2008 Cayley Problem 19

A box contains apple and pears. An equal number of apples and pears are rotten. \frac{2}{3} of all of the apples are rotten. \frac{3}{4} of all of the the pears are rotten. What fraction of the total number of pieces of fruit in the box is rotten?

\textbf{(A)}\ \frac{17}{24}\quad \textbf{(B)}\ \frac{7}{12}\quad \textbf{(C)}\ \frac{5}{8}\quad \textbf{(D)}\ \frac{12}{17}\quad \textbf{(E)}\ \frac{5}{7}

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Cayley contests here.