Question

Akbar age is one third of the age of the father. the sum of their age is 40. what is there age

Answer 1

let father's age = x

Akbar = 1/3rd of x = x / 3

sum of their ages = 40

(x)+ (x/ 3) = 40

4x = 120 => x = 30 yrs

Akbar's age = x/ 3 = 30/ 3 = 10 yes

father's age = x = 30 yrs

Answer 2

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

Akbar's father is 30 years old.

Akbar is 10 years old.

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

$\textsf{\large{Given :-}}$

Akbar = one third of the age of the father.

Sum of their ages = 40

$\textsf{\large{To find :-}}$

Their present ages

$\textsf{\large{Solution :-}}$

Consider the age of his father as x

So, Equation -

$\tt {\rightarrow \dfrac{1}{3}x \: + \: x = 40}$

To add the fractions, we need to make them like fractions.

To make them like fraction, we need to find the LCM

LCM of 1 and 3 = 3

$\tt{\implies \: \dfrac{x}{3} \: + \: \dfrac{3x}{3} = 40 }$

$\tt{\implies \dfrac{4x}{3} = 40}$

$\tt{\implies4x = 40 \times 3}$

$\tt{\implies4x = 120}$

$\tt{\implies \: x \: = \dfrac{120}{4} }$

$\tt{\implies \: x = \dfrac{120}{4}}$

$\tt{\implies \: x = 30}$

Therefore the age of the father is 30 years.

Akbar's age = one third of his father

$\tt{\implies \dfrac{1}{3} \: of \: 30}$

$\tt{\implies \: \dfrac{1}{3} \times 30 }$

$\tt{\implies10}$

Therefore the age of Akbar is 10 years.

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

$\tt{\implies( \dfrac{1}{3} \: of \: 30 )+ 30 = 40}$

$\tt{\implies (\dfrac{1}{3} \times 30) + 30 = 40 }$

$\tt{\implies10 + 30 = 40}$

$\tt{\implies40 = 40}$

LHS = RHS

Therefore,

$\textbf{\underline{Akbar's father is 30 years old.}}$

$\textbf{\underline{Akbar is 10 years old.}}$