Question

The students of a class are made to stand in rows. If 3 student 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.
(class 10 CBSE SAMPLE PAPER 2017-18 MATHS)

Answer 1

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


HOPE THIS WILL HELP YOU....

Answer 2

Step-by-step explanation:

let no. of rows=x

no. of students = y

total no. of students = xy