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.

Let there be x rows

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

Total number of students x^{2} + 24

According to the question,

(x + 1)^{2} – 25 = x^{2} + 24 using (a + b)^{2} = a^{2} + 2ab + b^{2}

x^{2} + 2x + 1 – 25 – x^{2} – 24 = 0

2x – 48 = 0

x = 24

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

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