Question:medium

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?

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Translate all statements into fixed \emph{age gaps}; add or subtract gaps to move between births, then shift the known parent’s age accordingly.
Updated On: Jul 15, 2026
  • 32
  • 34
  • 37
  • 30
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The Correct Option is A

Approach Solution - 1

Step 1: Set Kiran's birth year as year 0. Since the brother is 5 years older than Kiran, the brother was born in year \( -5 \).

Step 2: Since the sister was 2 years old when the brother was born, the sister is 2 years older than the brother, so the sister was born in year \( -5-2=-7 \).

Step 3: The father was 30 years old when the sister was born, in year \( -7 \). By the brother's birth, in year \( -5 \), 2 more years have passed, so the father's age at that point is \( 30+2=32 \).
\[ \boxed{32} \]
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Approach Solution -2

We can assign concrete calendar years to check this cleanly. Suppose Kiran was born in the year 2000. Since the brother is 5 years older, he was born in 1995, and since the sister is 2 years older than the brother, she was born in 1993. We can test each option by treating it as the father's birth year offset and checking whether it puts him at exactly 30 years old in 1993.

  1. 32: If the father was 32 in 1995, he was born in \( 1995-32=1963 \), making his age in 1993 equal to \( 1993-1963=30 \), matching the given fact exactly.
  2. 34: If the father was 34 in 1995, he was born in \( 1995-34=1961 \), making his age in 1993 equal to \( 1993-1961=32 \), not the given 30.
  3. 37: If the father was 37 in 1995, he was born in \( 1995-37=1958 \), making his age in 1993 equal to \( 1993-1958=35 \), not 30.
  4. 30: If the father was 30 in 1995, he was born in \( 1995-30=1965 \), making his age in 1993 equal to \( 1993-1965=28 \), not 30.

Fixing concrete birth years for each sibling shows that only a father's age of 32 at the brother's birth is consistent with him being exactly 30 two years earlier, at the sister's birth.

Therefore, the correct answer is 32.

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