Given: 'A' sells an article to 'B' at a profit of 10%. 'B' sells the article back to 'A' at a loss of 10%. Formula used: Cost Price (CP) and Selling Price (SP) relationship for profit and loss: SP = CP × \(\left(1+\frac{\text{Profit%}}{100}\right) \) CP = SP × \(\left(1-\frac{\text{Loss%}}{100}\right) \) Calculations: Let the initial cost price of the article for 'A' be ₹100. When 'A' sells to 'B' at a 10% profit: SP for 'A' = 100 × \(\left(1+\frac{10}{100}\right) \) = ₹110 'B' buys at ₹110 and sells it back to 'A' at a 10% loss: SP for 'B' = 110 × \(\left(1-\frac{10}{100}\right) \) = ₹99 Now, 'A' bought the article back at ₹99. His cost price was ₹100 initially. Net gain for 'A' = Initial CP - Final SP Net profit% = \(\frac{\text{Gain}}{\text{Initial CP}} \times 100\) ⇒ Net profit% = \(\frac{100-99}{100} × 100\) ⇒ Net profit% = 1% ∴ The correct answer is option (2).