# The numbers 50, 42, 35, (2x + 10), (2x – 8), 12, 11, 8 have been written in a descending order.

Question:

The numbers 50, 42, 35, (2x + 10), (2x – 8), 12, 11, 8 have been written in a descending order. If their median is 25, find the value of x.

Solution:

Arranging the given data in ascending order:
8, 11, 12, (2x – 8), (2x + 10), 35, 42, 50

Number of terms = 8 (even)

$\therefore$ Median $=$ mean of $\left[\left(\frac{n}{2}\right)^{\text {th }}\right.$ term and $\left(\frac{n}{2}+1\right)^{\text {th }}$ term $]$

$\Rightarrow 25=$ mean of $\left[\left(\frac{8}{2}\right)^{\text {th }}\right.$ term and $\left(\frac{8}{2}+1\right)^{\text {th }}$ term $]$

$\Rightarrow 25=$ mean of $\left[(4)^{\text {th }}\right.$ term and $(5)^{\text {th }}$ term $]$

$\Rightarrow 25=$ mean of $[2 x-8$ and $2 x+10]$

$\Rightarrow 25=\frac{2 x-8+2 x+10}{2}$

$\Rightarrow 25 \times 2=4 x+2$

$\Rightarrow 50=4 x+2$

$\Rightarrow 4 x=50-2$

$\Rightarrow 4 x=48$

$\Rightarrow x=12$

Hence, the value of x is 12.