If x, y and z are in continued proportion then $z : x :: z^{2} : y^{2}$ .

True

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False

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Solution

The correct option is A
True

If x, y, and z are in continued proportion then $y^{2} = x z$
Multiply both sides of the equation by $z$
equation becomes, $z y^{2} = x z^{2}$
$⟹$ $(z / x) = (z^{2} / y^{2})$
$⟹$ $z : x :: z^{2} : y^{2}$

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\frac{x - y}{x - z} = \frac{y}{y + z}

If x, y and z are in continued proportion then $z : x :: z^{2} : y^{2}$ .

Continued proportion means a:b : : b:c

z : x :: z^{2} :

\frac{(x + y)^{2}}{(y + z)^{2}} = \frac{x}{z}

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