Student of a class are made to stand in rows. If 4 student are extra in a row, there would be 2 rows

Let x be a number of students in a row and y be a number of students in a column. Then the amount of kids is xy.
(x+4)(y-2)=(x-4)(y+4)=xy
xy+4y-2x-8=xy-4y+4x-16=xy
4y-2x-8= -4y+4x-16=0 add two first equations.
2x-24=0
x=12
4y-24-8=0
4y=32
y=8
xy=12*8=96

let,
no. of students in a row = y
no. of rows = x
so no. of studenta in class = no. of student in a row*no. of rows = xy
according to question,
(y+4)(x-2)=no. of student=xy
xy-2y+4x-8=xy
4x-2y=8
2x-y=4------------(1)

(y-4)(x+4)=no. of students in class=xy
xy+4y-4x-16=xy
-x+y=4-----------(2)
by solving equation (1) & (2)
x=8
y=12
so number of students in class = xy = 12*8 = 96.

If no. of student = x
and no of row =y
then from given:
total student = xy
xy = (x+4)(y-2)
xy = (x-4)(y+4)

Solving the above
x=12
y=8
Hence total no. of student = 12x8 = 96
The option seven 7) is answer

let x = number students in a row
let y = number of rows
then No of students = xy
"If four students are extra in a row there would be two rows less."
(x-2)(y+4) = xy
xy + 4x - 2y - 8 = xy
4x - 2y - 8 = 0
2x - y = 4
"If four students are less in a row there would be four more rows."
(x+4)(y-4) = xy
xy - 4x + 4y - 16 = xy
-4x + 4y = 16
-x + y = 4

Adding these two equations eliminates s
2x - y = 4
-x + y = 4
-------------
x = 8 rows
find s:
-8 + y = 4
y = 4 + 8
y = 12 students in a row

the number of students in the class?
8 * 12 = 96 students

Let no. of student in each row=x
let no. of rows=y
total no. of student=xy
now,
(x+4)(y-2)=xy (eqn1)
(x-4)(y+4)=xy (eqn2)
solving eqn1 & eqn2
we get,x=12,y=8
hence no. of student=xy=12*8=96

there would be 12 students in each row and it contains 8 rows,
so total no of students=12*8=96
if we increase 4 students in each row i.e 16 and it decreases 2 rows i.e 6 (total=16*6=96)
next,
if we decrease 4 students in each row i.e 8 and it will increases 4 students in each row that will be 12 students in each row(total=8*12=96)
so,
the ans will be 96...ANS

let s = number students in a row
let r = number of rows
then
No of students = rs
;
"If four students are extra in a row there would be two rows less."
(r-2)(s+4) = rs
FOIL
rs + 4r - 2s - 8 = rs
rs - rs + 4r - 2s - 8 = 0
4r - 2s = 8
2r - s = 4; simplified, divided by 2
:
"If four students are less in a row there would be four more rows."
(r+4)(s-4) = rs
rs - 4r + 4s - 16 = rs
rs - rs - 4r + 4s = 16
-4r + 4s = 16
-r + s = 4; simplified, divided by 4
:
Adding these two equations eliminates s
2r - s = 4
-r + s = 4
-------------
r = 8 rows
:
find s:
-8 + s = 4
s = 4 + 8
s = 12 students in a row
:
Find the number of students in the class?
8 * 12 = 96 students
:
:
See if that's true
"If four students are extra in a row there would be two rows less."
(12+4)*(8-2) =
16 * 6 = 96
and
"If four students are less in a row there would be four more rows."
(12-4)*(8+4) =
8 * 12 = 96

Let us assume that x is the no. of rows & y is the no. of student per row.
so, total no. of student = xy
a/c to question-
xy=(x-2)(y+4)
or, xy=xy-2y+4x-8
or, 2x-y=4.......(1)
again, a/c to question-
xy=(y-4)(x+4)
or, xy=xy+4y-4x-16
or, 2y-2x=8......(2)
adding eq(1) & eq(2) we have,
y = 12
substituting the value of y in eq(1) we get,
x=(4+12)/2=16/2=8.
thus the no. of students=12*8=96.

