ABC26GN3014 · Ratio and Proportion

$$\begin{aligned} & \frac{4 x^{2}-3 y^{2}}{2 x^{2}+5 y^{2}}=\frac{12}{19} \Rightarrow 19\left(4 x^{2}-3 y^{2}\right)=12\left(2 x^{2}+5 y^{2}\right) \\ & \Rightarrow 76 x^{2}-57 y^{2}=24 x^{2}+60 y^{2} \\ & \Rightarrow 52 x^{2}=117 y^{2} \Rightarrow 4 x^{2}=9 y^{2} \\ & \Rightarrow \frac{x^{2}}{y^{2}}=\frac{9}{4} \Rightarrow\left(\frac{x}{y}\right)^{2}=\left(\frac{3}{2}\right)^{2} \Rightarrow \frac{x}{y}=\frac{3}{2} . \\ & \therefore x: y=3: 2 . \end{aligned}$$