3 years ago, the average age of a family of 5 members was 17 years. A baby having been born, the average age of the family is same today. The present age of the baby is
1). 1 year
2). \(1\frac{1}{2}\) year
3). 2 years
4). 3 years
The average age of a family of 5 members was 17 years.
Sum of their ages = 17 × 5 = 85.
After, 3 years their sum of ages = 85 + 5 × 3 = 100. [?everyone in the family will get older by 3 years.]
The ratio remains same.
Let the age of the baby be ‘x’.
$(\Rightarrow \frac{{100 + x}}{6} = 17)$
⇒ 100 + x = 102
⇒ x = 102 – 100
⇒ x = 2 years.
∴ the present age of the baby = 2 years.