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

16 : 64

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9 : 64

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16 : 81

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1 : 36

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Solution

The correct option is C $1 : 36$
$x : y = 4 : 9$
$y : z = 3 : 8$
$∴ \frac{x}{y} \times \frac{y}{z} = \frac{4}{9} \times \frac{3}{8}$
$∴ \frac{x}{z} = \frac{1}{6} \Rightarrow x : z = 1 : 6$
$∴$ The duplicate ratio of $x : z$ is $(1)^{2} : (6)^{2} = 1 : 36$ .

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