If the median of x/5 , x, x/4 , x/2 and x/3 (where x > 0) is 8, then the value of x will be

The correct option is 24.

To find the value of $x$, we need to analyze the given numbers and their median. The given set of five numbers is:

$\frac{x}{5},x,\frac{x}{4},\frac{x}{2},\text{ and }\frac{x}{3}$

We are given that $x>0$. Since $x$ is positive, we can determine the relative order of these fractions by comparing their denominators. A larger denominator results in a smaller value. Arranging these terms in ascending (increasing) order, we get:

$\frac{x}{5}<\frac{x}{4}<\frac{x}{3}<\frac{x}{2}<x$

The total number of observations ($n$) is 5, which is an odd number. For an odd number of observations, the median is the middle term, which is the
${\left(\frac{n+1}{2}\right)}^{\text{th}}$
term when arranged in order.

Here, the middle term is the 3^rd term in our ordered sequence:

$\text{Median}=\frac{x}{3}$

We are given that the median of these observations is 8. Therefore, we can set up the equation:

$\frac{x}{3}=8$

Multiplying both sides of the equation by 3 to solve for $x$:

$x=8\times 3$
$x=24$

Thus, the value of $x$ is 24.