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

1:4

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4:1

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7:1

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1:7

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Solution

The correct option is C 7:1
$\begin{matrix} \frac{3 x + 4 y}{x + 2 y} & = \frac{9}{4} Hence, 12 x + 16 y & = 9 x + 18 y or 3 x & = 2 y x & = \frac{2}{3} y \end{matrix}$
Substituting $x = \frac{2}{3} y$ in the required expression we have
$\frac{3 x \frac{2}{3} y + 5 y}{3 x \frac{2}{3} y - y} = \frac{7 y}{y} = \frac{7}{1} = 7 : 1$

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