Question

A man's age is three times that of his son and in twelve years he will be twice as old as his son would be.What are their present ages?​

Answer 1

Answer:

The present ages of father and son are 36 years and 12 years respectively.

Step-by-step explanation:

Given :

Man's age = thrice the age of his son

After 12 years = Father will be twice the age of his son

To find :

Their present ages

Solution :

$\textsf{\underline{\underline{Let the present ages be - }}}$

• Son as y
• Father as 3y

$\rule{300}{1.5}$

$\textsf{\underline{\underline{After 12 years -}}}$

• Son = (y + 12)
• Father = (3y + 12)

$\rule{300}{1.5}$

$\textsf{\underline{\underline{According to the question -}}}$

After 12 years = Father will be twice the age of his son

$\boxed{\sf{3y + 12 = 2(y + 12)}}$

$\sf{\implies} \: 3y + 12 = 2y + 24 \\ \\ \sf{\implies} \:3y - 2y = 24 - 12 \\ \\ \sf{\implies} \:y = 12$

Son's present age = 12 years

$\rule{300}{1.5}$

★ Value of 3y

$\sf{\implies} \:3(12) \\ \\ \sf{\implies} \:36$

Father's present age = 36 years

$\therefore$ The present ages of father and son are 36 years and 12 years respectively.

Answer 2

$\Large\underline{\underline{\sf \green{Given}:}}$

• A man's age is three times that of his son and in twelve years he will be twice as old as his son would be

$\Large\underline{\underline{\sf \green{To\:Find}:}}$

• What are there present ages.

$\Large\underline{\underline{\sf \green{Solution}:}}$

Let the present age of son is x

and the present age of man is 3x

In twelve years

• Age of Son = ( x + 12 ) yrs
• Age of Man = (3x + 12) yrs

$\large\underline{\underline{\sf \pink{According\:to\: question}:}}$

He will be twice as old as his old his son :

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

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

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

$\implies{\sf x=12}$

$\Large\underline{\underline{\sf \green{Answer}:}}$

•°• Age of son is = x

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 12 years

Age of man is = 3x

⠀⠀⠀⠀⠀⠀⠀⠀⠀= 3 × 12

⠀⠀⠀⠀⠀⠀⠀⠀⠀= 36 years.

Age of Son is 12years and Age of man is 36 years.