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Triplicate Ratio

If x : y = ...

Question

If $x : y = 2 : 5, y : z = 15 : 8$ and $z : w = 3 : 2$ , then find the triplicate ratio of $x : w$

\sqrt[3]{9} : \sqrt[3]{8}

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3 : 4

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729 : 512

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81 : 64

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Solution

The correct option is C $729 : 512$
$x : y = 2 : 5, y : z = 15 : 8, z : w = 3 : 2$
$∴ \frac{x}{y} \times \frac{y}{z} \times \frac{z}{w} = \frac{2}{5} \times \frac{15}{8} \times \frac{3}{2} = \frac{9}{8}$
$∴ x : w = 9 : 8$
$∴$ The triplicate ratio of $9 : 8$ is $9^{3} : 8^{3} = 729 : 512$

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