Advertisements
Advertisements
Question
The sum of ages of a man and his son is 45 years. Five years ago, the product of their ages was four times the man's age at the time. Find their present ages.
Advertisements
Solution
Let the present age of the man be x years
Then present age of his son is (45 - x) years
Five years ago, man’s age = (x - 5) years
And his son’s age (45 - x - 5) = (40 - x) years
Then according to question,
(x - 5)(40 - x) = 4(x - 5)
40x - x2 + 5x - 200 = 4x - 20
-x2 + 45x - 200 = 4x - 20
-x2 + 45x - 200 - 4x + 20 = 0
-x2 + 41x - 180 = 0
x2 - 41x + 180 = 0
x2 - 36x - 5x + 180 = 0
x(x - 36) -5(x - 36) = 0
(x - 36)(x - 5) = 0
So, either
x - 36 = 0
x = 36
Or
x - 5 = 0
x = 5
But, the father’s age never be 5 years
Therefore, when x = 36 then
45 - x = 45 - 36 = 9
Hence, man’s present age is36 years and his son’s age is 9 years.
APPEARS IN
RELATED QUESTIONS
Solve the following quadratic equation for x : 4x2 − 4a2x + (a4 − b4) =0.
In a class test, the sum of Shefali’s marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210. Find her marks in the two subjects
Solve the following quadratic equations by factorization:
`x^2+(a+1/a)x+1=0`
Two squares have sides x cm and (x + 4) cm. The sum of this areas is 656 cm2. Find the sides of the squares.
Solve:
x(x + 1) + (x + 2)(x + 3) = 42
Solve:
`1/(x + 1) - 2/(x + 2) = 3/(x + 3) - 4/(x + 4)`
Solve the following quadratic equations by factorization:
`x^2 – (a + b) x + ab = 0`
Find the values of p for which the quadratic equation
If 2 is a root of the equation x2 + ax + 12 = 0 and the quadratic equation x2 + ax + q = 0 has equal roots, then q =
Three years ago, a man was 5 times the age of his son. Four years hence, he will be thrice his son's age. Find the present ages of the man and his son.
The area of the isosceles triangle is 60 cm2, and the length of each one of its equal side is 13cm. Find its base.
Solve equation using factorisation method:
(x + 1)(2x + 8) = (x + 7)(x + 3)
Find two consecutive positive even integers whose squares have the sum 340.
Solve the following by reducing them to quadratic form:
`sqrt(y + 1) + sqrt(2y - 5) = 3, y ∈ "R".`
In each of the following, determine whether the given values are solution of the given equation or not:
`x^2 - sqrt(2) - 4 = 0; x = -sqrt(2), x = -2sqrt(2)`
Solve the following equation by factorization
x2 – 3x – 10 = 0
Solve the quadratic equation by factorisation method:
x2 – 15x + 54 = 0
Solve the quadratic equation: x2 – 2ax + (a2 – b2) = 0 for x.
Using quadratic formula find the value of x.
p2x2 + (p2 – q2)x – q2 = 0
