The students of a class are made to stand in rows. If 3 students are extra in a row, there would be 1 row 2. If2 students are less in a row, there would be I rows more. Find the number of students in the class.
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Solution:

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

Total students of the class= Number of rows × Number of students in a row

Total students of the class= xy

Condition I:

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

xy = (y-1) (x+ 3)

xy= xy - x + 3y-3

3y − x-3 = 0

3y − x= 3

-x+3y=3…………,...(1)

Condition II:

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

xy = xy + 2x-3y− 6

2x− 3y = 6………….. (2)

On multiplying equation (1) by (2)

2(-x+3y=3)

-2x+6y=6……………….(3)

On adding equation 2 and 3

2x− 3y = 6

-2x+6y=6

3y=12

y=12/3

y=4

On putting y= 4 in eq 1.

-x+3y=3

-x+3(4)=3

-x+12=3

-x=3-12

-x=-9

x=9

number of students in class= xy=9×4=36.

Hence, the number of students in class=36

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