The family at the youngest's birth — Aptitude Question
The family at the youngest's birth: The average age of a family of five is 20 years. The youngest is 5 years old. Answer and worked solution on CodeKairo.
- Topic: Problems on Ages
- Section: Quantitative Aptitude
- Difficulty: Hard
- Time target: 135 seconds
Question
The average age of a family of five is 20 years. The youngest is 5 years old. What was the average age of the family at the birth of the youngest?
Options
- 15
- 16.25
- 18.75
- 20
Show the answer and the worked solution
Correct answer: C. 18.75
Worked solution
- Present total = 5 × 20 = 100.
- The other four now total 100 − 5 = 95.
- Five years ago they totalled 95 − 4 × 5 = 75.
- Average of four = 75 ÷ 4 = 18.75.
Answer: 18.75.
The idea
Count the members who existed at that time and age each of them back individually. The youngest is excluded entirely, not aged back to zero.
Shortcut. Take five years off all five members: 100 − 25 = 75. The youngest drops to exactly 0, so 75 is the other four's total, and 75 ÷ 4 = 18.75.
Common trap. 15 comes from dividing 75 by five instead of four — the youngest adds nothing to that total, yet is still counted as a member.