If x : y = 3 : 1, then x3 - y3 : x3 + y3 = ?

Answer: Option C

$$\begin{array}{rl}& =\frac{x}{y}=\frac{3}{1}\\ & \Rightarrow \frac{x^3}{y^3}=\frac{27}{1}\\ & \Rightarrow \frac{x^3-y^3}{x^3+y^3}=\frac{\left(\frac{x^3}{y^3}\right)-1}{\left(\frac{x^3}{y^3}\right)+1}\\ & =\frac{27-1}{27+1}\\ & =\frac{26}{28}\\ & =\frac{13}{14}\\ & =\left(x^3-y^3\right):\left(x^3+y^3\right)\\ & =13:14\end{array}$$