2011 AMC 12B Problem 4

In multiplying two positive integers $a$ and $b$ , Ron reversed the digits of the two-digit number $a$ . His erroneous product was 161. What is the correct value of the product of $a$ and $b$ ?

$\textbf{(A)}\ 116 \qquad \textbf{(B)}\ 161 \qquad \textbf{(C)}\ 204 \qquad \textbf{(D)}\ 214 \qquad \textbf{(E)}\ 224$

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