AHSME 1979 Problem 15

Two identical jars are filled with alcohol solutions, the ratio of the volume of alcohol to the volume of water being $p : 1$ in one jar and $q : 1$ in the other jar. If the entire contents of the two jars are mixed together, the ratio of the volume of alcohol to the volume of water in the mixture is $\textbf{(A) }\frac{p+q}{2} \textbf{(B) }\frac{p^2+q^2}{p+q} \textbf{(C) }\frac{2pq}{p+q} \textbf{(D) }\frac{2(p^2+pq+q^2)}{3(p+q)} \textbf{(E) }\frac{p+q+2pq}{p+q+2}$