# The students of a class are made to stand in rows. If 3 students are extra in a row, there would be 1 row less. If 3 students are less in a row, there would be 2 rows more. Find the number of students in the class.

Let the number of rows be x and number of students in a row be y.

Total students of the class = Number of rows x Number of students in a row = xy

Using the information given in the question,

Condition 1

Total number of students = (x - 1) (y + 3)

= (x - 1) (y + 3)

= xy - y + 3x - 3

3x - y - 3 = 0

3x - y = 3 ....(i)

Condition 2

Total number of students = (x + 2) (y - 3)

= xy + 2y - 3x - 6

⇒3x - 2y = -6  ... (ii)

Subtracting equation (ii) from (i),

(3x - y) - (3x - 2y) = 3 - (-6)

⇒- y + 2y = 9

⇒3 + 6 y = 9

By using equation (i), we obtain 3x - 9 = 3,

⇒3x = 9 + 3

⇒3x = 12

⇒ x = 4

From (i),

⇒ 3(4) - y = 3

⇒ 12 - y = 3

⇒ 9 = y

Number of rows = x = 4

Number of students in a row = y = 9

Number of total students in a class = Number of students in 1 row × Number of rows

= xy

= 4 x 9

= 36

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