If the median of $\frac{x}{7},\frac{x}{5},\frac{x}{6},x,\frac{x}{4},\frac{x}{3},\frac{x}{2}$ is $8$, then the value of $x$ is _____

The correct option is C: $32$

Given observations are

$\frac{x}{7},\frac{x}{5},\frac{x}{6},x,\frac{x}{4},\frac{x}{3},\frac{x}{2}$

Arranging in ascending order
$\frac{x}{7},\frac{x}{5},\frac{x}{6},\frac{x}{4},\frac{x}{3},\frac{x}{2},x(=\frac{x}{1})$

[When numerators are same in fractions, then least denominator fraction is the largest fraction.]

Given, Median $=8$

No. of observations, $n=7$
Since number of observation is odd
Median $={\left(\frac{n+1}{2}\right)}^{th}={\left(\frac{7+1}{2}\right)}^{th}$ observation. $=4^{th}$ observation $=$

$\therefore 8=\frac{x}{4}$
$\Rightarrow x=32$