If $3 x + 4 y : x + 2 y = 9 : 4,$ then $3 x + 5 y : 3 x - y$ is equal to -

4 : 1

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1 : 4

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7 : 1

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1 : 7

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Solution

The correct option is C $7 : 1$
Given- $3 x + 4 y : x + 2 y = 9 : 4$
$\Rightarrow \frac{3 x + 4 y}{x + 2 y} = \frac{9}{4}$
$\Rightarrow 4 (3 x + 4 y) = 9 (x + 2 y)$
$\Rightarrow 3 x = 2 y$
Now substituting $3 x = 2 y$ in the ratio in question, we have
$3 x + 5 y : 3 x - y = 2 y + 5 y : 2 y - y = 7 y : y = 7 : 1$
$∴ 3 x + 5 y : 3 x - y = 7 : 1$

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