A person sells two cows for Rs. 9900 each; on one cow he gains 10% and on the other he loses 20%; which of the following statements about his overall result is correct?

Introduction / Context:
This profit and loss problem shows that having a gain on one item and a loss on another item, even at different percentages, does not necessarily cancel out. The trader sells both cows at the same price but with different percentage outcomes. The question asks us to determine his overall financial result and to match it with the most appropriate statement among the options.

Given Data / Assumptions:

• The person sells each of the two cows for Rs. 9900.
• On the first cow he gains 10%.
• On the second cow he loses 20%.
• We need to determine whether he has an overall gain, overall loss or breaks even, and compare with given statements.

Concept / Approach:
Profit or loss percentage is calculated on cost price, so we must find individual cost prices for both cows from their selling prices and given percentages. For the cow sold at profit, cost price is selling price divided by 1 plus profit percentage. For the cow sold at loss, cost price is selling price divided by 1 minus loss percentage. Summing both cost prices gives total cost. Summing both selling prices gives total revenue. Comparing total revenue with total cost tells us the net result in rupees and whether it is a profit or loss.

Step-by-Step Solution:
Step 1: Selling price of first cow, SP1 = Rs. 9900 with a gain of 10%.Step 2: If profit is 10%, then SP1 = 1.10 * Cost price of first cow.Step 3: Therefore, Cost price of first cow, CP1 = 9900 / 1.10 = Rs. 9000.Step 4: Selling price of second cow, SP2 = Rs. 9900 with a loss of 20%.Step 5: If loss is 20%, then SP2 = 0.80 * Cost price of second cow.Step 6: Therefore, Cost price of second cow, CP2 = 9900 / 0.80 = Rs. 12375.Step 7: Total cost price = CP1 + CP2 = 9000 + 12375 = Rs. 21375.Step 8: Total selling price = SP1 + SP2 = 9900 + 9900 = Rs. 19800.Step 9: Net result = Total selling price minus Total cost price = 19800 - 21375 = -1575.Step 10: The negative sign shows a loss. So he loses Rs. 1575 overall.

Verification / Alternative check:
We can also compute the individual profit and loss in rupees and then combine them. Profit on first cow = SP1 - CP1 = 9900 - 9000 = Rs. 900. Loss on second cow = CP2 - SP2 = 12375 - 9900 = Rs. 2475. Net effect = 900 profit minus 2475 loss = 1575 loss. This matches the earlier calculation, confirming that the overall outcome is a loss of Rs. 1575, not Rs. 200 or zero.

Why Other Options Are Wrong:

• He gained Rs. 200: This is incorrect because detailed calculations show a net loss, not a gain.
• He lost Rs. 200: Although he does lose money, the actual loss is Rs. 1575, not Rs. 200.
• He neither gained nor lost: A gain on one cow and a loss on the other do not cancel because the cost prices are different.

Common Pitfalls:

• Assuming that a 10% gain and 20% loss on equal selling prices cancel into a small or zero net effect without doing proper calculations.
• Using selling prices directly to compute profit and loss percentages instead of cost prices.
• Making arithmetic mistakes in division when finding cost prices from the given percentages.

Final Answer:
The trader suffers a loss of Rs. 1575, which does not match any of the specified amounts, so the correct choice is None of the above.