# Aptitude Question ID : 94248

If x : y = 3 : 2, then the ratio $2x^{2}+3y^{2} : 3x^{2}-2y^{2}$ is equal to :
[A]5 : 3
[B]6 : 5
[C]12 : 5
[D]30 : 19

30 : 19
$x : y = 3 : 2$
$=> x^{2} : y^{2} = 9 : 4$
$\therefore \frac{2x^{2}+3y^{2}}{3x^{2}-2y^{2}} = \frac{2\frac{x^{2}}{y^{2}}+3}{3\frac{x^{2}}{y^{2}}-2}$
$= \frac{2\times \frac{9}{4}+3}{3\times \frac{9}{4}-2} = \frac{\frac{18+12}{4}}{\frac{27-8}{4}}$
$= 30 : 19$
Hence option [D] is correct answer.