If x : y = 3 : 2 then the ratio $2 x^{2} + 3 y^{2} : 3 x^{2} - 2 y^{2}$ is

12 : 5

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6 : 5

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30 : 19

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5 : 3

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Solution

The correct option is C 30 : 19
$\frac{x}{y}$ $= \frac{3}{2}$
$= \frac{x^{2}}{y^{2}}$ $= \frac{9}{4}$
$= \frac{2 x^{2} + 3 y^{2}}{3 x^{2} - 2 y^{2}}$
$= \frac{2 \times \frac{9}{4} + 3}{3 \times \frac{9}{4} - 2}$
$= \frac{\frac{4}{18 + 12}}{\frac{27 - 8}{4}} = \frac{30}{19} = 30 : 19$

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