Advertisements
Advertisements
प्रश्न
The age of a father is twice the square of the age of his son. Eight years hence, the age of the father will be 4 years more than three times the age of the son. Find their present ages.
Advertisements
उत्तर
Let the present age of the son be x years.
∴ Present age of father = 2x2 years
Eight years hence,
Son’s age = (x + 8) years
Father’s age = (2x2 + 8) years
It is given that eight years hence, the age of the father will be 4 years more than three times the age of the son.
∴ 2x2 + 8 = 3(x + 8) + 4
2x2 + 8 = 3x + 24 + 4
2x2 – 3x – 20 = 0
2x2 – 8x + 5x – 20 = 0
2x(x – 4) + 5(x – 4) = 0
(x – 4)(2x + 5) = 0
`x = 4, (-5)/2`
But, the age cannot be negative, so, x = 4.
Present age of son = 4 years
Present age of father = 2(4)2 years = 32 years.
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?
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.
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.
A trader bought a number of articles for Rs. 1,200. Ten were damaged and he sold each of the remaining articles at Rs. 2 more than what he paid for it, thus getting a profit of Rs. 60 on the whole transaction. Taking the number of articles he bought as x, form an equation in x and solve it.
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.
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.
In a certain positive fraction, the denominator is greater than the numerator by 3. If 1 is subtracted from the numerator and the denominator both, the fraction reduces by `1/14`. Find the fraction.
Two years ago the ages of Radha and Meena were in the ratio 5 : 2. If the sum of their present ages is 39 years, their ages, 2 years ago, were ______.
