The students of a class are made to stand in rows. If 3 students are more 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.
The students of a class are made to stand in rows. If 3 students are more 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 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, we get
-2x+6y=6……………….(3)
On adding equations (2) and (3),
3y=12
⇒ y=4
On putting y= 4 in equation 1, we get x = 9.
Hence, the number of students in class= xy=9×4=36.
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, we get
-2x+6y=6……………….(3)
On adding equations (2) and (3),
3y=12
⇒ y=4
On putting y= 4 in equation 1, we get x = 9.
Hence, the number of students in class= xy=9×4=36.
