The present ages of a father and his son are 48 years and 28.8 years respectively. The father says to his son, “I was a certain fraction of your present age when you were born.” What fraction of the son present age was the father age when the son was born?

Introduction / Context:
This problem is about relating present ages to ages at the time of birth using fractions. The father compares his age at the time his son was born to the son present age. Such questions reinforce understanding of how age differences remain constant over time and how to express one quantity as a fraction of another.

Given Data / Assumptions:

• The present age of the father is 48 years.
• The present age of the son is 28.8 years.
• We need to find what fraction of the son present age the father age was at the time of the son birth.
• Ages are in years, and fractional ages are allowed.

Concept / Approach:
The key concept is that the difference between the father age and the son age remains constant throughout their lives. To find the father age when the son was born, we subtract the son present age from the father present age. After that, we compare this age to the son present age by forming a fraction. Simplifying the fraction using basic arithmetic then lets us match it to the given options like half, two third and so on.

Step-by-Step Solution:
Step 1: The present age of the father is 48 years and the present age of the son is 28.8 years. Step 2: At the time the son was born, his age was 0, so the number of years that have passed since then is equal to the son present age, 28.8 years. Step 3: Therefore, at the time of the son birth, the father age was 48 - 28.8 years. Step 4: Compute this difference: 48 - 28.8 = 19.2 years. Step 5: We must express 19.2 as a fraction of the son present age 28.8. Step 6: Form the fraction 19.2 / 28.8. Step 7: Simplify this fraction. Divide numerator and denominator by 9.6 to get (19.2 / 9.6) / (28.8 / 9.6) = 2 / 3. Step 8: So the father age at the son birth was two third of the son present age.

Verification / Alternative check:
Consider that two third of the son present age 28.8 is (2 / 3) * 28.8 = 19.2 years. Adding the time since the son birth, which is 28.8 years, to this 19.2 gives 19.2 + 28.8 = 48 years, which is exactly the father present age. This confirms that our fraction is correct and consistent with the ages given in the question.

Why Other Options Are Wrong:
Option A (half) would mean the father was 14.4 years old at the son birth, which is not consistent with the actual difference between the present ages.
Option C (one-fifth) would give a father age of 5.76 years at the birth, which is impossible and clearly inconsistent.
Option D (one-third) would make the father 9.6 years old at the birth, which again does not match the given values or realistic age differences.

Common Pitfalls:
Some students mistakenly divide the present age difference by the father age instead of the son present age, or they may attempt to use the wrong base for the fraction. Another common mistake is to misinterpret the phrase “when you were born” and incorrectly use the son present age instead of the father age at that time. Carefully following the timeline and using the age difference concept helps avoid these errors.

Final Answer:
The father age at the time of the son birth was two-third of the son present age.