1959 AHSME Problem 24

A chemist has m ounces of salt water that is m% salt. How many ounces of salt must he add to make a solution that is 2m% salt?

\textbf{(A)}\ \frac{m}{100+m} \qquad\textbf{(B)}\ \frac{2m}{100-2m}\qquad\textbf{(C)}\ \frac{m^2}{100-2m}\qquad\textbf{(D)}\ \frac{m^2}{100+2m}\qquad\textbf{(E)}\ \frac{2m}{100+2m}

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