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A class's students are required to stand in rows. There would be one lesser row if three extra students were in a row. There would be 2 rows more if 3 fewer students were in each row. How many students are there in the class?

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answer is C.

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Detailed Solution

It is given that the students of a class are standing in a row.
Let’s assume that the number of rows be

x

and the number of students in a row be

y .

Therefore the total number of students will be

x y .

There was one lesser row if three extra students were in a row, therefore

x y = x − 1 y + 3 ⇒ x y = x y − y + 3 x − 3 ⇒ 3 x − y = 3 ​ ​ (1)

There were two more rows if three fewer students were in a row, therefore

x y = x + 2 y − 3 ⇒ x y = x y + 2 y − 3 x − 6 ⇒ 3 x − 2 y = − 6 (2)

Subtracting equation (2) from equation (1), we get,

− y + 2 y = 3 + 6 ⇒ y = 9

∵ 3 x − y = 3 (using eq (1)) ⇒ 3 x − 9 = 3 (∵ y = 9) ⇒ x = 4

Thus, the number of students in the class

= x y = 49 = 36.

Therefore there are 36 students in the class.
Hence option (3) is correct.

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