Question

11. A father is three times as old as his son. In 12 years time, he will be twice as old as his son. Find
their present ages.​

Answer 1

Answer:

12, 36

Step-by-step explanation:

Father's Age = 3 * Son's Age

After 12 Year's

Father's Age +12 years = 2 (son's age +12years)

3 * Son's Age +12 years = 2 (son's age +12years)

3 * Son's Age +12 years = 2 * son's age + 24years

Son's Age = 12 years

Father's Age = 3 * Son's Age

Father's Age = 3 * 12 = 36 years

Answer 2

Given :

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

To Find :

• Present age of Father
• Present age of Son.

Solution :

Let the present age of Father be x years.

Let the present age of son be y years.

Case 1 :

Father's age is three times the age of son.

Equation :

$\sf{\longrightarrow{x=3y}}$

$\sf{\dfrac{x}{3}=y\:\:\:\:(1)}$

Case 2 :

In 12 years, the age of father will be twice the age of son.

Age of Father after 12 years, (x+12) years.

Age of son after 12 years, (y+12) years.

Equation :

$\sf{\longrightarrow{(x+12)=2(y+12)}}$

$\sf{\longrightarrow{x+12=2y+24}}$

$\sf{\longrightarrow{x-2y=24-12}}$

$\sf{\longrightarrow{x-2y=12}}$

$\sf{\longrightarrow{x-2\Big(\dfrac{x}{3}\Big)=12}}$

$\sf{\longrightarrow{x-\Big(\dfrac{2x}{3}\Big)=12}}$

$\sf{\longrightarrow{x-\dfrac{2x}{3}=12}}$

$\sf{\longrightarrow{\dfrac{3x-2x}{3}=12}}$

$\sf{\longrightarrow{\dfrac{x}{3}=12}}$

$\sf{\longrightarrow{x=12\:\times\:3}}$

$\sf{\longrightarrow{x=36}}$

Substitute, x = 36 in equation (1),

$\sf{\longrightarrow{\dfrac{x}{3}=y}}$

$\sf{\longrightarrow{\dfrac{36}{3}=y}}$

$\sf{\longrightarrow{y=12}}$

$\large{\boxed{\bold{Present\:age\:of\:father\:=\:x\:=\:36\:years}}}$

$\large{\boxed{\bold{Present\:age\:of\:son\:=\:y\:=\:12\:years}}}$