A person sold two different items at the same price. He made 10% profit in one item and 10% loss in the other item. In selling these two items, the person made a total of:
A. 1% profit
B. 2% profit
C. 1% loss
D. 2% loss
GATE 2024 · General Aptitude · Profit Loss · medium
Answer: Net result is a 1% loss (Option C)
Find cost price of item sold at 10% profit: Let SP = 100. Cost_1 = 100 / (1 + 10/100) = 100 / 1.10 = 1000/11
Find cost price of item sold at 10% loss: Cost_2 = 100 / (1 - 10/100) = 100 / 0.90 = 1000/9
Compute total cost, total SP, and net result: Total SP = 200. Total Cost = 1000/11 + 1000/9 = 9000/99 + 11000/99 = 20000/99. Net = 200 - 20000/99 = 19800/99 - 20000/99 = -200/99. Net% = (-200/99) / (20000/99) * 100 = -200/20000 * 100 = -1%. Net loss = 1%.