If an item is sold for $x$ dollars, there is a loss of $15\%$ based on the cost. If, however, the same item is sold for $y$ dollars, there is a profit of $15\%$ based on the cost. The ratio of $y:x$ is:
$\text{(A) } 23:17\quad \text{(B) } 17y:23\quad \text{(C) } 23x:17\quad \\ \text{(D) dependent upon the cost} \quad \text{(E) none of these.}$
Let $c$ be the cost. Selling the item for $x$ dollars equates to losing $15\%$ of $c$, so $x=.85c$. Selling the item for $y$ dollars equates to profiting by $15\%$ of $c$, so $y=1.15c$. Therefore $\frac{y}{x}=\frac{1.15c}{.85c}=\frac{23}{17}$. The answer is $\fbox{A}$.