Mr. Kapur purchases two toy cycles at Rs 750 each. He sells one toy cycle at a gain of 6% and the other at a loss of 4%. What is his overall gain or loss percentage on the entire transaction?

Introduction / Context:
This problem involves unequal gain and loss on two identical items purchased at the same cost price. The question tests the learner's ability to compute total cost, total selling price, and then derive the overall profit or loss percentage, rather than just averaging percentages.

Given Data / Assumptions:
- Cost price of each toy cycle = Rs 750. - One cycle is sold at a gain of 6%. - The other cycle is sold at a loss of 4%. - We assume no extra costs beyond the purchase price.

Concept / Approach:
Because both cycles have the same cost price, we can find the selling price of each easily using profit and loss percentages. Then we add the two selling prices to get total selling price, compare it to total cost price, and find the overall profit or loss percentage using:
profit or loss percent = (total profit or loss / total cost price) * 100

Step-by-Step Solution:
Step 1: Total cost price for two cycles = 2 * 750 = Rs 1500. Step 2: Selling price of the first cycle (6% gain) = 750 * 1.06 = Rs 795. Step 3: Selling price of the second cycle (4% loss) = 750 * 0.96 = Rs 720. Step 4: Total selling price = 795 + 720 = Rs 1515. Step 5: Overall profit = total selling price - total cost price = 1515 - 1500 = Rs 15. Step 6: Overall profit percent = (15 / 1500) * 100 = 1%.

Verification / Alternative check:
We can also compute average selling price per cycle: 1515 / 2 = Rs 757.50. Average cost per cycle is 750. Profit per cycle on average = 7.50. Profit percent per cycle on average = 7.50 / 750 * 100 = 1%. This matches the result obtained from total values, confirming the calculation is correct.

Why Other Options Are Wrong:
Option 1% loss is wrong because total selling price is greater than total cost price, so there is no loss. Option 1.5% loss and 1.5 gain do not match the actual numeric difference between 1500 and 1515. They might result from incorrect averaging of percentages instead of calculating based on cost.

Common Pitfalls:
A common error is to simply average 6% and minus 4% to get 1% and then assume it is a gain or loss without checking direction. Another mistake is to average without considering that percentages are applied to the same base cost price. In this special case it works, but only because the cost prices are equal; in general, total values must be checked.

Final Answer:
Mr. Kapur makes an overall 1% gain on the two toy cycles.