Question

A father is three times as old as his son. In 12 years time he will be twice as old as his son. find the present ages of the father and the son.

Answer 1

Father is = x

Son is = y

x = 3y
x + 12 = 2 (12+y)
3y + 12 = 24 + 2y
3y - 2y = 24 - 12
y = 12
x = 12 × 3 = 36

∴Son's age = 12 yrs

Father's age = 36 yrs

Answer 2

Given,

• A father is three times old as his son .
• After 12 years he will be twice as old as his son .

To Find,

• Present age of the Father and son .

Solution,

⇒Suppose the present age of father be a

And , Suppose the present age of his son be b

According to First Condition of this Question :-

$\implies \boxed{\sf{a = 3b}}$.....1)

According to Second Condition of this Question :-

• Age of Father after 12 years = (a + 12) years.
• Age of son after 12 years = (b + 12) years.

$\implies \sf{a + 12 = 2(b +12)}$

$\implies \sf{a + 12 = 2b + 24}$

Put the value of a From Equation First :-

$\implies \sf{3b + 12 = 2b + 24}$

$\implies \sf{3b - 2b = 24 - 12}$

$\implies \boxed{\sf{ b = 12}}$

Now Put the value of b in Equation First :-

$\implies \sf{ a = 3b}$

$\implies \sf{ a = 3(12)}$

$\implies \boxed{\sf{ a = 36}}$

Therefore ,

$\boxed{\bold{\purple{Present \ age \ of \ Father = a = 36 \ years}}}$

$\boxed{\bold{\purple{Present \ age \ of \ Son = b = 12 \ years}}}$

$\rule{200}1$