If $x : y = 3 : 4$ , then $4 x + 5 y : 5 x - 2 y$ =?

7 : 32

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32 : 7

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4 : 3

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5 : 2

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Solution

The correct option is B $32 : 7$
$\frac{x}{y} = \frac{3}{4}$ (Given)
Dividing by y on numerator and denominator,
$\frac{4 x + 5 y}{5 x - 2 y} = \frac{4 \frac{x}{y} + 5}{5 \frac{x}{y} - 2} = \frac{4 \times \frac{3}{4} + 5}{5 \times \frac{3}{4} - 2} = \frac{8}{\frac{15 - 8}{4}} = \frac{8 \times 4}{7} = \frac{32}{7}$

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If x : y = 4 : 7, Find the value of (3x+ 2y) : (5x + y).

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