A trader sells two items at Rs. 400 each. On the first item he gains 15%, and on the second item he loses 15%. What is the trader's net loss on the whole transaction in rupees?

Introduction / Context:
This question involves equal selling prices with opposite profit and loss percentages on two different items. The trader sells both items at the same selling price, one at a gain and the other at a loss of equal percentage. It is a well known result that when equal percentage profit and loss occur on equal selling prices (or equal cost prices in another variant), the overall result is a loss. We must compute the exact net loss amount in rupees for this specific situation.

Given Data / Assumptions:

• Selling price (SP) of each item = Rs. 400.
• First item: profit = 15%.
• Second item: loss = 15%.
• We must find the net loss in rupees over both items combined.

Concept / Approach:
Let the cost prices of the two items be CP1 and CP2. For the first item, SP1 = 1.15 * CP1. For the second item, SP2 = 0.85 * CP2. Given that SP1 = SP2 = Rs. 400, we can find CP1 and CP2 separately. Then, total cost price is CP1 + CP2 and total selling price is SP1 + SP2 = Rs. 800. The difference between total cost price and total selling price gives the net loss, which we then interpret numerically.

Step-by-Step Solution:
Let CP1 be the cost price of the first item and CP2 the cost price of the second item. For the first item: SP1 = 1.15 * CP1 and SP1 = Rs. 400. So, 1.15 * CP1 = 400. CP1 = 400 / 1.15 ≈ 347.83. For the second item: SP2 = 0.85 * CP2 and SP2 = Rs. 400. So, 0.85 * CP2 = 400. CP2 = 400 / 0.85 ≈ 470.59. Total cost price = CP1 + CP2 ≈ 347.83 + 470.59 = 818.42 (approximately). Total selling price = SP1 + SP2 = 400 + 400 = 800. Net loss = Total CP − Total SP ≈ 818.42 − 800 = 18.42 (approximately). Rounded to two decimal places, net loss ≈ Rs. 18.41.

Verification / Alternative check:
We can check with more exact fractions. CP1 = 400 / 1.15 = 40000 / 115 ≈ 347.826. CP2 = 400 / 0.85 = 40000 / 85 ≈ 470.588. Total CP = (40000 / 115) + (40000 / 85). Computing numerically again gives about 818.414. Subtracting 800 from this total yields approximately 18.414 rupees, which matches the closest option Rs. 18.41.

Why Other Options Are Wrong:
22.14, 20.25, 24.36 and 16.80: These all represent different loss amounts that do not match the precise calculation based on the given percentages and selling prices. If substituted into reverse calculations, none of them lead back to consistent 15% profit and 15% loss values at a selling price of Rs. 400 for each item.

Common Pitfalls:
A common misconception is to think the profit and loss cancel out because the percentages are the same in magnitude. They do not cancel, because they are applied on different base cost prices, not on the same amount. Another mistake is to incorrectly average the percentages and conclude zero net effect. Always compute cost prices individually using SP = CP * (1 ± percentage) and then compare total cost and total sales.

Final Answer:
The trader incurs a net loss of approximately Rs. 18.41 on the whole transaction.