Question

While arranging certain students of a school in rows containing equal number of students; if three rows are reduced, then three more students have to be arranged in each of the remaining rows. If three more rows are formed, then two students have to be taken off from each previously arranged rows. Find the number of students arranged.

Answer 1

Final Answer : 12 students in each row.
=> 12*15 = 180

Assumptions : Total no. of students are same all cases.

Steps:
1) Let the number of rows and students in each row be 'x'and 'y' respectively .
=> Total no. of students = xy

2)
According to the question,
if 3 rows are reduced (x+3), then 3 more students(y-3) have to be placed in each remaining rows.
=> Total No. of students (initial) = Total No. of students (final)
=> xy = (x-3)(y+3)
=> y +3 = x ---(1)

3) Similarly,
xy = (x+3) (y-2)
=> 3y-6=2x ---(2)

Substituting equation (1),
3y-6 = 2(y+3)
=> y = 12
=> x = 15 :

Hence, Total Number of students are 12 in each row
=> 12*15 = 180

Answer 2

Dear Student,

Answer: Number of rows formed = 15

number of student in each row = 12

Total students arranged = 15(12) = 180 students.

Solution:

Let there would be x number of rows.

In each row number of students are y.

so, total students = xy

Now ATQ if three rows decreased ; now rows become (x-3)

number of student in each row increased by 3; i.e. (y+3)

but number of students remain same in the school

So, xy = (x-3)(y+3)

xy = xy +3x -3y -9

3x-3y-9 =0

x-y = 3 ............eq1

in case 2: number of rows (x+3) number of student in each row (y-2)

xy = (x+3)(y-2)

xy = xy -2x+3y -6

2x-3y =-6 ............eq2

now you have pair of linear equation in two variable.

multiply eq 1 by 3 and subtract eq1 and 2

3x-3y-2x+3y = 9+6

x = 15

x-y = 3

15 - y = 3

-y = 3-15

-y = -12

y = 12

So number of rows formed = 15

number of student in each row = 12

Total students arranged = 15(12) = 180 students.

Hope it helps you.