Question

Students of a class are made to stand in rows. If 3 students are extra in a row, there

would be 2 rows less. If 4 students are less in a row, there would be 5 more rows. Find
the number of students in the class.​

Answer 1

Let the number of rows be x and number of students in a row be y.

Total students of the class= Number of rows × Number of students in a row

=x×y=xy

Case 1

Total number of students =(x−1)(y+3)

⇒xy=(x−1)(y+3)=xy−y+3x−3

⇒3x−y−3=0

⇒3x−y=3..... (i)

Case 2

Total number of students=(x+2)(y−3)

⇒xy=xy+2y−3x−6

⇒3x−2y=−6..... (ii)

Subtracting equation (ii) from (i),

⇒(3x−y)−(3x−2y)=3−(−6)

⇒−y+2y=3+6

⇒y=9

By substituting value of y in (i), we get

⇒3x−9=3

⇒3x=9+3=12

⇒x=4

Number of rows =x=4

Number of students in a row =y=9

Number of total students in a class =x×y=4×9=36

Explanation: