1965 AHSME Problem 32

An article costing C dollars is sold for 100 at a loss of x percent of the selling price. It is then resold at a profit of x percent of the new selling price S'. If the difference between S' and C is 1\frac {1}{9} dollars, then x$ is:

\textbf{(A)}\ \text{undetermined} \qquad \textbf{(B) }\ \frac {80}{9} \qquad \textbf{(C) }\ 10 \qquad \textbf{(D) }\ \frac{95}{9}\qquad \textbf{(E) }\ \frac{100}{9}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.