Question

A teacher on attempting to arrange the students for mass drill in the form of a solid square found that $24$ students students were left. When he increased the size of the square by one student, he found that he was short of $25$ students. Find the number of students.

Answer 1

We know that area of square $=sid{e}^2$

Let no of student in the line be $x$

As there where $24$ extra student

so, number of student $=x^2+24$

number of student after increasing $1$ stident in square

$=(x+1{)}^2$ as there where $25$ less students

So

$\begin{array}{c}\Rightarrow x^2+24=(x+1{)}^2-25\\ \Rightarrow x^2+24=x^2+1+2x-25\\ \Rightarrow x^2-x^2+24+25-1=2x\\ \Rightarrow 48=2x\\ \Rightarrow x=24\end{array}$

so number of students

$\begin{array}{c}=x^2+24\\ ={24}^2+24\\ =576+24\\ =600\end{array}$

Hence,

number of students is $600$