Average
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Solved Examples
Study MaterialSolved Examples – Average
Solved examples help students understand the practical application of Average concepts in competitive examinations. These examples are designed from basic to advanced level and cover important questions frequently asked in SSC, Banking, Railway, CDS, NDA, CAT, UPSC, and placement aptitude tests.
Topics Covered in Solved Examples
- Basic Average Problems
- Consecutive Number Averages
- Average Age Problems
- Addition and Removal Concepts
- Replacement Problems
- Average Speed Problems
- Weighted Average
- Arithmetic Progression Concepts
- Deviation Method
- Combined Average Problems
Example 1: Basic Average Calculation
Question: Find the average of 12, 18, 24, and 30.
Solution:
Average = Sum of observations / Number of observations
= (12 + 18 + 24 + 30) / 4
= 84 / 4
= 21
Example 2: Average of Consecutive Numbers
Question: Find the average of numbers from 21 to 31.
Solution:
For consecutive numbers:
Average = (First Number + Last Number) / 2
= (21 + 31) / 2
= 52 / 2
= 26
Example 3: Average of First n Natural Numbers
Question: Find the average of first 50 natural numbers.
Solution:
Formula:
Average = (n + 1) / 2
= (50 + 1) / 2
= 51 / 2
= 25.5
Example 4: Average of First n Odd Numbers
Question: Find the average of first 15 odd numbers.
Solution:
Formula:
Average = n
Therefore:
Average = 15
Example 5: Average of First n Even Numbers
Question: Find the average of first 20 even numbers.
Solution:
Formula:
Average = n + 1
= 20 + 1
= 21
Example 6: Average Age Problem
Question: The average age of 5 students is 18 years. Find their total age.
Solution:
Total age = Average × Number of students
= 18 × 5
= 90 years
Example 7: Addition of a New Member
Question: The average age of 10 students is 16 years. A new student joins and the average becomes 17 years. Find the age of the new student.
Solution:
Old total age:
= 10 × 16
= 160
New total age:
= 11 × 17
= 187
Age of new student:
= 187 − 160
= 27 years
Example 8: Removal of a Member
Question: The average weight of 8 persons is 65 kg. One person leaves and the average becomes 63 kg. Find the weight of the person who left.
Solution:
Original total weight:
= 8 × 65
= 520
New total weight:
= 7 × 63
= 441
Weight of removed person:
= 520 − 441
= 79 kg
Example 9: Replacement Problem
Question: The average of 12 numbers is 40. If one number 56 is replaced by 80, find the new average.
Solution:
Increase in total:
= 80 − 56
= 24
Increase in average:
= 24 / 12
= 2
New average:
= 40 + 2
= 42
Example 10: Average Speed for Equal Distances
Question: A person travels equal distances at 40 km/h and 60 km/h. Find the average speed.
Solution:
Formula:
Average Speed = 2AB / (A + B)
= (2 × 40 × 60) / (40 + 60)
= 4800 / 100
= 48 km/h
Example 11: Average Speed for Three Equal Distances
Question: A person travels equal distances at 30 km/h, 15 km/h, and 10 km/h. Find the average speed.
Solution:
Formula:
Average Speed = 3ABC / (AB + BC + CA)
= (3 × 30 × 15 × 10) / (450 + 150 + 300)
= 13500 / 900
= 15 km/h
Example 12: Weighted Average
Question: The average marks of 30 students is 60 and the average marks of 20 students is 80. Find the combined average.
Solution:
Combined average:
= [(30 × 60) + (20 × 80)] / (30 + 20)
= (1800 + 1600) / 50
= 3400 / 50
= 68
Example 13: Arithmetic Progression Average
Question: Find the average of:
7, 12, 17, 22, 27
Solution:
These numbers are in arithmetic progression.
Middle term = 17
Therefore:
Average = 17
Example 14: Deviation Method
Question: Find the average of:
48, 49, 50, 51, 52
Solution:
Take base = 50
Deviations:
−2, −1, 0, +1, +2
Sum of deviations = 0
Average = 50
Example 15: Average with Zero Included
Question: Find the average of 0, 12, and 24.
Solution:
Average:
= (0 + 12 + 24) / 3
= 36 / 3
= 12
Example 16: Combined Group Average
Question: The average age of 15 boys is 14 years and the average age of 10 girls is 12 years. Find the average age of the entire group.
Solution:
Total age of boys:
= 15 × 14
= 210
Total age of girls:
= 10 × 12
= 120
Combined average:
= (210 + 120) / 25
= 330 / 25
= 13.2 years
Example 17: Missing Number in Average
Question: The average of 5 numbers is 24. Four numbers are 20, 22, 26, and 28. Find the fifth number.
Solution:
Total sum:
= 24 × 5
= 120
Sum of known numbers:
= 20 + 22 + 26 + 28
= 96
Missing number:
= 120 − 96
= 24
Example 18: Average of Multiples
Question: Find the average of first 8 multiples of 5.
Solution:
Formula:
Average = Number × (n + 1) / 2
= 5 × (8 + 1) / 2
= 45 / 2
= 22.5
Important Exam Tips
- Use middle-term shortcut for arithmetic progression.
- Memorize all average formulae properly.
- Apply harmonic mean formula in equal-distance speed problems.
- Use deviation method for faster calculations.
- Be careful while adding or removing observations.
- Always check total number of observations.
- Practice mental calculations regularly.
Practicing solved examples regularly improves calculation speed, conceptual clarity, and accuracy in solving Average questions in competitive examinations.