Let's denote the cost price of each item as C.
For the item in which the person made a 10% profit:
Selling price = Cost price + 10% of cost price
Selling price = C + 0.1*C = 1.1C
For the item in which the person made a 10% loss:
Selling price = Cost price -10% of cost price
Selling price = C — O.1*C = 0.9C
Given that the total profit is $100, we can set up the equation:
1.1C + 0.9C = C + 100
2C = C + 100
C = 100
So, the cost price of each item is $100.
Now, let's calculate the total selling price:
I.IC = 1.1 \times 100 = $110
For the item with 10% profit:
o.9C = 0.9 \times 100 = $90
For the item with 10% loss:
Total selling price = $110 + $90 = $200
The total profit is the difference between the total selling price and the total cost price:
Total profit = $200 - $200 = $0
So, the correct option is:
C. 2% loss