Share

In an Auditorium, Seats Were Arranged in Rows and Columns. the Number of Rows Was Equal to the Number of Seats in Each Row. When the Number of Rows Was Doubled and the Number of Seats in Each R - ICSE Class 10 - Mathematics

Question

In an auditorium, seats were arranged in rows and columns. The number of rows was 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:
(1) the number of rows in the original arrangement.
(2) the number of seats in the auditorium after re-arrangement.

Solution

Let the number of rows in the original arrangement be x.
Then, the number of seats in each row in original arrangement = x
Total number of seats = x × x = x²
From the given information,
2x(x – 10) = x2 + 300
2x2 – 20x = x2 + 300
x2 – 20x – 300 = 0
(x – 30) (x + 10) = 0
x = 30, -10
Since, the number of rows or seats cannot be negative. So, x = 30.

1) The number of rows in the original arrangement = x = 30

2) The number of seats after re-arrangement = x2 + 300 = 900 + 300 = 1200

Is there an error in this question or solution?

APPEARS IN

Selina Solution for Selina ICSE Concise Mathematics for Class 10 (2018-2019) (2017 to Current)
Chapter 6: Solving (simple) Problems (Based on Quadratic Equations)
Ex.6E | Q: 10

Video TutorialsVIEW ALL 

Solution In an Auditorium, Seats Were Arranged in Rows and Columns. the Number of Rows Was Equal to the Number of Seats in Each Row. When the Number of Rows Was Doubled and the Number of Seats in Each R Concept: Quadratic Equations.
S