2015 AMC 10A Problem 15

Consider the set of all fractions \tfrac{x}{y}, where x and y are relatively prime positive integers. How many of these fractions have the property that if both numerator and denominator are increased by 1, the value of the fraction is increased by 10\%?

\textbf{(A) }0\qquad\textbf{(B) }1\qquad\textbf{(C) }2\qquad\textbf{(D) }3\qquad\textbf{(E) }\text{infinitely many}

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