Question

A father is 3 times as old as his son. In 12 years times he will be twice as old as his son. Find the present ages of father and son.\

Answer 1

$\mathfrak{\large{\underline{\underline{Answer :- }}}}$

The Presnet Ages of Father and Son are 36 years and 12 Years respectively.

$\mathfrak{\large{\underline{\underline{Explanation :-}}}}$

Given :

Presently, Father is 3 times old as his son

12 years later, Father will be twice the age of Son.

◆ $\textbf{\small{\underline{Consider the Present ages as -}}}$

• Son as x
• Father as 3x

◆ $\textbf{\small{\underline{12 Years later -}}}$

• Son will be (x + 12)
• Father will be (3x + 12)

◆ $\textbf{\small{\underline{According to the Question -}}}$

After 12 years, father will be twice as old as his son.

★ $\boxed{\bf{(3x + 12) = 2(x + 12)}}$

$\longrightarrow$ (3x + 12) = 2(x + 12)

$\longrightarrow$ 3x + 12 = 2x + 24

$\longrightarrow$ 3x - 2x = 24 - 12

$\longrightarrow$ x = 12

Son's present age is 12 Years.

$\rule{300}{1.5}$

★ Value of 3x

$\longrightarrow$ 3 × 12

$\longrightarrow$ 36

Father's present age is 36 years.

$\therefore$ The Presnet Ages of Father and Son are 36 years and 12 Years respectively.

$\rule{300}{1.5}$

$\mathfrak{\large{\underline{\underline{Verification :-}}}}$

Place the Value of x in the Equation and check of both the sides of the equation are same or not.

$\longrightarrow$ (3x + 12) = 2(x + 12)

$\longrightarrow$ 3(12) + 12 = 2(12 + 12)

$\longrightarrow$ 36 + 12 = 24 + 24

$\longrightarrow$ 48 = 48

$\longrightarrow$ LHS = RHS

$\therefore$ The Presnet Ages of Father and Son are 36 years and 12 Years respectively.

Answer 2

Answer:-

Present age of son = 12 years

Present age of Father = 36 years

Explanation:-

Given

Father age = 3 times the age of son

After, 12 years

father age = 2 times the age of son

To Find

Present ages of son and father

Solution

Let,

son's age be x

fathers's age be 3x

After 12 years

Age of father = (3x+12) years

Age of son = (x+12) years

Acc. to the question

$\mathsf{3x+12 = 2(x+12)}$

$\mathsf{3x+12 = 2x+24}$

$\mathsf{3x -2x = 24 - 12}$

$\mathsf{ x = 12}$

Present age of son = 12 years

Now

Father's present age = 3x

Father's present age = 3(12) = 36 years