If the digit $1$ is placed after a two digit number whose tens' digit is $t$, and units' digit is $u$, the new number is:
$\textbf{(A)}\ 10t+u+1\qquad\textbf{(B)}\ 100t+10u+1\qquad\textbf{(C)}\ 1000t+10u+1\qquad\textbf{(D)}\ t+u+1\qquad\\ \textbf{(E)}\ \text{None of these answers}$
By placing the digit $1$ after a two digit number, you are changing the units place to $1$ and moving everything else up a place. Therefore the answer is $\boxed{\textbf{(B)}\ 100t+10u+1}$.