let no. of stdnts in row x and row is r.
total no. of stdnts = xr
from 1st condition,
xr = (x+4)(r-2)
or, xr = xr-2x+4r-8
or, x = 2r-4 -------------(i)

from 2nd condition,
xr = (x-4)(r+4)
so, x = r+4 ---------------(ii)
by compairing eqn (i) & (ii), we get
r=8
& x=12

so,no.of stdnt in the class = 12*8 = 96

Let no of students in the class=x
No. of student in a row=y
so total no of rows=x/y
Now according to question
x/y - 2 = x/(y+4).....(1)
x/y + 4 = x/(y-4)......(2)
solve (1) & (2) then
y=12 and x=96
so our required answer is 96 i.e option 7)

initially, number or rows = 8
and number of students in each row = 12
total = 8*12=96

Let number of students be x, number of students in a row be y and number of rows be n
x=ny-----(1)
x = (n - 2) (y + 4)

ny = ny + 4n - 2y - 8

Or, 4n - 2y - 8 = 0 ----------------- (2)

Or, 2n - y - u = 0

and x = (n + 4) (y - 4)

ny = ny - 4n + 4y - 16

Or, -4n + 4y - 16 = 0

Or, -n + y - u = o -------------------- (3)

Adding (2) & and (3)

From (3) y = n + 4 = 8 + 4 = 12

so that x=ny=96

Students of a class are made to stand in rows. If four students are extra in a
row there would be two rows less. If four students are less in a row there
would be four more rows. Find the number of students in the class?
:
let s = number students in a row
let r = number of rows
then
No of students = rs
;
\"If four students are extra in a row there would be two rows less.\"
(r-2)(s+4) = rs
FOIL
rs + 4r - 2s - 8 = rs
rs - rs + 4r - 2s - 8 = 0
4r - 2s = 8
2r - s = 4; simplified, divided by 2
:
\"If four students are less in a row there would be four more rows.\"
(r+4)(s-4) = rs
rs - 4r + 4s - 16 = rs
rs - rs - 4r + 4s = 16
-4r + 4s = 16
-r + s = 4; simplified, divided by 4

:
Adding these two equations eliminates s
2r - s = 4
-r + s = 4
-------------
r = 8 rows
:
find s:
-8 + s = 4
s = 4 + 8
s = 12 students in a row
:
Find the number of students in the class?
8 * 12 = 96 students
:
:
See if that\'s true
\"If four students are extra in a row there would be two rows less.\"
(12+4)*(8-2) =
16 * 6 = 96
and
\"If four students are less in a row there would be four more rows.\"
(12-4)*(8+4) =
8 * 12 = 96

The number of student in the class is 96.

There are 8 rows earlier containing 12 students each, a total of 96 students.
If 4 student are extra in a row, there would be 2 rows less. i.e, in 6 rows of 16 students each = 96 students.

If 4 student are less in a row, there would be 4 more rows, i.e, in 12 rows of 8 students of each = 96 students.

"If four students are extra in a row there would be two rows less."
(12+4)*(8-2) =
16 * 6 = 96
and
"If four students are less in a row there would be four more rows."
(12-4)*(8+4) =
8 * 12 = 96

let s = number students in a row
let r = number of rows
then
No of students = rs
;
\"If four students are extra in a row there would be two rows less."
(r-2)(s+4) = rs

rs + 4r - 2s - 8 = rs
rs - rs + 4r - 2s - 8 = 0
4r - 2s = 8
2r - s = 4; simplified, divided by 2
:
\"If four students are less in a row there would be four more rows.\"
(r+4)(s-4) = rs
rs - 4r + 4s - 16 = rs
rs - rs - 4r + 4s = 16
-4r + 4s = 16
-r + s = 4; simplified, divided by 4
Adding these two equations eliminates s
2r - s = 4
-r + s = 4
-------------
r = 8 rows
:
find s:
-8 + s = 4
s = 4 + 8
s = 12 students in a row
:
Find the number of students in the class?
8 * 12 = 96 students
:
:
See if that\'s true
\"If four students are extra in a row there would be two rows less.\"
(12+4)*(8-2) =
16 * 6 = 96
and
\"If four students are less in a row there would be four more rows.\"
(12-4)*(8+4) =
8 * 12 = 96

let X=number of rows
y=number of student in each row
then total number of student=xy
as stated in question
first case
(x-2)(y+4)=xy
4x-2y-8=0 ----- 1

second case
(x+4)(y-4)=xy
4y-4x-16=0 -------------- 2

solving eq 1 and 2
2y=24
y=12
puting value of y in eq 1 we got x=8
so total num of student=12*8 = 96

