Question

Kiran's brother is 5 years older to her. Her father was 30 years old when Kiran's sister was born, while her mother was 28 years old when Kiran was born. If Kiran's sister was 2 years old when her brother was born, what was the age of their father when Kiran's brother was born?

• A. 32
• B. 34
• C. 37
• D. 30

Answer 1

The Correct Option is A

The correct option is (A): 32.

Answer 2

We are asked for the father's age when Kiran's brother was born. We can work this out by picking a convenient birth year for Kiran and building a full timeline, then checking which option matches.

1. Option (A): 32: Say Kiran is born in year 0. Her brother, being 5 years older, was born in year -5. Her mother was 28 when Kiran was born, so the mother was born in year -28. Since the sister was 2 years old when the brother was born, the sister was born 2 years before the brother, in year -7. The father was 30 when the sister was born, so the father was born in year -37. The father's age when the brother was born (year -5) is -5 minus -37, which is 32 years. This matches the timeline exactly.
2. Option (B): 34: For the father to be 34 when the brother was born, the father would need to be born in year -39, which would make him 33, not 30, when the sister was born in year -7. This breaks the given condition.
3. Option (C): 37: This would put the father's birth year at -42, making him 35 when the sister was born, not 30. This does not fit the timeline either.
4. Option (D): 30: This is the father's age when the sister was born, not when the brother was born, so it does not answer the question that was actually asked.

Only 32 is consistent with every relationship given in the question.

Therefore, the correct answer is 32.

Answer 3

We need the father's age at the moment Kiran's brother was born. Instead of assigning specific birth years, we can work with the age gaps between family members directly. Let \( F \) be the father's current age, \( S \) be the sister's current age, and \( Br \) be the brother's current age (any fixed point in time works, since we only need differences). The father was 30 when the sister was born, so \( F - S = 30 \). The sister was 2 years old when the brother was born, meaning the sister is 2 years older than the brother, so \( S - Br = 2 \). Adding these two gaps gives the father's age gap over the brother: \( F - Br = (F - S) + (S - Br) = 30 + 2 = 32 \). Let's check each option against this fixed relationship.

1. Option (A): 32: This exactly matches \( F - Br = 32 \), obtained by adding the 30-year gap between father and sister to the 2-year gap between sister and brother.
2. Option (B): 34: If the father's age gap over the brother were 34, then since \( F - S = 30 \) is fixed by the question, the sister-brother gap would have to be \( 34 - 30 = 4 \) years, contradicting the given fact that the sister was only 2 years old when the brother was born.
3. Option (C): 37: This would force the sister-brother gap to be \( 37 - 30 = 7 \) years, again contradicting the stated 2-year gap between the sister's and brother's births.
4. Option (D): 30: This is the father's age gap over the sister, not the brother; it would require the sister and brother to be born in the same year (a zero-year gap), which contradicts the sister being 2 years old when the brother was born.

Since the age gaps chain together as \( F - Br = (F - S) + (S - Br) \), and both of those gaps are fixed by the question at 30 and 2 years, the father's age gap over the brother must be 32.

Therefore, the correct answer is 32.