# 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.

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## In an auditorium seats were arranged in rows and columns. The number of rows are 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 seats in the auditorium after re

Click here👆to get an answer to your question ✍️ In an auditorium seats were arranged in rows and columns. The number of rows are 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 seats in the auditorium after re - arrangement.

In an auditorium seats were arranged in rows and columns. The number of rows are 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. FindQuestion

i) the number of rows in the original arrangement.

ii) the number of seats in the auditorium after re-arrangement.

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## 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 ?

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.

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In an auditorium, seats are ar...

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 ?

Updated On: 27-06-2022

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Text Solution Open Answer in App A x 2 −20x−300=0 x2-20x-300=0 B x 2 +20x−300=0 x2+20x-300=0 C x 2 −20x+300=0 x2-20x+300=0 D x 2 +20x+300=0 x2+20x+300=0 Answer

The correct Answer is A

Solution

Since number of rows were equal to the number of seats in each row in original arrangement, total seats are

x 2 x2 .

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 x2+300 . Thus 2x(x−10)= x 2 +300 2x(x-10)=x2+300 2 x 2 −20x= x 2 +300 2x2-20x=x2+300 x 2 −20x−300=0 x2-20x-300=0

Thus (a) is correct option.

Answer

Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams.

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

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

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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.

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### 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

Concept: Quadratic Equations

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Chapter 6: Solving (simple) Problems (Based on Quadratic Equations) - Exercise 6 (E) [Page 79]

Q 10 Q 9 Q 11

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Selina Concise Maths Class 10 ICSE

Chapter 6 Solving (simple) Problems (Based on Quadratic Equations)

Exercise 6 (E) | Q 10 | Page 79

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