The mean of first n odd natural numbers is

The first n odd natural numbers are 1, 3, 5, ... , (2n − 1).

$\therefore$ Mean of first $n$ odd natural numbers

$=\frac{1+3+5+\ldots+(2 n-1)}{n}$

$=\frac{\frac{n}{2}(1+2 n-1)}{n} \quad\left[S_{n}=\frac{n}{2}(a+l)\right]$

$=\frac{2 n}{2}$

$=n$

Now,

Mean of first $n$ odd natural numbers $=\frac{n^{2}}{81}$ (Given)

$\therefore n=\frac{n^{2}}{81}$

$\Rightarrow n=81$

Hence, the correct option is (b).