Question

All the students of a class are made to stand in rows. Each row has same no of students. If 5 students were extra in each row, there would be 1 row less. If 4 students were less in each row then there would be 2 more rows. Find the no of students in the class

Answer 1

Let number of students and rows be s and r respectively.

s÷(s/r + 5)=r-1 ————1

s÷(s/r - 4)=r+1 ————2

From 1,

s = (r-1)(s/r + 5)

s = s+5r - s/r - 5 ———1'

From 2,

s = (r+1)(s/r - 4)

s = s-4r + s/r - 4 ———2'

1'+2',

s + s = (s+s)+(5r-4r)+(-s/r+s/r)+(-5-4)

2s=2s+r-9

2s-2s=r-9

r-9=0

r=9

From 1',

s=s+5r - s/r - 5

s-s + s/r = 5r - 5

s/r=5r-5

s=r(5r-5)

s=9(5×9-5)

s=9×(45-5)

s = 9×40= 360

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