A man sells two flats for Rs. 4.15 lakhs each. On the first flat he gains 2 percent and on the second flat he loses 2 percent. What is the net percentage effect on his overall transaction for both flats together?

Introduction / Context:
This question tests an important profit and loss concept where equal selling prices are involved but one item is sold at a gain and the other at a loss. In such cases the seller always incurs a net loss, and the percentage loss has a special formula which often appears in competitive exams.

Given Data / Assumptions:

• Selling price of each flat = Rs. 4.15 lakhs.
• Gain on the first flat = 2 percent.
• Loss on the second flat = 2 percent.
• Total number of flats sold = 2.
• We need the net percentage gain or loss on the combined transaction.

Concept / Approach:
When two items are sold at the same selling price, and one yields a gain of x percent while the other yields a loss of x percent, the overall result is always a loss. The approximate net loss percent is given by x^2 / 100. This result can also be derived by computing the individual cost prices from the given selling prices and then comparing total cost and total selling price.

Step-by-Step Solution:
Let the common selling price of each flat be S. For the first flat, gain is 2 percent, so S = 1.02 * cost price of flat one. Thus cost price of flat one = S / 1.02. For the second flat, loss is 2 percent, so S = 0.98 * cost price of flat two. Thus cost price of flat two = S / 0.98. Total cost price = S / 1.02 + S / 0.98. Total selling price = S + S = 2S. Instead of heavy calculation, we use the known result: net loss percent = (2^2 / 100) = 4 / 100 = 0.04 percent.

Verification / Alternative check:
Take a convenient selling price S = Rs. 100. First flat: S = 100 is 2 percent above cost, so cost = 100 / 1.02 ≈ 98.04. Second flat: S = 100 is 2 percent below cost, so cost = 100 / 0.98 ≈ 102.04. Total cost ≈ 98.04 + 102.04 ≈ 200.08. Total selling price = 100 + 100 = 200. Loss ≈ 0.08 on a cost of 200, which is 0.04 percent loss. This confirms the formula based result.

Why Other Options Are Wrong:
0.25 % and 0.5 %: These are larger magnitudes and result from incorrect approximations or from wrongly averaging gains and losses. 0 %: This assumes gains and losses cancel completely, which is not true when selling price is the same for both items. Only 0.04 percent correctly reflects the very small net loss.

Common Pitfalls:
A typical mistake is to assume that a 2 percent gain and a 2 percent loss cancel out, leading to zero net effect. This is incorrect because the base amounts for gain and loss (their cost prices) are different. Another common error is to average the percentages directly without using the correct relationship or formula. Remember the special case formula x^2 / 100 for equal selling prices with equal gain and loss percentages.

Final Answer:
The overall effect is a very small net loss of 0.04 %, not a gain.