Question

In an auditorium , the number of rows was equal to the number of seats in each row . If the number of rows is doubled and the number of seats in each row is reduced by 5 , then the total number of seats is increased by 375 . How many rows were there initially ???


Chap : Quadratic Equations , Class 10 .

Plz help !!

Answer 1

let the numbers of rows be x
so the number of seat in each row will also Be x
so the total number of seats in the auditorium=x²
when the number of rows is doubled and the number of seats in each rows is decreased by 5
so now the total number of seat in the auditorium will be 2x(x-5)=2x²-10x
given
2x²-10x-x²=375
x²-10x-375=0
on factorising it by method of completing square we get
x²-2.x.5+25-400=0
(x-5)²=400
x-5=±20
x=25 or -15
so the number of rows was initially 25
ask where you didn't get it

Answer 2

Hello friend!
Here's ur answer!

Let number of rows be x.
Number of seats =x2
Number of rows =2x.
Number of seats in each row =x -5
Number of seats =2x (x -5 )
According to question:
2x (x-5) = x2 +375
2x2 - 10x =x2 +375
2x2 - x2 -10x - 375 = 0
X2 - 10x - 375 =0
X2 - (25x - 15x) - 375 =0
X2 - 25x +15x - 375 =0
X (x - 25) +15 (x - 25)=0
(X- 25) (x +15)
Therefore, x =25
Or x =-15
X cannot be a negative integer so x =25.

Hope it helps!!☺
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