If x + 5 = 5 + y and x, y are positive integers, then the value of x + yx + y is?

Answer: Option A

$$\begin{array}{rl}& x+\sqrt{5}=5+\sqrt{y}\\ & \text{Put , }x=5\text{ and }y=5\\ & 5+\sqrt{5}=5+\sqrt{5}\\ & \text{L}\text{.H}\text{.S}=\text{R}\text{.H}\text{.S}\\ & \frac{\sqrt{x}+y}{x+\sqrt{y}}\\ & =\frac{\sqrt{5}+5}{5+\sqrt{5}}\\ & =1\end{array}$$