Question

If $x$ is proportional to $y$ and $y$ is proportional to $z$, then which of the following statements is correct?

• A. $x$ and $z$ are linear but not proportional.
• B. $x$ is not proportional to $z$
• C. $x$ equals to $z$
• D. $x$ is proportional to$z$

Answer 1

The correct option is D $x$ is proportional to$z$

x is proportional to y.
Therefore,
$\frac{x}{y}=a$ ($a$ is a constant)

$y$ is proportional to $z$, so:
$\frac{y}{z}=b$ ($b$ is a constant)

Multiplying both the equations, we get:
$\frac{x}{y}\times \frac{y}{z}=a\times b$
$\frac{x}{z}=ab$ ($ab$ is a constant)
Hence, $x$ and z are proportional .