The weight of B — Averages Aptitude Question
The weight of B: The average weight of A, B and C is 45 kg. The average of A and B is 40 kg and of B and C is 43 kg. Answer and worked solution on CodeKairo.
- Topic: Averages
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 90 seconds
Question
The average weight of A, B and C is 45 kg. The average of A and B is 40 kg and of B and C is 43 kg. What is B's weight?
Options
- 17 kg
- 20 kg
- 26 kg
- 31 kg
Show the answer and the worked solution
Correct answer: D. 31 kg
Worked solution
- A + B + C = 135; A + B = 80; B + C = 86.
- (A + B) + (B + C) = 166, which is (A + B + C) + B.
- B = 166 − 135 = 31 kg.
Answer: 31 kg.
The idea
Adding the two pair totals counts B twice; subtracting the three-person total leaves B alone. This is faster than solving for A and C first.
Shortcut. Take C out first: C = 135 − 80 = 55 from the three-person and A–B totals, then B = 86 − 55 = 31 kg.
Common trap. "26 kg" — it keeps B well below both pair averages and looks plausible, but it makes A = 54 and C = 60, and 54 + 26 + 60 = 140, not 135.