AHSME 1950 Problem 30

From a group of boys and girls, $15$ girls leave. There are then left two boys for each girl. After this $45$ boys leave. There are then $5$ girls for each boy. The number of girls in the beginning was: $\textbf{(A)}\ 40 \textbf{(B)}\ 43 \textbf{(C)}\ 29 \textbf{(D)}\ 50 \textbf{(E)}\ \text{None of these}$