Twice As Old in 20 Years

Let the father's age be $f$ .

Let the sun's age be $s$ .

$f=4s$

$f+20=2*(s+20)=2s+40$

$f=2s+20$

$f=0.5f+20$

$0.5f=20$

$f=40$

$F=current~age~of~the~father$

$S=current~age~of~the~son$

$F=4S$ $\implies$ $S=\dfrac{F}{4}$ $\color{#D61F06}(1)$

$F+20=2(2S+40)$ $\color{#D61F06}(2)$

Substitute $\color{#D61F06}(1)$ in $\color{#D61F06}(2)$ .

$F-2S=40-20$

$F-2\left(\dfrac{F}{4}\right)=20$

$F-\dfrac{F}{2}=20$

$\color{#3D99F6}\boxed{F=40~years~old}$

Let present age of son be x yrs then his father's age is 4x yrs. After 20 yrs his father's age is twice the age of the son then. So, 4x + 20=2(x + 20), from this we get x = 10, and 4x = 40 Hence his father's age is 40 yrs.

Let $s$ be the son's current age and $f$ be the father's current age. Then,

$4s = f$

$2(s+20) = f+20\quad2s+40 = f+20\quad s = \frac{f-20}{2}$

$4(\frac{f-20}{2}) = f\quad2f-40 = f\quad f=\boxed{40}$

let father age is x and son is y as per question. today x= 4y after 20 years x+20 = 2y x= 4y x+20 = 2y --------------subtractive the equation 20 = 2y y = 10 by x= 4y x= 40