Question

(c) The average age of a family of eight is 30 years. The average age of the six children in the family is 19 years. If the mother is four years younger than the father, calculate the age of the father.​

Answer 1

Father's age = 65 years

Explanation:

Let the age of father = x years

Age of mother = (x - 4) years

`\sf Average = (Sum \ of \ all \ the \ data)/(number \ of \ data)\\\\\boxed{\text{Sum of all data =average * number of data}}`

Average age of six children = 19 years

Sum of age of 6 children = 19 *6 = 114 years

Average of all 8 members = 30 years

Sum of age of all members = 30*8 = 240 years

sum of age of 6 children + father's age + mother's age = sum of all age of members

114 + x + x -4 = 240

110 + 2x = 240

2x = 240 -110

2x = 130

x = 130/2

x = 65 years

Father's age = 65 years