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 ?

The correct option is 1 year.

Let us break down the solution step-by-step to understand how we arrive at this answer:

Step 1: Calculate the average age of the family 3 years ago
Initially, there were 5 members in the family.
The sum of the ages of these 5 members 3 years ago was 80 years.
We can find their average age 3 years ago using the formula:
Average Age = (Sum of ages) / (Number of members)

$$\text{Average age 3 years ago}=\frac{80}{5}=16\text{years}$$

Step 2: Determine the sum of the ages of the original 5 members today
In the intervening 3 years, each of the 5 original family members has aged by 3 years.
Therefore, the sum of their ages increases by:
5 members × 3 years = 15 years
So, the sum of the ages of these 5 members today is:
80 years + 15 years = 95 years.

Step 3: Analyze the family composition and average age today
Today, a baby has been added to the family, making the total number of members 6 (the 5 original members plus the baby).
According to the question, the average age of the family today is the same as it was 3 years ago.
Thus, the average age of the 6 family members today is 16 years.

Step 4: Calculate the sum of the ages of all 6 members today
Using the average age today, the sum of the ages of all 6 members today is:
Sum of ages today = Average age today × Number of members today

$$\text{Sum of ages today}=16\times 6=96\text{years}$$

Step 5: Find the age of the baby
The difference between the sum of the ages of all 6 members today and the sum of the ages of the original 5 members today gives the age of the baby:
Age of the baby = (Sum of ages of 6 members today) - (Sum of ages of 5 members today)
Age of the baby = 96 years - 95 years = 1 year.

Hence, the baby is 1 year old today.