Question

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.
​

Answer 1

SOLUTION:-

Given:

The age of a father is 2x the square of the age of his son.

8 years hence, the age of the father will be 4 years more than 3 times the age of the son.

Therefore,

Let the present age of son be x & then present age of son will be 2x²

After 8 years,

father's age = 2x² + 8

& son's age= x+8

According to the question;

=) 3(x+8)+ 4= 2x² +8

=) 3x+ 24 +4= 2x²+ 8

=) 3x + 28 = 2x² + 8

=) 3x + 28 - 8= 2x²

=) 3x + 20= 2x²

=) 2x² -3x -20= 0

=) 2x²-8x+5x-20=0 [by splitting method]

=) 2x(x-4)+ 5(x-4)=0

=) (x-4)(2x+5)=0

=) x-4=0 or 2x+5=0

=) x= 4 or x= -5/2

We know that the age can't be in negative.

So,

x= 4

Therefore,

Son's present age= 4 years.

Father's present age= 2x²

=) 2(4)²

=) 2×16

=) 32 years

So, father's present age= 32 years.

Hope it helps ☺️

Answer 2

$\Large{\textbf{\underline{\underline{According\;to\;the\;Question}}}}$

Assumption,

Present age of son = p

Also

Present age of man = 2p²

Eight years hence :-

Age of son = p + 8 years

Age of man = 2p² + 8 years.

Situation,

⇒ (2p² + 8) = 3(p + 8) + 4

⇒ 2p² - 3p - 20 = 0

⇒ 2p² - 8p + 5p - 20 = 0

⇒ 2p(p - 4) + 5(p - 4) = 0

⇒ (p - 4) (2p + 5) = 0

⇒ p - 4 = 0 or 2p + 5 = 0

⇒ p = 4, - 5/2 (Negative value is not applicable)

So,

⇒ p = 4

Present age of son = p = 4 years.

Present age of man = 2p²

= 2(4)²

= 2(16)

= 32 years.

Therefore,

Present age of son = 4 years.

Present age of man = 32 years.