Question

while arranging the students in rows if two rows are reduced then one more student has to be arranged in each of the remaining rows and if 3 more rows are formed then one student has to taken off from each previously arranged rows. Find the number of students

Answer 1

let total number of rows = x
let number of students in each row = y
therefore total number of students = xy
according to first condition,
(x-2)(y+1) = xy
xy + x -2y -2 = xy
x-2y = 2..............(i)
according to second condition,
(x+3)(y-1) = xy
xy-x+3y-3 = xy
x-3y = -3..............(ii)

from (i) and (ii)
x-2y-x+3y = 2+3
y = 5

on putting this value of y in (i)
x-2(5) = 2
x-10 = 2
x= 12

therefore total number of students (xy) = 12×5 = 60 students