Question

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

• A. $24$
• B. $600$
• C. $480$
• D. $48$

Answer 1

Answer: (B)

$600$

Let no of student in the line be x
We know that the area of square =side${}^2$
As they student were standing in the form of square.
As there where 24 extra student.
So, number of student=$x^2+24$..........(i)
Number of student after increasing 1 student in square=$(x+1{)}^2$
at this time there where 25 less students.
So, total number students=$(x+1{)}^2-25$..........(ii)
From equation (i) and (ii), we get
$(x+1{)}^2-25=x^2+24x^2+2x+1-x^2=49\therefore 2x=48\therefore x=24thentotalno.ofstudents={25}^2-25=600$