Question

In an auditorium seats were arranged on rows and columns. the number of rows was equal to number of seats in each row. when the number of rows was doubled by 10 the total number of seats increased by 10.the total number of seats increased by 300.find 1. the number of rows in original arrangements
2. the number of seats in auditorium after re arrangements.

Answer 1

simple h ... 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 = x
now , acc. to the question,
2x(x – 10) = x + 300
2x – 20 = x + 300
x – 20x – 300 = 0
x – (30 – 10)x – 300 = 0
x – 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 = x + 300 = (30) + 300 = 900 + 300 = 1200

Answer 2

Answer:

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