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

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