Three years ago, the average age of a family of six members was 19 years. Since then a boy has been born and the average age of the family is the same today as it was three years ago. What is the age of the boy?

Correct option is D

​Given:

3 years ago, average age = 19

Number of members = 6.

A boy was born since then, and the average remains the same today.

Formula Used:

​$$\text{Total age} = \text{Average} \times \text{Number of members}$$​​

Solution:

Total age 3 years ago:

​$$\text{Total age} = 19 \times 6 = 114 \, \text{years}$$​​

Today, each of the 6 members has aged 3 years, so:

​$$\text{Total age} = 114 + (6 \times 3) = 114 + 18 = 132 \, \text{years}$$​​

With the boy added:

​$$\text{Average today} = \frac{132 + \text{Boy's age}}{7}$$​​

Since the average remains 19:

​$$\frac{132 + \text{Boy's age}}{7} = 19$$

​$$132 + \text{Boy's age} = 133 \\ \ \\ \Rightarrow \quad \text{Boy's age} = 1 \, \text{year}$$​​