Question

the age of father 8 years ago was 8 times the age of his son. after 10 years the age of the father will be twice the age of the son find their present ages​

Answer 1

Answer:

• Son's present age is 11 yrs.
• Father present age is 32 yrs.

Explanation:

Given,

8 years ago father was 8 times his son's age.

Assume son's age 8 years ago as $x$ years.

∴ Father's age 8 years ago = $8x$

Their present age :-

• Son = $(x + 8)$ yrs.
• Father's = $(8x + 8)$ yrs.

After 10 years:-

• Son = $(x + 18)$ yrs.
• Father's = $(8x + 18)$ yrs.

According to the question,

$\implies \: (8x + 18) = 2(x + 18)$

Solving for $\boldsymbol x$

$\implies \: 8x + 18 = 2x + 36$

$\implies \: 8x - 2x = 36 - 18$

$\implies \: 6x = 18$

$\implies \: x = \dfrac{18}{6}$

$\implies \: x = 3$

Hence, their present age :-

• Son = $(x + 8)$ = 11 yrs.
• Father = $(8x + 8)$ = 32 yrs.

_____________________________

Answer 2

Answer:

Given :-

• The age of father 8 years ago was 8 times the age of his son.
• After 10 years the age of the father will be twice the age of the son.

To Find :-

• What is their present ages.

Solution :-

Let,

$\mapsto \sf Age_{(Son)} =\: x\: years$

$\mapsto \sf Age_{(Father)} =\: 8x\: years$

☆ After 8 years ago, their present age will be :

$\leadsto \bf Present\: Age_{(Son)} =\: (x + 8)\: years$

$\leadsto \bf Present\: Age_{(Father)} =\: (8x + 8)\: years$

☆ After 10 years, their ages will be :

$\small \longrightarrow \sf Age_{(Son)} =\: (x + 8 + 10) =\: (x + 18)\: years$

$\small \longrightarrow \sf Age_{(Father)} =\: (8x + 8 + 10) =\: (8x + 18)\: years$

According to the question :

$\bigstar$ The age of father will be twice the age of the son.

$\implies \sf \bigg\{Age_{(Father)}\bigg\} =\: 2\bigg\{Age_{(Son)}\bigg\}$

$\implies \sf (8x + 18) =\: 2(x + 18)$

$\implies \sf 8x + 18 =\: 2x + 36$

$\implies \sf 8x - 2x =\: 36 - 18$

$\implies \sf 6x =\: 18$

$\implies \sf x =\: \dfrac{18}{6}$

$\implies \sf x =\: \dfrac{3}{1}$

$\implies \sf\bold{\underline{x =\: 3}}$

Hence, the required present ages are :

$\dag$ Present Age Of Son :

$\dashrightarrow \sf Present\: Age_{(Son)} =\: (x + 8)\: years$

$\dashrightarrow \sf Present\: Age_{(Son)} =\: (3 + 8)\: years$

$\dashrightarrow \sf\boxed{\bold{Present\: Age_{(Son)} =\: 11\: years}}$

$\dag$ Present Age Of Father :

$\dashrightarrow \sf Present\: Age_{(Father)} =\: (8x + 8)\: years$

$\dashrightarrow \sf Present\: Age_{(Father)} =\: \{8(3) + 8\}\: years$

$\dashrightarrow \sf Present\: Age_{(Father)} =\: (24 + 8)\: years$

$\dashrightarrow \sf\boxed{\bold{Present\: Age_{(Father)} =\: 32\: years}}$

$\therefore$ The present age of son is 11 years and the present age of father is 32 years .