Question

Two years ago, a man's age was thrice the square of his son's age. In 3 years time, his age will be 4 times his son's age. The age of the son now is .

• A. 29 years
• B. 5 years
• C. 24 years
• D. 7 years

Answer 1

The correct option is B 5 years

Let the current ages of the father and son be $x$ and $y$ years respectively.

Then, from the first statement in the question,

$x-2=3(y-2{)}^2.$ ..............(1)

From the second statement, we have

$x+3=4(y+3).$ ............(2)

$\Rightarrow x=4y+9$

Substituting this value of $x$ in (1)

$\Rightarrow 4y+9-2=3(y-2{)}^2$

$\Rightarrow 4y+7=3(y^2-4y+4)$

$\Rightarrow 4y+7=3y^2+12-12y$

$\Rightarrow 3y^2-16y+5=0$

$\Rightarrow 3y^2-15y-y+5=0$

$\Rightarrow 3y(y-5)-(y-5)=0$

$\Rightarrow (y-5)\times (3y-1)=0$

$\Rightarrow y=5,\frac{1}{3}$

Though 5 and $\frac{1}{3}$ are both roots of the equation
Ignoring the fraction value,we have the age of son = 5 years.