If ( x + 1/x ) : ( x - 1/x ) = 5 : 3 the value of x is/are ?

Answer: Option B

$$\frac{\left(x+\frac{1}{x}\right)}{\left(x-\frac{1}{x}\right)}=\frac{5}{3}$$
By Componendo and Dividendo
$$\begin{array}{rl}& \Rightarrow \frac{x+\frac{1}{x}+x-\frac{1}{x}}{x+\frac{1}{x}-x+\frac{1}{x}}=\frac{5+3}{5-3}\\ & \Rightarrow \frac{2x}{\frac{2}{x}}=\frac{8}{2}\\ & \Rightarrow x^2=4\\ & \Rightarrow x=\pm 2\end{array}$$