Question

If x is inversely proportional to y and y is proportional to z, then xz

• A. is proportional to y
• B. is inversely proportional to y
• C. is a constant
• D. is proportional to $y^2$

Answer 1

Answer: (C)

is a constant

Given:-

$x\propto \frac{1}{y}$

$\Rightarrow x=\frac{k}{y}.....\left(1\right)$

$y\propto z$

$\Rightarrow y=kz$

$\Rightarrow z=\frac{y}{k}.....\left(2\right)$

Now, from ${eq}^n\left(1\right)\&\left(2\right)$, we have

$xz=\frac{k}{y}\times \frac{y}{k}$

$\Rightarrow xz=1=\text{constant}$

Hence $xz$ is a constant.

Hence $\left(C\right)$ is the correct answer.