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Question

The students of a class are made to stand in rows. If 3 students 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.

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Solution

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 =(x1)(y+3)
xy=(x1)(y+3)=xyy+3x3
3xy3=0
3xy=3..... (i)

Case 2
Total number of students=(x+2)(y3)
xy=xy+2y3x6
3x2y=6..... (ii)

Subtracting equation (ii) from (i),
(3xy)(3x2y)=3(6)
y+2y=3+6
y=9

By substituting value of y in (i), we get
3x9=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

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