15. Consider the set of fractions $\frac{x}{y}$ (where $x$ and $y$ are two coprime positive integers). If both the numerator and the denominator are increased by 1, the value of the fraction increases by $10\%$. Then, the number of such fractions in the set is $(\quad)$.
(A) 0
(B) 1
(C) 2
(D) 3
(E) infinitely many
15. B.

From the problem, we have
$$
\begin{array}{l}
\frac{x+1}{y+1}=\frac{11 x}{10 y} \Rightarrow x y+11 x-10 y=0 \\
\Rightarrow(x-10)(y+11)=-110 .
\end{array}
$$

Since \( x \) and \( y \) are positive integers,
$$
x-10>-10, y+11>11 \text { . }
$$

Thus, \((x-10, y+11)\)
$$
\begin{array}{l}
=(-1,110),(-2,55),(-5,22) \\
\Rightarrow(x, y)=(9,99) \text { or }(8,44) \text { or }(5,11) .
\end{array}
$$

Noting that \( x \) and \( y \) are coprime,
$$
\text { so, }(x, y)=(5,11) \text { . }
$$