This would require the total selling price to be 10% less than the total cost price, which is not the case here. The loss is much smaller.
• 1% gain: This would mean total selling price is greater than total cost, which contradicts the calculations.
• Neither loss nor profit: Many students mistakenly choose this because gains and losses look symmetric, but profit and loss percentages work on different bases, so they do not cancel out.

Common Pitfalls:

• Assuming that a 10% gain and a 10% loss will always cancel out and give no profit or loss.
• Calculating percentage changes incorrectly by using selling price instead of cost price as the base.
• Not adding cost prices correctly before comparing with total selling price, which can give a wrong impression about net profit or loss.

Final Answer:
The dealer suffers a net loss of about 1% loss on the entire transaction.