A person sells two cars, each at a price of Rs. 3,25,475. On the first car he makes a profit of 12%, while on the second car he incurs a loss of 12%. Considering both cars together, what is his overall percentage profit or loss on the whole transaction?

Introduction / Context:
This is a classic profit and loss question where two items are sold at the same selling price but with equal and opposite percentage gain and loss. Many students think that a 12% gain and a 12% loss will cancel out, leading to no overall profit or loss. However, that is incorrect because the gain and loss percentages are applied on different cost prices. Questions like this are designed to test conceptual clarity that percentage changes around the same selling price do not simply offset each other; we must compute the actual cost prices and compare total selling price with total cost price.

Given Data / Assumptions:
- Selling price of first car (SP1) = Rs. 3,25,475. - Selling price of second car (SP2) = Rs. 3,25,475. - Profit on first car = 12% of its cost price. - Loss on second car = 12% of its cost price. - We must find the overall profit or loss percentage on both cars together.

Concept / Approach:
Let the cost prices of the two cars be CP1 and CP2 respectively. For the first car, SP1 = CP1 * 1.12. For the second car, SP2 = CP2 * 0.88. Both selling prices are equal and known, so we can compute each cost price separately. Once we have CP1 and CP2, we can add them to get the total cost price. Total selling price is simply SP1 + SP2. The overall profit or loss percentage is then (Total SP - Total CP) / Total CP * 100. The result will show whether the trader gains or loses on the entire deal.

Step-by-Step Solution:
Let SP = Rs. 3,25,475 for each car. For the first car, SP1 = CP1 * 1.12, so CP1 = SP / 1.12. For the second car, SP2 = CP2 * 0.88, so CP2 = SP / 0.88. Compute CP1: CP1 = 3,25,475 / 1.12. Compute CP2: CP2 = 3,25,475 / 0.88. Total selling price = SP1 + SP2 = 2 * 3,25,475 = Rs. 6,50,950. Total cost price = CP1 + CP2. If you perform the calculations, total CP is greater than total SP, so there is a loss. The net loss percentage comes out to be 1.44% of the total cost price.

Verification / Alternative check:
A well-known formula states that when one item is sold at r% profit and another at r% loss, both at the same selling price, the net result is always a loss of (r^2 / 100) percent. Here, r = 12, so net loss% = (12^2) / 100 = 144 / 100 = 1.44%. This quick formula perfectly matches the detailed calculation, confirming that the overall result is a 1.44% loss.

Why Other Options Are Wrong:
- 14.4% loss or 14.4% profit are much too large; they ignore the actual relationship between gain and loss. - 0% assumes that equal gain and loss cancel out, which is a common misconception. - 1.44% profit contradicts the formula and the fact that the loss side dominates in such paired transactions.

Common Pitfalls:
Students often think that +12% and -12% around the same selling price will net to zero, which is not true because percentage is always on cost price. Another error is to average 12% gain and 12% loss directly, without considering the multiplicative nature of profit and loss. Forgetting that in such paired problems the net result is always a loss (unless both percentages are zero) is another common conceptual mistake.

Final Answer:
The trader incurs an overall 1.44% loss on the whole transaction.