Question

The sum of the ages of father and his son is $65$ years. After 5 years, fathers age will be twice the age of his son. Express this as a pair of linear equations in two variables and hence find the presents ages of father and his son.

Answer 1

Let the ages of father and his son be x and y respectively.

Case I:- The sum of the ages of father and his son is 65 years.

age of father + age of son = 65

$\Rightarrow x+y=65⟶\left(i\right)$

Case II:- After 5 years, fathers age will be twice the age of his son.

Age of father = 2 (age of son)

$\Rightarrow x+5=2(y+5)$

$\Rightarrow x+5=2y+10$

$\Rightarrow x=2y+5⟶\left(ii\right)$

From ${eq}^n\left(i\right)\&\left(ii\right)$, we have

$(2y+5)+y=65$

$\Rightarrow 3y=65-5$

$\Rightarrow y=20$

Substituting the value of y in ${eq}^n\left(i\right)$, we have

$x+20=65$

$\Rightarrow x=45$

Hence, the present age of father and son is 45 and 20 respectively and equation $\left(i\right)\&\left(ii\right)$ are the pair of linear equations in two variables.