(3x - 2y) : (2x + 3y) = 5 : 6, then one of the value of ( 3 x + 3 y 3 x - 3 y )^2 is?

Answer: Option D

$$\begin{array}{rl}& \frac{\left(3x-2y\right)}{\left(2x+3y\right)}=\frac{5}{6}\\ & \Rightarrow 18x-12y=10x+15y\\ & \Rightarrow 8x=27y\\ & \Rightarrow \frac{x}{y}=\frac{27}{8}\\ & \therefore {\left(\frac{\text{root}3\text{of}x+\text{root}3\text{of}y}{\text{root}3\text{of}x-\text{root}3\text{of}y}\right)}^2\\ & \Rightarrow {\left(\frac{\text{root}3\text{of}27+\text{root}3\text{of}8}{\text{root}3\text{of}27-\text{root}3\text{of}8}\right)}^2\\ & \Rightarrow {\left(\frac{3+2}{3-2}\right)}^2\\ & \Rightarrow {\left(5\right)}^2\\ & \Rightarrow 25\end{array}$$