Question

the age of a father is seven times the age of this Sun .is the Sun of their age is 32 years find the age of each of them

Answer 1

$\textbf{\underline{\underline{Answer :-}}}$

The age of the Son is 4 years and father is 28 years.

$\textbf{\underline{\underline{Explanation :-}}}$

Given :

Age of father = 7 times the age of son

Sum of their ages = 32 years

To find :

Their ages

Solution :

Consider the age of the Son as x

Consider the age of the father as 7x

Equation :

$\tt{\implies7x + x = 32}$

$\tt{\implies8x = 32}$

$\tt{\implies \: x = \dfrac{32}{8} }$

$\tt{\implies \: x = 4}$

${\boxed{\bigstar{\sf\:{x = 4}}}}$

Value of 7x

$\tt{\implies \: 7 \times x}$

$\tt{\implies \: 7\times4}$

$\tt{\implies \: 28}$

${\boxed{\bigstar{\sf\:{Father \: is \: 28 \: years \: old}}}}$

${\boxed{\bigstar{\sf\:{Son \: is \: 4 \: years \: old}}}}$

$\therefore$ The age of the Son is 4 years and father is 28 years.

$\textbf{\underline{\underline{Verification :-}}}$

$\tt{\implies(7 \times 4) + 4 = 32}$

$\tt{\implies28 + 4 = 32}$

$\tt{\implies32 = 32}$

Here, we placed the value of x (4) and got the required answer 32

${\boxed{\sf\:{LHS = RHS}}}$

$\therefore$ The age of the Son is 4 years and father is 28 years.

Answer 2

$\bf\huge\textbf{\underline{\underline{According\:to\:the\:Question}}}$  

Age of father is 7 times the age of son  

Sum of their ages is 32 years

Suppose the age of son be p and father be 7p

$\bf\huge\bf\huge{\boxed{\bigstar{{Put\: it\: in\: an\: Equation}}}}$

7 p + p = 32

8p = 32

$\tt{\rightarrow p = \dfrac{32}{8}}$    

p = 4

Put in in the father age

= 7p

= 7(4)

= 28

$\bf\huge\bf\huge{\boxed{\bigstar{{Son \:age = 4}}}}$        

$\bf\huge\bf\huge{\boxed{\bigstar{{Father\:age=\:28}}}}$