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Question

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


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Solution

Step 1: Find the linear equation to obtain the number of students:

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

The number of students will be xy.

It is given that if 4 students are extra in each row, then there would be 2 rows less.

x+4y-2=xyxy+4y-2x-8=xy-x+2y-4=0...1

Also, given that if four students are less in each row, then there would be 4 more rows.

x-4y+4=xyxy-4y+4x-16=xyx-y-4=0...2

Hence, equations (1) and (2) formed the required system of linear equations.

Step 2: Solve the obtained system of linear equation by elimination method.

-x+2y-4=0x-y-4=0

Now, by adding both equations, we will get:

-x+2y+x-y=4+4y=8

Now, substitute the value of y in equation (2) to get:

x-y-4=0x-8-4=0x=12

The total number of students, xy=12×8=96.

Hence, the total number of students in the class is 96.


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