Question

The sum of the ages of son and father is 56 years . after 4 years ,the age of the son will be one -third of his father .find the age of the father

Answer 1

$\Large{\underline{\underline{\bf{GIVEN:-}}}}$

• The sum of the ages of son and father is 56 years.
• After 4 years, the age of the son will be one -third of his father.

$\Large{\underline{\underline{\bf{TO \: FIND:-}}}}$

• What is the age of the father ?

$\Large{\underline{\underline{\bf{SOLUTION:-}}}}$

Let the present age of Father be 'x' years and the age of son be 'y' years

CASE:- 1)

◇ The sum of the ages of son and father is 56 years.

According to question:-

➾ x + y = 56....❶

➾ x = 56 –y

CASE:- 2)

◇ After 4 years, the age of the son will be one -third of his father.

• Father's age = (x + 4) years
• Son's age = (y + 4) years

According to question:-

➾ $\sf{ (y +4) = \dfrac{1}{3} (x+4)}$

➾ 3(y + 4) = x + 4

➾ 3y + 12 = x + 4

➾ 12–4 = x –3y

➾ 8 = x –3y....❷

Put the value of 'x' from equation 1) in equation 2)

➾ 8 = 56 –y –3y

➾ 8 –56 = –4y

➾ –48 = –4y

➾ $\sf{\cancel\dfrac{-48}{-4} = y}$

⠀⠀⠀❛ 12 = y ❜

Put the value of 'y' in equation 1)

➾ x + 12 = 56

➾ x = 56 –12

⠀⠀⠀❛ x = 44 ❜

❝ Hence, the age of Father is 44 years and that of the age of son is 12 years ❞

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