Correct Answer - Option 3 : 9 years
Given:
Average age 10 years ago of five-member = 25 years
The present average age of 7 members = 27 years
Elder child = 4 years + younger child
Formula used:
Average = Sum of observation/Total number of observation
Calculation:
Sum of the age of the 5 members 10 years ago
25 × 5 = 125 years
The present age of the 5 members
125 + 5 × 10 = 175 years
The sum of the present age of 7 members
7 × 27 = 189 years
The sum of the age of the two children is
189 - 175 = 14 years
Let the age of the younger child be x years
According to the question
Elder + younger = 14
⇒ x + 4 + x = 14
⇒ x = 5 years
Age of elder child = 5 + 4 = 9 years
∴ The age of the elder child is 9 years.