The following observations are arranged in ascending order:

Arranging the given data in ascending order:
26, 29, 42, 53, x, x + 2, 70, 75, 82, 93

Number of terms = 10 (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 $]$

$\Rightarrow 65=$ mean of $\left[\left(\frac{10}{2}\right)^{\text {th }}\right.$ term and $\left(\frac{10}{2}+1\right)^{\text {th }}$ term $]$

$\Rightarrow 65=$ mean of $\left[(5)^{\text {th }}\right.$ term and $(6)^{\text {th }}$ term $]$

$\Rightarrow 65=$ mean of $[x$ and $x+2]$

$\Rightarrow 65=\frac{x+x+2}{2}$

$\Rightarrow 65 \times 2=2 x+2$

$\Rightarrow 130=2 x+2$

$\Rightarrow 2 x=130-2$

$\Rightarrow 2 x=128$

$\Rightarrow x=64$

Hence, the value of x is 64.