2009 AMC 8 Problem 21

Andy and Bethany have a rectangular array of numbers greater than 0 with 40 rows and 75 columns. Andy adds the numbers in each row. The average of his 40 sums is A. Bethany adds the numbers in each column. The average of her 75 sums is B. What is the value of \frac{A}{B}?

\textbf{(A)}\ \frac{64}{225}\qquad\textbf{(B)}\ \frac{8}{15}\qquad\textbf{(C)}\ 1\qquad\textbf{(D)}\ \frac{15}{8}\qquad\textbf{(E)}\ \frac{225}{64}

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