Advertisements
Advertisements
प्रश्न
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:
- the number of rows in the original arrangement.
- the number of seats in the auditorium after re-arrangement.
Advertisements
उत्तर
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.
- The number of rows in the original arrangement:
x = 30 - The number of seats after re-arrangement = x2 + 300
= 900 + 300
= 1200
APPEARS IN
संबंधित प्रश्न
The sum of the ages of Vivek and his younger brother Amit is 47 years. The product of their ages in years is 550. Find their ages.
The sum S of n successive odd numbers starting from 3 is given by the relation: S = n(n + 2). Determine n, if the sum is 168.
One year ago, a man was 8 times as old as his son. Now his age is equal to the square of his son’s age. Find their present ages.
Mr. Mehra sends his servant to the market to buy oranges worth Rs. 15. The servant having eaten three oranges on the way, Mr. Mehra pays Rs. 25 paise per orange more than the market price. Taking x to be the number of oranges which Mr. Mehra receives, form a quadratic equation in x. Hence, find the value of x.
Rs. 250 is divided equally among a certain number of children. If there were 25 children more, each would have received 50 paise less. Find the number of children.
An employer finds that if he increases the weekly wages of each worker by Rs. 5 and employs five workers less, he increases his weekly wage bill from Rs. 3,150 to Rs. 3,250. Taking the original weekly wage of each worker as Rs. x; obtain an equation in x and then solve it to find the weekly wages of each worker.
The total cost price of a certain number of identical articles is Rs. 4800. By selling the articles at Rs. 100 each, a profit equal to the cost price of 15 articles is made. Find the number of articles bought.
A hotel bill for a number of people for overnight stay is Rs. 4800. If there were 4 people more, the bill each person had to pay, would have reduced by Rs. 200. Find the number of people staying overnight.
The ages of two sisters are 11 years and 14 years. In how many years’ time will the product of their ages be 304?
₹ 320 were divided equally among 8 children. If 2 more children join them, each will get, how many rupees more or less?
