Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Number of oranges = y
Cost of one orange = Rs. 15/y
The servant ate 3 oranges, so Mr. Mehra received (y – 3) oranges.
So, x = y – 3
`\implies` y = x + 3 ...(1)
Cost of one orange paid by Mr. Mehra = Rs. `15/y + 0.25`
= Rs. `15/(x + 3) + 1/4` ...[Using (1)]
Now, Mr. Mehra pays a total of Rs. 15
∴ `(15/(x + 3) + 1/4) xx x = 15`
`(60 + x + 3)/(4(x + 3)) xx x = 15`
63x + x2 = 60x + 180
x2 + 3x – 180 = 0
(x + 15)(x – 12) = 0
x = –15, 12
But, the number of oranges cannot be negative.
So, x = 12.
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.
A stone is thrown vertically downwards and the formula d = 16t2 + 4t gives the distance, d metres, that it falls in t seconds. How long does it take to fall 420 metres?
The speed of a boat in still water is 15 km/hr. It can go 30 km upstream and return downstream to the original point in 4 hours 30 minutes. Find the speed of the stream.
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.
Rs. 6500 was divided equally among a certain number of persons. Had there been 15 persons more, each would have got Rs. 30 less. Find the original number of persons.
Mohan takes 16 days less than Manoj to do a piece of work. If both working together can do it in 15 days, in how many days will Mohan alone complete the work?
Two years ago, a man’s age was three times the square of his son’s age. In three years time, his age will be four times his son’s age. Find their present ages.
The sum of the ages of a father and his son is 45 years. Five years ago, the product of their ages (in years) was 124. Determine their present ages.
