Question

The father's age is six times his
hence the age of father will be four times his son’s age. Find their Present ages??

Answer 1

Correct question :

The father's age is six times his son's age. Four years hence, the age of the father will be four times his son's age. Find their present ages.

Answer:

Father's age is 36 years old and son is 6 years old.

Step-by-step explanation:

Given :

Father's age = 6 times son's age

Father will be = 4 times his son's age after 4 years

To find :

Their present ages

Solution :

Let the present ages be -

• Son's age as y
• Father as 6y

Ages 4 years hence -

• Son's age = (y + 4)
• Father's age = (6y + 4)

⇒ 6y + 4 = 4(y + 4)

⇒ 6y + 4 = 4y + 16

⇒ 6y - 4y = 16 - 4

⇒ 2y = 12

⇒ y = 12/2

⇒ y = 6

Son's age = 6 years

$\rule{300}{1.5}$

★ Father's age -

⇒ 6 × 6

⇒ 36

Father's age = 36 years

Therefore, Father's age is 36 years old and son is 6 years old.

Answer 2

Correct question :

The father's age is six times his son. Hence 4 years, the age of father will be four times his son age. Find their present ages.

$\bf{\blue{\underline{\underline{\bf{Solution\::}}}}}$

Let the present age of son's be r years.

Let the present age of father's be m years

A/q

m = 6r................(1)

$\star\bf{\underline{\underline{\bf{After\:4\:years\::}}}}}$

The son's age be = (r+4) years

The father's age be = (m+4) years

So;

$\implies\tt{(m+4)=4(r+4)}\\\\\implies\tt{m+4=4r+16}\\\\\implies\tt{6r+4=4r+16\:\:\:\:\:[From(1)]}\\\\\implies\tt{6r-4r=16-4}\\\\\implies\tt{2r=12}\\\\\implies\tt{r=\cancel{\dfrac{12}{2} }}\\\\\implies\tt{\red{r=6\:years}}$

Putting the value of r in equation (1),we get;

$\implies\tt{m=6(6)}\\\\\implies\tt{\red{m=36\:years}}$

Thus;

$\underbrace{\sf{The\:present\:age\:of\:son\:=r=6\:years}}}}}\\\underbrace{\sf{The\:present\:age\:of\:Father\:=m=(6\times 6)=36\:years}}}}}$