When Rajesh was born, his father was 30 years older than his brother, and his…
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When Rajesh was born, his father was 30 years older than his brother, and his mother was 25 years older than his sister. If Rajesh's brother is 5 years older than Rajesh, and his mother is 4 years younger than his father, how old was Rajesh's sister when Rajesh was born?
- A.
10 years
- B.
9 years
- C.
8 years
- D.
6 years
Attempted by 15 students.
Show answer & explanation
Correct answer: D
Concept: In age-comparison problems, the difference in age between two people stays constant over time. If one person is a fixed number of years older or younger than another, that gap holds at every point in their lives, including a past moment such as another person's birth — so every stated "is X years older/younger than" relationship can be converted into a fixed offset and combined directly.
Application:
Rajesh's brother is 5 years older than Rajesh, a constant gap, so at the moment Rajesh was born, the brother was already 5 years old.
At that same moment, the father was 30 years older than the brother, so the father's age then = 5 + 30 = 35.
The mother is 4 years younger than the father, a constant gap, so the mother's age at that moment = 35 minus 4 = 31.
At that same moment, the mother was 25 years older than the sister, so the sister's age then = 31 minus 25 = 6.
Cross-check: Working back from these figures confirms every stated relationship: 35 minus 5 = 30 (father is 30 years older than brother), and 31 minus 6 = 25 (mother is 25 years older than sister) — both hold exactly, so the chain is consistent.
Answer: Rajesh's sister was 6 years old when Rajesh was born.