When Ranjeev was born, his father was 32 years older than his brother and his mother was 25 years older than his sister. If Ranjeev's brother is 6 years older than Ranjeev and his mother is 3 years younger than his father, how old was Ranjeev's sister when he was born?

Options

A. 15 years
B. 14 years
C. 7 years
D. 10 years

Answer

To solve the problem step by step, we will define the ages of Ranjeev and his family members at the time of his birth.

### Step-by-Step Solution:

1. **Define Variables**:
- Let Ranjeev's age when he was born be \( R = 0 \) (since we are considering the time of his birth).
- Let Ranjeev's brother's age when Ranjeev was born be \( B \).
- Let Ranjeev's father's age when Ranjeev was born be \( F \).
- Let Ranjeev's mother's age when Ranjeev was born be \( M \).
- Let Ranjeev's sister's age when Ranjeev was born be \( S \).

2. **Establish Relationships**:
- From the problem, we know:
- Ranjeev's brother is 6 years older than Ranjeev:
\[ B = R + 6 = 0 + 6 = 6 \]
- Ranjeev's father is 32 years older than Ranjeev's brother:
\[ F = B + 32 = 6 + 32 = 38 \]
- Ranjeev's mother is 3 years younger than his father:
\[ M = F - 3 = 38 - 3 = 35 \]
- Ranjeev's mother is 25 years older than his sister:
\[ M = S + 25 \implies S = M - 25 = 35 - 25 = 10 \]

3. **Conclusion**:
- Therefore, Ranjeev's sister was **10 years old** when he was born.

### Final Answer:
Ranjeev's sister was 10 years old when he was born.

---