Three years ago, the average age of a family of five members was 17 years. A new baby was born after that, and today the average age of the family remains the same as before. What is the present age, in years, of the baby?

Introduction / Context:
This question is about averages and ages in a family before and after the birth of a child. Such problems commonly appear in aptitude tests because they combine the concept of average with changes in group size. Understanding how the total sum of ages changes while the average may remain constant is essential for solving these questions quickly and correctly.

Given Data / Assumptions:

• Three years ago, there were 5 family members and their average age was 17 years.
• After that, a baby was born, so now there are 6 family members.
• The current average age of the 6 members is still 17 years.
• We must find the present age of the baby in years.
• All ages are measured in years and are non negative.

Concept / Approach:
Average age is defined as total sum of ages divided by the number of people. When we know the average, we can easily compute the total sum. Over time, ages of existing members increase, which changes the total sum even if the average remains the same. By writing expressions for total ages three years ago and today, and then comparing them, we can isolate the contribution of the baby and calculate the baby age.

Step-by-Step Solution:
Step 1: Three years ago, there were 5 members with an average age of 17 years, so the total age then was 5 * 17 = 85 years. Step 2: In the next three years, each of those 5 members became 3 years older, adding 3 * 5 = 15 years to the total. Step 3: Therefore, the total age of the original 5 members today is 85 + 15 = 100 years. Step 4: Now there are 6 members (including the baby) and the current average age is still 17 years. Step 5: So the total age of all 6 members today is 6 * 17 = 102 years. Step 6: The total age contributed by the baby today is 102 - 100 = 2 years. Step 7: Therefore the present age of the baby is 2 years.

Verification / Alternative check:
To verify, distribute the total ages. The 5 original members currently have 100 years combined, and the baby has 2 years, so the total is 102 years. Dividing 102 by 6 gives 17, matching the stated average. This confirms that 2 years is the correct age for the baby. No contradictions arise from this value, so the solution is sound.

Why Other Options Are Wrong:
Option B (2.4 years) would mean the total age of all 6 members is 100 + 2.4 = 102.4 years, which does not give an average of exactly 17 years.
Option C (3 years) would make the total 103 years, giving an average of 103 / 6 which is greater than 17, so it is wrong.
Option D (1.5 years) would give a total of 101.5 years and again the average would not be exactly 17 years, so this option is incorrect.

Common Pitfalls:
Students often forget to increase the ages of the original members over the three year period, or they directly assume the baby age is 3 years because three years have passed. It is also common to confuse the number of family members at different times. Always compute totals step by step and pay close attention to how many members are present at each moment.

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