Question

The sum of the ages of 5 members comprising a family, 3 years ago, was 80 years. The average age of the family today is the same as it was 3 years ago, because of an addition of a baby during the intervening period. How old is the baby ?
(a) 6 months

 (b) 1 year 

(c) 2 years 

(d) 2 years and 6 months

Answer 1

(b) Let x₁, x₂, x₃, x₄ and x5 be the present ages of the
family comprising of 5 members 3 years ago,

(x₁ + x₂ + x₃ + x₄ + x₅) – 3 × 5 = 80
 (x₁ + x₂ + x₃ + x₄ + x₅) – 15 = 80         ...(i)
Now, let the age of new born baby be x₆.
Given,
Average age of family today = Average age of family 3 years ago