Profit or Loss

Let $x$ be the amount the man paid for the article that he gained 10% on in the sale, and $y$ be the amount the man paid for the article that he lost 10% on in the sale. His profit can then be given by $0.1x-0.1y$ . We also have the relationship $1.1x=0.9y=1000$ . Now, the percent gain in the entire transaction is given by $\frac{0.1x-0.1y}{x+y}$ . This is how I simplified the expression for the percent gain to get the answer: Multiply the numerator and denominator by $11$ . This gives $\frac{1.1x-1.1y}{11x+11y}=\frac{0.9y-1.1y}{9y+11y}=\frac{-0.2y}{20y}=-1$ %. (Note that the amount of $1000 could've been anything, and it would not have affected the answer.)