Let $\left[k\right]$  denotes the greatest integer less than or equal to k. If  number of positive integral solutions of the equation.  $\left[\frac{x}{\left[{\pi }^2\right]}\right]=\left[\frac{x}{\left[11\frac{1}{2}\right]}\right]$ is n, then the value of $n=$. 

 $\left[\frac{x}{\left[{\pi }^2\right]}\right]=\left[\frac{x}{\left[{11}^{\frac{1}{2}}\right]}\right]\Rightarrow \left[\frac{x}{9}\right]=\left[\frac{x}{11}\right]$
Case 1: $0<\frac{x}{9}<1$  and $0\le \frac{x}{11}<1\Rightarrow 0\le x<9$  and $0\le x<11$
Hence, common positive integral values of x are  $\{1,2,3,\mathrm{....8}\}$ 8 values
Case 2: $1\le \frac{x}{9}<2$  and  $1\le \frac{x}{11}<2$
 $\Rightarrow 9\le x\le 18$ and  $\Rightarrow 11\le x<22$
$\Rightarrow x\in \{11,12,\mathrm{...17}\}$  hence 7 values
Case 3:  $2\le \frac{x}{9}<3$ and  $2\le \frac{x}{11}<3$
$\Rightarrow 18\le x<27$  and  $\Rightarrow 22\le x<33$
$\Rightarrow x\in \{22,23,\mathrm{...26}\}$  Hence, 5 values
Case 4: $3\le \frac{x}{9}<4$  and  $3\le \frac{x}{11}<4$
$\Rightarrow 27\le x<36$  and  $\Rightarrow 33\le x<44$
$\Rightarrow x\in \{33,34,35\}$ hence, 3 values
Case 5: $4\le \frac{x}{9}<5$  and  $4\le \frac{x}{11}<5$
 $\Rightarrow x=44\left(1value\right)$
  Hence, the total positive integer values of
$x=n=8+7+5+3+1=24$