1979 AHSME 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}\qquad \textbf{(B) }\frac{p^2+q^2}{p+q}\qquad \textbf{(C) }\frac{2pq}{p+q}\qquad \textbf{(D) }\frac{2(p^2+pq+q^2)}{3(p+q)}\qquad \textbf{(E) }\frac{p+q+2pq}{p+q+2}

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