Runs needed to raise the average — Aptitude Question
Runs needed to raise the average: A cricketer has an average of 48 runs in 12 innings. How many runs must he score… Answer and worked solution on CodeKairo.
- Topic: Averages
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 60 seconds
Question
A cricketer has an average of 48 runs in 12 innings. How many runs must he score in the 13th innings to raise his average by 5?
Options
- 93
- 103
- 113
- 123
Show the answer and the worked solution
Correct answer: C. 113
Worked solution
- Required total = 13 × 53 = 689.
- Present total = 12 × 48 = 576.
- Runs needed = 689 − 576 = 113.
Answer: 113.
The idea
Shortcut: new average + (old count × rise) = 53 + 12 × 5 = 113. The innings must reach the new average and also lift every earlier innings by the increase.
Shortcut. Runs needed = old average + new innings count × rise = 48 + 13 × 5 = 113.
Common trap. "103" — it looks close enough, but it would lift the average by only (103 − 48) ÷ 13 ≈ 4.2, not 5.