Question

In an Auditorium, seats were arranged in rows and columns. The number of rows was equal to the number of seats in each row. When the number of row was doubled and the number of seat in each row was reduced by 10, total number of seats increased by 300. Find :
a) ​​​​​​ the number of rows in the original arrangement.
b) ​​​​​​ the number of seats in the Auditorium after rearrangement.

Please solve this problem by Linear Equations

Answer 1

This is the answer of the question.

Answer 2

(a) 900
(b)1200

let no. of row =x
no. of seats in one row=y
total seats hence =xy
A.T.Q
x=y
also 2x .(y-10) =xy+300 •••••••1
put x=y in eq 1

substitution method
2x.(x-10)=x.x+300
2x^-20x=x^+300
x^-20x-300=0
(x-30)(x+10)=0
x=30. (10 is neglected as no. of rows cant be negative)

hence initial seats =xy
=x^
=30.30
=900

seats after new arrangement = xy+300
=900+300
=1200