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.**