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

Answer: Option A

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