Question : The students of a class are made to stand equally in rows. If 3 students are extra in each row, there would be 1 row less. If 3 students are less in a row, there would be 2 more rows. Find the number of students in the class.
CBSE 2025
Solution :
Let the number of students in each row = x
and the number of rows = y
Total number of students = xy
ATQ
(x+3)(y-1)=xy
x(y-1)+3(y-1)=xy
xy-x+3y-3=xy
-x+3y-3=0
-x+3y=3 — (1)
Also
(x-3)(y+2)=xy
x(y+2)-3(y+2)=xy
xy+2x-3y-6=xy
2x-3y-6=0
2x-3y=6 — (2)
Solving equation (1) and (2)
-x+3y=3
2x-3y=6
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x+0y=9
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x=9
putting in equation (1)
-9+3y=3
3y=3+9
3y=12
y=12/3
y=4
Number of students in each row = 9
and the number of rows = 4
Total number of students
=xy
=9×4
=36
Hence, the total number of students in the class is 36.