Question

Four years ago father's age was 6 times that of his son. Twelve years from now. father's age will be twice that of the son. What is the ratio of father and son's present ages ?

• A. $6:1$
• B. $7:1$
• C. $8:2$
• D. $7:2$

Answer 1

The correct option is D $7:2$

Let $x$ and $y$ be the present age of father and son respectively.

Now according to the question-

Condition I:- Four years ago father's age was $6$ times that of his son, i.e.,

$(x-4)=6(y-4)$

$x-4=6y-24$

$x-6y=-20.....\left(1\right)$

Condition II:- Twelve years from now. father's age will be twice that of the son.

$(x+12)=2(y+12)$

$x+12=2y+24$

$x-2y=12.....\left(2\right)$

Dividing equation $\left(1\right)$ by $\left(2\right)$, we have

$\frac{x-6y}{x-2y}=\frac{-20}{12}$

$\frac{\left(\frac{x}{y}\right)-6}{\left(\frac{x}{y}\right)-2}=\frac{-5}{3}$

$3(\left(\frac{x}{y}\right)-6)=-5(\left(\frac{x}{y}\right)-2)$

$3\left(\frac{x}{y}\right)-18=-5\left(\frac{x}{y}\right)+10$

$\Rightarrow 8\left(\frac{x}{y}\right)=28$

$\Rightarrow \frac{x}{y}=\frac{28}{8}=\frac{7}{2}$

Hence the ratio of father and son's present ages is $7:2$.