Question

In an auditorium the no. of rows was equal to the no. 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 find the total no. of seats increased by 375. How many rows were there

Answer 1

Let the number of rows in original arrangement = x

also, the number of seats in each row in original arrangement = x

therefore, total number of seats = x * x = x ²

now , according to the question,

2x(x – 5) = x ² + 375

2x ² – 10x = x ² + 375

x ² – 10x – 375 = 0

x ² – 25x + 15x – 375 = 0

x(x – 25) + 15(x – 25) = 0

(x – 25)(x +15) = 0

Either x – 25 = 0 or x +15 = 0

x = 25 or x = – 15

neglect the -ve value, we get,x = 25

Thus, no. of rows in the original arrangement , x = 25