If $x : y = 3 : 8$ and $y : z = 4 : 9$ , then the triplicate ratio of $x : z$ is _____

27 : 512

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1 : 216

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64 : 729

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3 : 9

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Solution

The correct option is A $1 : 216$
$x : y = 3 : 8$ and $y : z = 4 : 9$
$∴ \frac{x}{y} \times \frac{y}{z} = \frac{3}{8} \times \frac{4}{9} = \frac{1}{6}$
$∴ x : z = 1 : 6$
$∴$ The triplicate ratio of $x : z$ is $x^{3} : z^{3} = (1)^{3} : (6)^{3} = 1 : 216$

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