The students of a class are made to stand in rows. If three students a

1.	The students of a class are made to stand in rows. If three students are extra in a row, there would be one row less. If three students are less in a row, there would be 2 more rows. Find the number of students in the class.
Answer» 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-33y − x-3 = 03y − x= 3 -x+3y=3…………,...(1) Condition II:Total number of students = (y + 2) (x− 3)xy = xy + 2x-3y− 62x− 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

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

Answer»

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-33y − x-3 = 03y − x= 3

-x+3y=3…………,...(1)

Condition II:Total number of students = (y + 2) (x− 3)xy = xy + 2x-3y− 62x− 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