Question

A man is 5 times old as his son.2 years ago the sum of the square of their ages was 114 .find the present age of son?

Answer 1

Answer:

Say son is s years

so papa is 5s

now s-2 square

+ (5s-2) squared

=114

Explanation:

so s^2 + 4 - 4s +

25s^2 +4-20s=114

or 26s^2 +8-24s=114

so by solving this quadratic equation we can get s

which is age of son.

Answer 2

From the given details, the son is 2 and a half years old presently.

Given:

Man is 5 times old as his son.

The sum of their ages two years ago was 114.

To find:

The present age of the son.

Solution:

Let the present age of the son = x

Let the present age of the man = y

Given y = 5x

Also given, two years ago

           ⇒ (x-2)² + (y-2)² = 114  

           ⇒ (x-2)² + (y-2)² = 114

           ⇒ x² - 4x + 4 + y² - 4y + 4 = 114

           ⇒ x² + y² -4(x+y) + 8 = 114

Replacing y with 5x

           ⇒ x² + 25x² - 4x -20x + 8 = 114

           ⇒ 26x² - 24x = 108

Solving this equation using the factorization method for quadratic equations, the value of x is found to be approximately 2.5.

Then according to this given problem;

The son's present age is 2 and a half years and The man is 12 and a half years old presently.