Question

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 was doubled and the number of seats in each row was reduced by 10, the total number of seats increased by 300. Find :-

i ) The number of rows in the original arrangement

ii ) The number of rows in the auditorium after rearrangement

Answer 1

Let the number of rows in original arrangement = x

also, the number of seats in original arrangement = x

therefore, total number of seats = x * x = x²

now , acc. to the question,

2x(x – 10) = x² + 300

2x² – 20 = x² + 300

x² – 20x – 300 = 0

x² – (30 – 10)x – 300 = 0

x² – 30x + 10x – 300 = 0

x(x – 30) + 10(x – 30) = 0

(x – 30)(x +10) = 0

Either x – 30 = 0 or x +10 = 0

x = 30 or x =-10

neglect the -ve value, e get, rows = 30

Thus, no. of rows in the original arrangement , x = 30

and

no. of seats after rearrangement = x² + 300 = (30)² + 300 = 900 + 300 = 1200