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?
$\textbf{(A) } 23\qquad \textbf{(B) } 24\qquad \textbf{(C) } 25\qquad \textbf{(D) } 26\qquad \textbf{(E) } 27$
Since the [average](https://artofproblemsolving.com/wiki/index.php/Arithmetic_mean) of the first $20$ numbers is $30$, their sum is $20\cdot30=600$. 
Since the average of $30$ other numbers is $20$, their sum is $30\cdot20=600$. 
So the sum of all $50$ numbers is $600+600=1200$
Therefore, the average of all $50$ numbers is $\frac{1200}{50}=\boxed{\textbf{(B) }24}$