A number was misread — Averages Aptitude Question
A number was misread: The average of 10 numbers was found to be 42. It was later noticed that 64 had been read as 46. Answer and worked solution on CodeKairo.
- Topic: Averages
- Section: Quantitative Aptitude
- Difficulty: Easy
- Time target: 50 seconds
Question
The average of 10 numbers was found to be 42. It was later noticed that 64 had been read as 46. What is the correct average?
Options
- 43.2
- 43.8
- 44.0
- 44.4
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 shifts the average by (correct − wrong) ÷ n. There is never any need to recompute the whole total.
Shortcut. Swapped digits change a number by 9 × their difference: 64 − 46 = 9 × 2 = 18, and 18 over 10 numbers adds 1.8.
Common trap. "44.0" — rounding the correction 18 ÷ 10 = 1.8 up to 2.