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

Ans: Let the side of the square be x.

No. of students = x² + 24

New side = x + 1

No. of students = (x + 1)2 - 25

APQ ⇒ x² + 24 = (x + 1)2 - 25

⇒ x² + 24 = x² + 2 x + 1 - 25

⇒ 2x = 48

⇒ x = 24

∴ side of square = 24

No. of students = 576 + 24

= 600