Given data or values:
The average age of 2 children is '12 years'.
The average age of the father, mother, and 2 children is '30 years'.
The father is '4 years elder than the mother.
Concept or formula used:
The average age is calculated by dividing the total age by the number of people.
Solution:
Calculate the total age of the 2 children.
⇒ Total age of 2 children = Average age of 2 children * Number of children
⇒ Total age of 2 children = 12 years * 2
⇒ Total age of 2 children = 24 years
Calculate the total age of the father, mother, and 2 children.
⇒ Total age of father, mother, and 2 children = Average age * Number of people
⇒ Total age of father, mother, and 2 children = 30 years * 4
⇒ Total age of father, mother, and 2 children = 120 years
Calculate the combined age of the father and mother.
⇒ Combined age of father and mother = Total age of father, mother, and 2 children - Total age of 2 children
⇒ Combined age of father and mother = 120 years - 24 years
⇒ Combined age of father and mother = 96 years
Calculate the age of the father.
Given that the father is 4 years elder than the mother,
Let's denote the mother's age as 'x'.
Therefore, the father's age would be 'x + 4'.
⇒ x + (x + 4) = 96
⇒ 2x = 92
⇒ x = 46 years
⇒ The father's age = x + 4 = 46 years + 4 years = 50 years
Therefore, the age of the father is 50 years.