AMC 12 2005a Problem 5

The average (mean) of $20$ numbers is $30$, and the average of $30$ other numbers is $20$. What is the average of all $50$ numbers?

$\textbf{(A) } 23 \textbf{(B) } 24 \textbf{(C) } 25 \textbf{(D) } 26 \textbf{(E) } 27$