A teacher on attempting to arrange the students for mass drill in the form of a solid square found that 24 students were left.

Let there be $x$ rows.

Then, the number of students in each row will also be $x$.

$\therefore$ Total number of students $=\left(x^{2}+24\right)$

According to the question:

$(x+1)^{2}-25=x^{2}+24$

$\Rightarrow x^{2}+2 x+1-25-x^{2}-24=0$

$\Rightarrow 2 x-48=0$

$\Rightarrow 2 x=48$

$\Rightarrow x=24$

$\therefore$ Total number of students $=24^{2}+24=576+24=600$