Question

Hey plz solve this soon... In an auditorium, seats were arranged in rows and columns. The number of rows were equal to the number of seats in each row. When the number of rows were doubled and number of seats were reduced by 10, the total number Of seats increased by 300.
Find,
1. The number of rows in the original arrangement.
2. The number of seats in the auditorium after arrangement.

Answer 1

hey dear your answer is here
originalnumber of row =x
original number of seats in each row=x

new rows=2x
number of seats in each row=x-10

so
2x*(x-10)=x^2+300
2x^2-20x=x^2+300

x^2-20x-300=0

by solving this we get

x=30 or x=-10

but x=-10 not possible

so x=30

Answer 2

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