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$i f \frac{(3 a^{2} + 2 b^{2})}{(2 b^{2} - a^{2})} = \frac{15}{7} t h e n w h a t w o u l d b e t h e v a l u e o f a : b$ .

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a

3

b

$\frac{2}{3}$

c

$\frac{1}{2}$

d

$\frac{1}{3}$

answer is B.

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Detailed Solution

$\begin{array}{l} \frac{3 a^{2} + 2 b^{2}}{2 b^{2} - a^{2}} = \frac{15}{7} \\ 7 (3 a^{2}) + 7 {(2)}^{2} = 15 (2 b^{2}) - 15 a^{2} \\ 21 a^{2} + 14 b^{2} = 30 b^{2} - 15 a^{2} \\ 36 a^{2} = 30 b^{2} - 14 b^{2} \\ 36 a^{2} = 16 b^{2} . \\ \frac{a^{2}}{b^{2}} = \frac{4}{9} \\ \frac{a}{b} = \frac{2}{3} \end{array}$

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