Let x be a number of students in a row and y be a number of students in a column. Then the amount of kids is xy.
(x+4)(y-2)=(x-4)(y+4)=xy
xy+4y-2x-8=xy-4y+4x-16=xy
4y-2x-8= -4y+4x-16=0 add two first equations.
2x-24=0
x=12
4y-24-8=0
4y=32
y=8
xy=12*8=96

Let x be the number of rows and y be the number of students
Total no.of students=no. of rows * no of students=xy
In given case 1,xy=(y+4)(x-2)
solving the above we get 4x-2y=8---------(1)

In given case2, xy=(y-4)(x+4)
solving the above we get 4x-4y=-16---------(2)

Solving eqns. (1) and (2) we get,
x=8 and y=12
Total no. of students=8*12=96

total rows=r
Studnt in one row=s
case 1
if 4 student are extra in a row then two rows are less
Total student=(r-2)(s+4)
Case 2
similarly total students=(s-4)(r+4)
find the value of s and r
then total students=s*r=96

let s = number students in a row
let r = number of rows
then
No of students = rs
;
"If four students are extra in a row there would be two rows less."
(r-2)(s+4) = rs
FOIL
rs + 4r - 2s - 8 = rs
rs - rs + 4r - 2s - 8 = 0
4r - 2s = 8
2r - s = 4; simplified, divided by 2
:
"If four students are less in a row there would be four more rows."
(r+4)(s-4) = rs
rs - 4r + 4s - 16 = rs
rs - rs - 4r + 4s = 16
-4r + 4s = 16
-r + s = 4; simplified, divided by 4

:
Adding these two equations eliminates s
2r - s = 4
-r + s = 4
-------------
r = 8 rows
:
find s:
-8 + s = 4
s = 4 + 8
s = 12 students in a row
:
Find the number of students in the class?
8 * 12 = 96 students
:
:
See if that's true
"If four students are extra in a row there would be two rows less."
(12+4)*(8-2) =
16 * 6 = 96
and
"If four students are less in a row there would be four more rows."
(12-4)*(8+4) =
8 * 12 = 96

(x-4)(y+4) = xy = (x+4)(y-2)
solving these equation :
x=12
y=8
so total no of students = 96

let there be x rows and y students in each row
(x-2)(y+4)=Xy
(x+4)(y-4)=xy solving we get 96

let no of rows=x
& no of students in each row=y
a/q, (x-2)(y+4)=xy
4x-2y=8
2x-y=4------(1)
again, (x+4)(y-4)=xy
-4x+4y=16
-x+y=4------(2)
fron 1 & 2,
2x-y=4
-x+y=4
x=8
so y from eqn (2)
y=x+4
=8+4
=12
so, total no of students in a class=xy=8*12=96

Let the number of students in each row be x, and the number of rows be y.
xy = (x + 4)(y – 2)
xy = (x – 4)(y + 4)
From xy = (x + 4)(y – 2):
xy = xy – 2x + 4y – 8
xy – xy = xy – 2x + 4y – 8 – xy
0 = -2x + 4y – 8
0 = x – 2y + 4
x – 2y + 4 – 4 = 0 – 4
x – 2y = -4
From xy = (x – 4)(y + 4):
xy = xy + 4x – 4y – 16
xy – xy = xy + 4x – 4y – 16 – xy
0 = 4x – 4y – 16
0 = x – y – 4
x – y – 4 + y + 4 = 0 + y + 4
x = y + 4
Substitute x = y + 4 into x – 2y = -4:
y + 4 – 2y = -4
-y + 4 = -4
-y + 4 – 4 = -4 – 4
-y = -8
y = 8
Substitute y = 8 into x = y + 4:
x = 8 + 4
x = 12
xy = (12)(8) = 96
therefore answer is 96

x=no.students to each row
n=no. of rows
total no.of students=xn
(x+4)(n-2)=xn
(x-4)(n+4)=xn
after solving these two equations
2x-4n=-8
-4x+4n=-16
so..by solving
-2x=-24
x=12
then n=8
at last the total no of students= xn
=12*8
=96