1952 AHSME Problem 44

If an integer of two digits is k times the sum of its digits, the number formed by interchanging the the digits is the sum of the digits multiplied by

\textbf{(A) \ } 9-k \qquad \textbf{(B) \ } 10-k \qquad \textbf{(C) \ } 11-k \qquad \textbf{(D) \ } k-1 \qquad \textbf{(E) \ } k+1

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