If m : n = 3 : 2, then (4m + 5n) : (4m - 5n) is equal to = ?

Answer: Option C

$$\begin{array}{rl}& m:n=3:2\\ & \frac{m}{n}=\frac{3}{2}\\ & \Rightarrow \frac{4m+5n}{4m-5n}\\ & \Rightarrow \frac{n\left(4\frac{m}{n}+5\right)}{n\left(4\frac{m}{n}-5\right)}\\ & \Rightarrow \frac{4\times \frac{3}{2}+5}{4\times \frac{3}{2}-5}\\ & \Rightarrow \frac{6+5}{6-5}\\ & \Rightarrow \frac{11}{1}\\ & \Rightarrow 11:1\end{array}$$