In an auditorium, seats are 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 the number of seats in each row was reduced by 10, the total number of seats increased by 300.

If x is taken as number of row in original arrangement which of the following quadratic equation describe the situation ?

Options

A. `x^(2)-20x-300=0`
B. `x^(2)+20x-300=0`
C. `x^(2)-20x+300=0`
D. `x^(2)+20x+300=0`

Answer

A

Explanation

Since number of rows were equal to the number of seats in each row in original arrangement, total seats are `x^(2)`.
In new arrangement row are 2x and seats in each row are x - 10 . Total seats are 300 more than previous seats so total number of seats are `x^(2)+300`.
Thus `" "2x(x-10)=x^(2)+300`
`2x^(2)-20x=x^(2)+300`
`x^(2)-20x-300=0`
Thus (a) is correct option.