26, x + 4, x + 2 and 18 are in descending order of their values and their median is 20, then the value of x is :

1. 19

2. 17

3. 15

4. 13

Given observations: 26, x + 4, x + 2 and 18

Median = 20

Arranging the above observations in ascending order,

18, x + 2, x + 4, 26

Number of observations, n = 4 (even)

By formula,

Median = $\dfrac{1}{2}\Big[\text{the value of }\Big(\dfrac{n}{2}\Big)^{th} \text{ term } + \text{the value of }\Big(\dfrac{n}{2} + 1\Big)^{th} \text{ term }\Big]$

Substituting values we get :

$\Rightarrow 20 = \dfrac{1}{2}\Big[\text{the value of }\Big(\dfrac{4}{2}\Big)^{th} \text{ term } + \text{the value of }\Big(\dfrac{4}{2} + 1\Big)^{th} \text{ term }\Big] \\[1em] \Rightarrow 20 = \dfrac{1}{2}\Big[\text{2nd term + 3rd term}\Big]\\[1em] \Rightarrow 20 = \dfrac{1}{2}\Big[x + 2 + x + 4\Big]\\[1em] \Rightarrow 20 = \dfrac{1}{2}\Big[2x + 6 \Big]\\[1em] \Rightarrow 20 = x + 3\\[1em] \Rightarrow x = 20 - 3\\[1em] \Rightarrow x = 17.$

Hence, option 2 is the correct option.