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.

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Solution

we know that area of square = side²
So no. of students in the line if side was x (let)
No. of students = x²+24 (as there were 24 exrltra students)
No. Of students after increasing 1 student in square = (x+1)²-25 (as there were 25 less students)
So x²+24=(x+1)²-25
x²+ 24 = x²+1 +2x -25
x²-x² + 24+25-1=2x
48=2x
So x=24
So no. Of students = x²+24=24²+24=576+24=600
So no. Of students = 600

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