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A teacher attempting to arrange the students for a 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. The number of students is

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600

603

602

601

answer is D.

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Detailed Solution

Given that 24 students were left for a mass drill in the form of a solid square.
Let’s assume that there r number of rows.
Total number of students=

r^{2} + 24

According to the given condition, -1)
He increased the size of the square by one student, he found that he was short of 25 students. Then this can be represented in the equation form as,

{(r + 1)}^{2} - 25

-2)
By equating eq. 1) and 2) we will find the total number of students.

⟹ r^{2} + 24 = {(r + 1)}^{2} - 25

⟹ r^{2} + 24 = r^{2} + 2 r + 1 - 25

⟹ 2 r - 24 - 25 + 1 = 0

⟹ 2 r - 48 = 0

⟹ 2 (r - 24) = 0

⟹ r - 24 = 0

∴ r = 24

∴

Total number of students=

r^{2} + 24 = {(24)}^{2} + 24 = 576 + 24 = 600

Hence, the total number of students is 600.
Hence, option (4) is correct.

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