Question

Eight years ago, average age of 3 members of a family was 39 years. Two children were born and the average age of a family of 5 members becomes 30 years. If the age difference of children is 1 year. Then find the age of the younger child.
1. 5 years
2. 6 years
3. 4 years
4. 7 years

Answer 1

Correct Answer - Option 3 : 4 years

Given

Average age of 3 members of a family, 8 years ago = 39 years

Concept used

Average = Sum of all observation/ Number of observation

Calculation

Sum of the ages of 3 members, 8 years ago = 3 × 39

⇒ 117

Sum of the ages of 3 members, now = (3 × 39 + 8 × 3)

⇒ 117 + 24

⇒ 141

Sum of the ages of 5 members = 30 × 5

⇒ 150

Sum of the ages of children = 150 - 141

⇒ 9

According to question

let the age of younger child is x years and age of elder child is (x + 1) years

x + (x + 1) = 9

⇒ 2x = 9 - 1

⇒ 2x = 8

⇒ x = 4

∴ Age of younger children is 4 years.