1.

The average age of family of 4 members 5 years ago was 16 years. With the birth of a baby, the average of family is 1 more than what it was 5 years ago. Find the age of the baby.1). 1 year2). 2 years3). 3 years4). 4 years

Answer»

We know that, average = SUM of all quantities/Number of quantities

Average age of family = Sum of ages of all family members/Number of members

∴ 16 = Sum of ages of 4 family members five years AGO/4

⇒ Sum of ages of 4 family members 5 years ago = 4 × 16 = 64

In five years, each of these 4 members’ ages have increased by 5.

∴ Sum of present ages of 4 family members = Sum of ages of 4 family members 5 years ago + (5 × 4)

∴ Sum of present ages of 4 family members = 64 + 20 = 84

Let the age of the BABY be X years.

∴ Sum of present ages of all family members including baby = 84 + x

According to the information given in the question, average present age of family members including baby, is 1 more than what it was 5 years ago excluding baby, i.e. 16 + 1 = 17

∴ Average = 17

⇒ 17 = (84 + x)/5

⇒ 84 + x = 17 × 5 = 85

⇒ x = 1

∴ the age of the baby is 1 year.


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