One person is replaced — Averages Aptitude Question
One person is replaced: The average weight of 8 people increases by 2.5 kg when a person weighing 65 kg is replaced… Answer and worked solution on CodeKairo.
- Topic: Averages
- Section: Quantitative Aptitude
- Difficulty: Easy
- Time target: 50 seconds
Question
The average weight of 8 people increases by 2.5 kg when a person weighing 65 kg is replaced by someone new. What is the new person's weight?
Options
- 75 kg
- 80 kg
- 85 kg
- 90 kg
Show the answer and the worked solution
Correct answer: C. 85 kg
Worked solution
- Rise in total = 8 × 2.5 = 20 kg.
- New person = 65 + 20 = 85 kg.
Answer: 85 kg.
The idea
A swap changes the total by n × (change in average). Add that to the departing member's value; the count itself never changes.
Shortcut. The newcomer must match the leaver and add 2.5 kg for each of the 8 people: 65 + 20 = 85 kg.
Common trap. "75 kg" — it looks like a sensible 10 kg rise, but 10 kg shared by 8 people lifts the average by only 1.25 kg.