Final answer:
To determine the combined gain or loss percent from selling two cycles at an equal price with a 10% gain on one and a 10% loss on the other, you calculate the individual cost prices based on the given selling prices, find the total cost and total selling price, and then calculate the net loss or gain as a percentage of the total cost. However, due to the nature of percentage calculations, there will be a net loss.
Step-by-step explanation:
To determine the gain or loss percentage when selling two cycles, one at a 10% gain and the other at a 10% loss, we must perform a couple of calculations.
Let's suppose the cost price of the cycles is C. Then, selling the first cycle for Rs. 2376 earns a 10% profit, which means 1.1C = 2376. Solving for C, we get C (the cost price of one cycle) = 2376 / 1.1
For the second cycle, selling at a 10% loss means the selling price was 0.9C = 2376. Again, we solve for C to find the cost price, C = 2376 / 0.9.
After finding C, we can calculate the total cost price of both cycles (2C) and the total selling price (2 x 2376). The difference between the total selling price and the total cost price will give us the net loss or gain. Finally, we calculate the gain or loss percentage by dividing the net profit or loss by the total cost price and then multiplying by 100 to convert it into a percentage.
However, it must be noted that when the percentage gain and loss are the same, the seller will always incur a net loss due to how percentages work on different bases. This process of finding the overall percent change in transactions involving equal gains and losses is sometimes referred to as the marginal gain and loss. In this case, despite a 10% gain and a 10% loss, the overall result is not breakeven but a net loss.