Question

Students of a class are made to stand in rows. If four students are extra in each row there would be 2 rows less. If 4 students are less in each row, there would be 4 more rows. The number of students in the class is?

Answer 1

please find the attachment

Answer 2

Answer:

     96 students

Step-by-step explanation:

let no of rows = x

let no of students in each row = y

total no of students = xy

⇒ If 4 students are extra in each row, there would  be 2 rows less

(y + 4) ( x - 2) = xy  

xy - 2y + 4x - 8 = xy

4x - 2y - 8 = 0  

2(2x - y - 4) = 0

2x - y - 4= 0

y = 2x - 4 ------{i}

⇒ If 4 students are less in each row, there would be 4 more rows.

(y - 4) (x + 4) = xy  

xy + 4y - 4x - 16 = xy

-(-4y + 4x + 4) = 0

4(-y + x + 4) = 0

-y + x + 4  = 0 ------{ii}

from {i} and {ii}

-(2x - 4) + x + 4 = 0

-2x + 4 + x + 4 = 0

x - 8 = 0

x = 8

y = 2x - 4

y = 16 - 4

y = 12  

total no of students = xy = 8×12 = 96 students