Question

In which of the following relation, $y$ not varies proportionally with $x$ ?

• A. $x=12y$
• B. $\frac{x}{y}=8$
• C. $\frac{5}{x}=y$
• D. $x(y+4)=7$

Answer 1

The correct option is D $x(y+4)=7$

$\left(i\right)$$x=12y$
$\Rightarrow \frac{x}{y}=12$
As the value of $\frac{x}{y}$ is a constant $x$ is directly proportional to $y$.

$\left(ii\right)$$\frac{x}{y}=8$
As the value of $\frac{x}{y}$ is a constant $x$ is directly proportional to $y$.

$\left(iii\right)$ $\frac{5}{x}=y$
$\Rightarrow 5=xy$
As the value of $xy$ is a constant $x$ is inversely proportional to $y$.

$\left(iv\right)$$x(y+4)=7$
$xy+4x=7$
$xy=7-4x$ which is not a constant

And $\frac{x}{y}=\frac{7}{y(y+4)}$ which is also not a constant.

From the above conditions, we can say that $y$ is not in proportion with $x$.