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The average age of a five-member family 10 years ago was 25 years. Meanwhile 2 children were born. At present, the number of members in this family is 7 and the average age of the family is 27 years. It is known that if the older child is 4 years older than the younger child, then what will be the age of the older child?
1. 18 years 
2. 7 years 
3. 9 years 
4. Cannot be determined

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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.

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