When Ram was born, the age of his father was 32 years more than the age of his brother, and the age of his mother was 25 years more than the age of his sister. Ram's brother is currently 6 years older than Ram, and his mother is 3 years younger than his father. How old was Ram's sister when Ram was born?

Introduction / Context:
This is a family ages puzzle involving Ram, his brother, his sister, and his parents. The relationships among their ages are described at the time of Ram's birth and in the present. The goal is to find the age of Ram's sister at the time Ram was born. Such questions test understanding of constant age differences and careful interpretation of relational statements.

Given Data / Assumptions:
At the time of Ram's birth, the age of his father was 32 years more than the age of his brother. At the same time, the age of his mother was 25 years more than the age of his sister. At present, Ram's brother is 6 years older than Ram. The mother is 3 years younger than the father at present. We need the age of Ram's sister at the time of Ram's birth.

Concept / Approach:
Age differences between people do not change over time. Therefore, if Ram's brother is 6 years older than Ram now, he was also 6 years older at the time of Ram's birth. Similarly, the difference between the ages of the father and the mother is constant. By working backward to the time of Ram's birth and using the given differences, we can compute the sister's age at that time.

Step-by-Step Solution:
Step 1: At the time of Ram's birth, Ram's age was 0 years. His brother was older by 6 years, so the brother's age was 6 years.Step 2: At that time, the age of the father was 32 years more than the age of the brother. So father's age at Ram's birth = 6 + 32 = 38 years.Step 3: The mother is always 3 years younger than the father. So at Ram's birth, mother's age was 38 - 3 = 35 years.Step 4: At the time of Ram's birth, the age of the mother was 25 years more than the age of his sister. So sister's age at that time = 35 - 25 = 10 years.Step 5: Therefore, Ram's sister was 10 years old when Ram was born.

Verification / Alternative check:
We can verify the consistency. At Ram's birth: brother 6 years, sister 10 years, mother 35 years, father 38 years. The father is indeed 32 years older than the brother (38 - 6 = 32), and the mother is 25 years older than the sister (35 - 10 = 25). The mother is also 3 years younger than the father (38 - 35 = 3). Thus, all conditions match perfectly, so the answer is correct.

Why Other Options Are Wrong:
If the sister were 6 years old, the mother would be only 31 years old at Ram's birth, contradicting the 3-year difference with the father. If the sister were 8 years old or 12 years old, the difference between the mother's age and the sister's age would not be exactly 25 years. Only 10 years satisfies all the simultaneous conditions given in the problem.

Common Pitfalls:
Many learners mistakenly apply the age differences to the present instead of the time of Ram's birth, or they confuse which difference (32 or 25 years) applies to which pair of people. Another common mistake is forgetting that the difference between the parents' ages is fixed over time. Keeping track of who is older and by how many years at each stage is essential.

Final Answer:
Ram's sister was 10 years old when Ram was born.