CAYLEY 2008 Problem 19

A box contains apple and pears.
An equal number of apples and pears are rotten.
\displaystyle\frac23 of all of the apples are rotten.
\displaystyle\frac34 of all of the the pears are rotten.
What fraction of the total number of pieces of fruit in the box is rotten?

Answer Choices
A. \frac{17}{24}
B. \frac{7}{12}
C. \frac58
D. \frac{12}{17}
E. \frac57