Advertisements
Advertisements
Question
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.
Advertisements
Solution
Let Vivek’s present age be x years.
His brother’s age = (47 – x) years
According to question,
x(47 – x) = 550
⇒ 47x – x2 = 550
⇒ x2 – 47x + 550 = 0
⇒ x2 – 25x – 22x + 550 = 0
⇒ x(x – 25) – 22(x – 25) – 0
⇒ (x – 25)(x – 22) = 0
⇒ x – 25 = 0 or x – 22 = 0
⇒ x = 25 or x = 22
When x = 25, then 47 – x = 47 – 25 = 22
When x = 22, then 47 – x = 47 – 22 = 25 ...(Does not satisfy the given condition)
∴ Vivek's age = x = 25 years.
His younger brother's age = 22 years.
APPEARS IN
RELATED QUESTIONS
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.
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.
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.
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 ages of two sisters are 11 years and 14 years. In how many years’ time will the product of their ages be 304?
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.
₹ 320 were divided equally among 8 children. If 2 more children join them, each will get, how many rupees more or less?
