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:

Options

A. 1 year
B. `1(1/2)` year
C. 2 years
D. 3 years

Answer

To solve the problem step by step, we can follow this approach:

### Step 1: Calculate the total age of the family 3 years ago
The average age of the family 3 years ago was 17 years, and there were 5 members in the family.

Total age of the family 3 years ago = Average age × Number of members
= 17 years × 5 members
= 85 years

**Hint:** Remember that the total age can be found by multiplying the average age by the number of members.

### Step 2: Calculate the total age of the family now
Since 3 years have passed, each of the 5 members has aged 3 years. Therefore, the total increase in age for the 5 members is:

Total increase in age = 5 members × 3 years = 15 years

Now, we can find the total age of the family now:

Total age of the family now = Total age 3 years ago + Total increase in age
= 85 years + 15 years
= 100 years

**Hint:** When calculating the current age, consider how much each member has aged over the years.

### Step 3: Determine the new average age with the baby
A baby has been born, making the total number of family members 6. The average age remains the same at 17 years.

Total age of the family now with the baby = Average age × Number of members
= 17 years × 6 members
= 102 years

**Hint:** The average age remains constant, so you can use it to find the total age of the family with the new member.

### Step 4: Calculate the age of the baby
Now we know the total age of the family with the baby is 102 years, and the total age of the 5 members (without the baby) is 100 years.

To find the age of the baby:

Age of the baby = Total age with baby - Total age of the 5 members
= 102 years - 100 years
= 2 years

**Hint:** To find the age of the new member, subtract the total age of the existing members from the total age including the new member.

### Final Answer
The present age of the baby is **2 years**.