A number was misread — Averages Aptitude Question
A number was misread: The average of 10 numbers was calculated as 42. It was then found that one number, 64, had… Answer and worked solution on CodeKairo.
- Topic: Averages
- Section: Quantitative Aptitude
- Difficulty: Easy
- Time target: 45 seconds
Question
The average of 10 numbers was calculated as 42. It was then found that one number, 64, had been read as 46. What is the correct average?
Options
- 43.2
- 43.8
- 44.0
- 44.2
Show the answer and the worked solution
Correct answer: B. 43.8
Worked solution
- The total was short by 64 − 46 = 18.
- The average rises by 18 ÷ 10 = 1.8.
- Correct average = 42 + 1.8 = 43.8.
Answer: 43.8.
The idea
A corrected entry changes the average by (correct − wrong) ÷ n. Never recompute the whole total.
Shortcut. 64 and 46 are the same digits swapped, and a swap always errs by 9 × the digit gap = 9 × 2 = 18, so the average rises by 1.8.
Common trap. 44.2 — subtracting 46 from 64 digit by digit without borrowing (22 instead of 18), so the rise becomes 2.2.