Question

is a auditorium, seats are arranged in rows and columns. the number of rows was equal to the number of seats in each row. when the number of rows was doubled and the number of seats in each row was reduced by 10, the total number of seats increased by 300. find the number of rows in original arrangement.​

Answer 1

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