Question

students are made to stand in equal rows with equal number of students.if 4 students are added to each row ,the number of rows will be reduce by 2 otherwise if 4 students are deducted from each row, the numer of rows will be increased by 3. then find the number of students

Answer 1

number of rows --- x
number of students in a row --- y
Then the number of students = xy

case1:
4 students added to each row --- y+4
rows is reduced by 2 ----- x-2
(x-2)(y+4) = xy

case2:
4 student taken off each row --- y-4
number of rows is now --- x+3
(x+3)(y-4) = n

so (x-2)(y+4) = (x+3)(y-4)
xy + 4x - 2y -8 = xy-4x+3y-12
8x - 5y = -4 **

(x-2)(y+4) = xy
xy + 4x - 2y - 8 = xy
4x - 2y = 8
2x - y = 4
y = 2x-4 ***

sub *** into **
8x - 5(2x-4) = -4
8x - 10x + 20 = -4
-2x = -24
x = 12
y = 2(12)-4 = 20

number of students = n = xy = 240