Focused Study for Competitive Exams
Average – Shortcut Tricks & Tough Problems
Average is one of the easiest and fastest scoring topics in bank exams. Master shortcuts to solve quickly.
1. Basic Concept
Average = Total Sum ÷ Number of Items
Example:
Average of 10, 20, 30 = (10+20+30)/3 = 20
2. Shortcut Trick
If all values are equal, average = same value
Example:
Average of 5 numbers is 20
Total = 5 × 20 = 100
3. Assumed Mean Method
Useful for large data
Example:
Numbers: 48, 49, 50, 51, 52
Assume mean = 50
Deviations = -2, -1, 0, +1, +2
Sum = 0
Average = 50
4. Combined Average
Formula:
( n₁×a₁ + n₂×a₂ ) ÷ (n₁ + n₂)
Example:
Group1 → 5 students avg 20
Group2 → 5 students avg 30
Total = (100 + 150) ÷ 10 = 25
Tough Problems
Q1:
Average of 8 numbers is 15. If one number is removed, average becomes 14. Find removed number.
Solution:
Total = 8 × 15 = 120
New total = 7 × 14 = 98
Removed number = 120 - 98 = 22
Q2:
Average of first 10 numbers is 20. Find average of next 10 numbers if total average is 25.
Solution:
Total (20 numbers) = 20 × 25 = 500
First 10 = 10 × 20 = 200
Next 10 = 300 → Average = 30
Q3:
The average age of 5 people is 30. A new person joins, average becomes 32. Find age of new person.
Solution:
Old total = 5 × 30 = 150
New total = 6 × 32 = 192
New person = 192 - 150 = 42
Exam Strategy
- Use total = average × number
- Avoid adding all values directly
- Use assumed mean for speed
- Focus on difference method
Quantitative Aptitude • Bank Exams • Competitive Preparation
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