Advertisements
Advertisements
Question
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.
Solution
Let the present ages of father and his son be x years and (45 – x) years respectively.
Five years ago,
Father's age = (x – 5) years
Son's age = (45 – x – 5) years = (40 – x) years
From the given information, we have:
(x – 5)(40 – x) = 124
40x – x2 – 200 + 5x = 124
x2 – 45x + 324 = 0
x2 – 36x – 9x + 324 = 0
x(x – 36) – 9(x – 36) = 0
(x – 36)(x – 9) = 0
x = 36, 9
if x = 9,
Father's age = 9 years,
Son's age = (45 – x) = 36 years
This is not possible.
Hence, x = 36
Father's age = 36 years
Son's age = (45 – 36) years = 9 years.
APPEARS IN
RELATED QUESTIONS
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?
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 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.
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.
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.
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?
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'.
