# 1969 AHSME Problems/Problem 2

## Problem

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: $\text{(A) } 23:17\quad \text{(B) } 17y:23\quad \text{(C) } 23x:17\quad \\ \text{(D) dependent upon the cost} \quad \text{(E) none of these.}$

## Solution

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 $\fbox{A}$.

## See also

 1969 AHSC (Problems • Answer Key • Resources) Preceded byProblem 1 Followed byProblem 3 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 All AHSME Problems and Solutions

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