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Reciprocal Ratio

If x : y = ...

Question

If $x : y = 1 : 2$ and $y : z = 8 : 3$ , then the reciprocal ratio of $z : x$ is ____

3 : 8

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1 : 3

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3 : 4

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4 : 3

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Solution

The correct option is A $4 : 3$
$x : y = 1 : 2$ and $y : z = 8 : 3$
$∴ x : z = \frac{x}{y} \times \frac{y}{z} = \frac{1}{2} \times \frac{8}{3} = \frac{4}{3} = 4 : 3$
Now, the reciprocal ratio of $z : x$ is $x : z$
$∴ x : z = 4 : 3$

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