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.
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
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.
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.
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.
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.
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.
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?
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.
Rs. 480 is divided equally among 'x' children. If the number of children were 20 more, then each would have got Rs. 12 less. Find 'x'.
