A person sold two cows, each for Rs. 9900. On one cow he gained 10% and on the other he lost 20%. What is his overall result on the entire transaction?

Introduction / Context:
This question asks you to find the net effect when one item is sold at a profit and another similar item is sold at a loss, even though both have the same selling price. Many students mistakenly think that a 10% gain and 20% loss might somehow balance out in a simple way, but that is incorrect because they occur on different cost prices. The key is to compute the separate cost prices from the given selling prices and then compare the total selling price with the total cost price.

Given Data / Assumptions:
- Each cow is sold for Rs. 9900. - On the first cow, there is a gain of 10%. - On the second cow, there is a loss of 20%. - We must find the overall profit or loss in rupees for both cows combined.

Concept / Approach:
Let the cost price of the first cow be CP1 and that of the second cow be CP2. For the first cow, a 10% gain implies Selling Price SP1 = 1.10 * CP1. For the second cow, a 20% loss implies Selling Price SP2 = 0.80 * CP2. We are told that SP1 = SP2 = Rs. 9900. Using these relationships, we calculate CP1 and CP2. The total cost price is CP1 + CP2 and the total selling price is 9900 + 9900. The difference between total selling price and total cost price tells us the overall profit or loss.

Step-by-Step Solution:
Step 1: Let CP1 be the cost price of the first cow. Step 2: SP1 = 1.10 * CP1 = 9900, so CP1 = 9900 / 1.10 = Rs. 9000. Step 3: Let CP2 be the cost price of the second cow. Step 4: SP2 = 0.80 * CP2 = 9900, so CP2 = 9900 / 0.80 = Rs. 12375. Step 5: Total cost price = CP1 + CP2 = 9000 + 12375 = Rs. 21375. Step 6: Total selling price = SP1 + SP2 = 9900 + 9900 = Rs. 19800. Step 7: Net result = Total selling price - Total cost price = 19800 - 21375 = -1575. Step 8: The negative sign shows a loss of Rs. 1575.

Verification / Alternative check:
Another way to see the imbalance is to note that the cow sold at a loss must have had a higher cost price than the one sold at a gain, since both selling prices are the same. Because the loss is 20% on a higher cost price, it dominates the 10% gain on the lower cost price, leading to a net loss. The precise calculations confirm this intuition by providing the exact loss amount of Rs. 1575.

Why Other Options Are Wrong:
It is impossible for there to be a net gain of Rs. 1575 or Rs. 200 when the numbers clearly show total selling price is less than total cost price. The option stating neither gain nor loss would be correct only if total selling price equaled total cost price, which is not the case. The earlier misleading options like a gain or loss of Rs. 200 often appear when students mistakenly average the percentages instead of working with actual values. Only the calculated loss of Rs. 1575 is accurate.

Common Pitfalls:
A very common mistake is to average the percentages and assume that (10% gain - 20% loss) gives a 10% loss overall without considering the different bases (different cost prices). Another pitfall is to treat both cows as having the same cost price, which contradicts the fact that both selling prices are equal but the percentages of gain and loss differ. Always derive the actual cost prices from the given percentages and selling prices before summing up.

Final Answer:
The person incurs a net loss of Rs. 1575 on selling the two cows.