Question

a man's present age is 8 times more than his son after 10 years he will be twice the age of his son how old is son at present

Answer 1

Answer:

Present age of son 1 year 2 months.

Step-by-step explanation:

Given :-

• A man's present age is 8 times more than his son.
• After 10 years, he will be twice the age of his son.

To find :-

• Present age of son.

Solution :-

Consider,

• Present age of son = x years

★ A man's present age is 8 times more than his son.

Then,

• Present age of the man = 8x years

After 10 years,

• Son's age = (x+10) years
• Man's age = (8x+10) years

★After 10 years, he will be twice the age of his son.

According to the question,

8x+10 = 2(x+10)

→ 8x + 10 = 2x + 20

→ 8x-2x = 20-10

→ 6x = 10

→ x = 5/3

→ x = 1 year 2 months

★ Present age of son = 1 year 2 months.

★ Present age of man = 8 × 5/3 = 40/3 = 13 years 1 month.

Answer 2

Answer:

Let the present age of son be x years.

☢ It is given that the present age of father is 8 times

Then, the present age of father is 8x.

After 10 years,

★ Son's age will be (x + 10) years

★ Father's age will be (8x + 10) years.

☢ It is given that After 10 years he will be twice the age of his son :

☯ $\underline{\boldsymbol{According\: to \:the\: Question\:now :}}$

$:\implies\sf 8x + 10 = 2(x + 10) \\\\\\:\implies\sf 8x + 10 = 2x + 20\\\\\\:\implies\sf 8x - 2x = 20 - 10\\\\\\:\implies\sf 6x = 10\\\\\\:\implies\sf x = \dfrac{10}{6}\\\\\\:\implies\underline{\boxed{\sf x = \dfrac{5}{3}\:years}}\:\:\:\Bigg\lgroup \bf{Son's \:age}\Bigg\rgroup$

$\rule{130}1$

☯ $\underline{\boldsymbol{Present\: Age\:of\: Son\:\&\:Father:}}$

$\bullet\:\:\textsf{Son's age = \textbf{1 year 2 months}}\\\bullet\:\:\textsf{Father's age = 8x + 10 = \textbf{13 year 2 months}}$