A dealer sells two machines for Rs 12000 each; on the first machine the dealer gains 32% and on the second machine the dealer loses 32%. What is the overall percentage profit or loss on the entire transaction?

Introduction / Context:
This profit and loss question focuses on the combined effect of a given percentage profit on one item and an equal percentage loss on another item when both are sold for the same selling price. Many students assume that a 32% gain and a 32% loss cancel each other, but that is not correct because the base amounts (cost prices) are different.

Given Data / Assumptions:

• First machine is sold for Rs 12000 with 32% profit.
• Second machine is sold for Rs 12000 with 32% loss.
• We assume there are no additional costs or taxes.
• We must find the net percentage profit or loss on both machines together.

Concept / Approach:
Profit and loss percentages are always calculated on cost price, not on selling price. When the same selling price is used but the profit and loss percentages differ, the cost prices are different for the two items. We calculate individual cost prices from the given selling prices and percentages, sum the two cost prices to get total investment, then compare with the total selling price to determine overall gain or loss percentage.

Step-by-Step Solution:
Let CP1 be the cost price of the first machine. Given 32% profit, 12000 = CP1 * 1.32, so CP1 = 12000 / 1.32. Let CP2 be the cost price of the second machine. Given 32% loss, 12000 = CP2 * 0.68, so CP2 = 12000 / 0.68. Compute CP1 ≈ 9090.91 and CP2 ≈ 17647.06. Total CP = CP1 + CP2 ≈ 9090.91 + 17647.06 ≈ 26737.97. Total SP = 12000 + 12000 = 24000; net loss ≈ 26737.97 - 24000 ≈ 2737.97. Loss percentage ≈ (2737.97 / 26737.97) * 100 ≈ 10.24% loss.

Verification / Alternative check:
We can use the standard result that if an article is sold at gain x% and another at loss x% with same selling prices, there is always an overall loss. For actual calculation, using the cost price approach as above confirms a loss of approximately 10.24%. This fits the option that clearly states 10.24% loss.

Why Other Options Are Wrong:
“No gain and no loss” is incorrect because the gain and loss percentages do not cancel each other due to different cost bases. “1% loss” and “18% profit” are numerically far from the calculated percentage and do not match the derived net loss of around 10.24%.

Common Pitfalls:
A frequent mistake is to assume that +32% and -32% balance out to zero, leading to no gain or loss. Another common error is to average the percentages, which is also wrong. Ignoring the fact that profit and loss percentage is always on cost price, not selling price, causes incorrect reasoning in such problems.

Final Answer:
The dealer makes an overall loss of approximately 10.24% on the entire transaction.