Question

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

Answer 1

Let the number of students in each row be x and the number of rows be y. Then total number of students = xy

\(\therefore\) By the given conditions,

(x + 4) (y – 2) = xy \(\Rightarrow\) xy + 4y - 2x - 8 = xy

\(\Rightarrow\) – 2x + 4y = 8 .......…(1) 

and (x – 4) (y + 4) = xy

\(\Rightarrow\) xy – 4y + 4x – 16 = xy

\(\Rightarrow\) 4x – 4y = 16

Adding equations (1) and (2), we get

2x = 24

\(\Rightarrow\) x = 12

Putting x = 12 in equation (1), we get 

–2 × 12 + 4y = 8 \(\Rightarrow\) 4y = 8 + 24 = 32  \(\Rightarrow\) y = 8 

\(\therefore\)Total number of students in the class = x × y = 12 × 8 = 96