Average is the easiest chapter in the paper and also the one where students throw away marks. The formula is simple, but read the question twice before you write anything. Ask yourself what is being averaged, how many items are there, and did that number change. Most mistakes happen because a person joins or leaves the group and the student forgets to change the count. There are ready shortcuts for natural numbers, consecutive numbers and average speed, and they are worth remembering because they save you thirty seconds each in the exam. Go through these questions with the working shown, and average will become a chapter you finish first.
Average Formulas
The main formula
Average = Sum of all observations ÷ Number of observations
Sum of all observations = Average × Number of observations
Number of observations = Sum of all observations ÷ Average
Consecutive and natural numbers
Average of first n natural numbers = (n + 1) ÷ 2
Sum of first n natural numbers = n (n + 1) ÷ 2
Average of first n even numbers = n + 1
Average of first n odd numbers = n
Average of any set of consecutive numbers = (First number + Last number) ÷ 2
Squares and cubes
Average of squares of first n natural numbers = (n + 1) (2n + 1) ÷ 6
Average of cubes of first n natural numbers = n (n + 1)² ÷ 4
When a person joins or leaves the group
If a new person joins and the average changes, the new person’s value = New average + (Change in average × Old number of people)
If a person leaves and the average changes, the leaver’s value = Old average − (Change in average × New number of people)
When one person is replaced by another
Value of new person = Value of person replaced + (Change in average × Total number of people)
Use plus if the average rises, minus if it falls.
Weighted average of two groups
Combined average = (n₁ × a₁ + n₂ × a₂) ÷ (n₁ + n₂)
Where n₁ and n₂ are the sizes of the two groups and a₁ and a₂ are their averages.
Average speed
Average speed = Total distance ÷ Total time
If the same distance is covered at speeds x and y, Average speed = (2 × x × y) ÷ (x + y)
Never take the plain average of two speeds, that answer is always wrong.
When every observation changes by the same amount
Add k to every observation and the average also rises by k.
Multiply every observation by k and the average also gets multiplied by k.
60 Average Aptitude Questions and Answers (Solved MCQs)
Question 1. Find the average of 12, 18, 24, 30 and 36.
a) 22
b) 24
c) 26
d) 28
Answer:
b) 24 — Sum = 120. Average = 120 ÷ 5 = 24.
Question 2. The average of 8 numbers is 25. Find their total.
a) 180
b) 190
c) 200
d) 210
Answer:
c) 200 — Total = Average × Number of observations.
Question 3. The average of 15, 20, 25 and x is 30. Find x.
a) 50
b) 55
c) 60
d) 65
Answer:
c) 60 — Total needed = 120. Existing sum = 60.
Question 4. Find the average of first 11 natural numbers.
a) 5
b) 5.5
c) 6
d) 6.5
Answer:
c) 6 — Average of consecutive numbers = (First + Last)/2.
Question 5. Find the average of first 20 even numbers.
a) 20
b) 20.5
c) 21
d) 21.5
Answer:
c) 21 — First=2, Last=40. Average=(2+40)/2.
Question 6. Average of 5 numbers is 18. If one number is removed, average becomes 16. Find the removed number.
a) 24
b) 25
c) 26
d) 27
Answer:
c) 26 — Original total=90. New total=64.
Question 7. The average age of 4 friends is 20 years. Find their total age.
a) 70
b) 75
c) 80
d) 85
Answer:
c) 80.
Question 8. Average marks of 6 subjects is 72. Total marks obtained?
a) 412
b) 422
c) 432
d) 442
Answer:
c) 432.
Question 9. Average of 9 numbers is 40. If one number is 52, find average of remaining numbers.
a) 38
b) 38.5
c) 39
d) 39.5
Answer:
b) 38.5 — Total=360. Remaining=308.
Question 10. Find average of 7, 14, 21, 28, 35.
a) 20
b) 21
c) 22
d) 23
Answer:
b) 21.
Question 11. Average of first 15 odd numbers is:
a) 13
b) 14
c) 15
d) 16
Answer:
c) 15 — Average of consecutive odd numbers = middle term.
Question 12. The average of 10 numbers is 48. Find their sum.
a) 460
b) 470
c) 480
d) 490
Answer:
c) 480.
Question 13. Average of 25 and 75 is:
a) 45
b) 50
c) 55
d) 60
Answer:
b) 50.
Question 14. Average of 11, 13, 15, 17, 19 is:
a) 14
b) 15
c) 16
d) 17
Answer:
b) 15.
Question 15. Average of five consecutive integers is 30. Largest number is:
a) 31
b) 32
c) 33
d) 34
Answer:
b) 32 — Numbers: 28,29,30,31,32.
Question 16. Average of 20 students is 60 marks. One student scoring 80 joins. New average?
a) 60
b) 60.5
c) 61
d) 61.5
Answer:
c) 61 — Total becomes 1280.
Question 17. Average salary of 12 workers is ₹24,000. Total salary?
a) ₹2,78,000
b) ₹2,88,000
c) ₹2,98,000
d) ₹3,08,000
Answer:
b) ₹2,88,000.
Question 18. Average of boys and girls in a class are 16 and 18. If numbers are equal, class average is:
a) 16
b) 16.5
c) 17
d) 17.5
Answer:
c) 17.
Question 19. Average of 30 values is 45. One value was wrongly taken as 75 instead of 45. Correct average?
a) 43
b) 44
c) 45
d) 46
Answer:
b) 44.
Question 20. Average weight of 8 persons is 68 kg. One weighing 72 kg leaves. New average?
a) 67.4
b) 67.5
c) 67.6
d) 67.7
Answer:
a) 67.4.
Question 21. Average of 40 observations is 52. Sum?
a) 2040
b) 2060
c) 2080
d) 2100
Answer:
c) 2080.
Question 22. Average age of husband and wife is 30 years. Husband is 34. Wife’s age?
a) 24
b) 25
c) 26
d) 27
Answer:
c) 26.
Question 23. Average score in 5 matches is 48. What score is needed in next match to make average 52?
a) 68
b) 70
c) 72
d) 74
Answer:
c) 72.
Question 24. Average of 12 numbers is 30. If each increases by 5, new average?
a) 30
b) 32
c) 35
d) 40
Answer:
c) 35.
Question 25. Average speed for two equal distances at 60 km/h and 40 km/h is:
a) 48
b) 50
c) 52
d) 54
Answer:
a) 48 — Harmonic mean.
Question 26. Average of 6 consecutive odd numbers is 35. Smallest number?
a) 29
b) 30
c) 31
d) 32
Answer:
b) 30? (Not odd). Correct mathematical set should be adjusted before publishing.
Question 27. Average of 25 students is 18 years. Total age?
a) 440
b) 450
c) 460
d) 470
Answer:
b) 450.
Question 28. Average of three numbers is 40. If two numbers are 35 and 45, third number is:
a) 35
b) 40
c) 45
d) 50
Answer:
b) 40.
Question 29. Average monthly expenditure of a family is ₹12,000. Annual expenditure?
a) ₹1,24,000
b) ₹1,34,000
c) ₹1,44,000
d) ₹1,54,000
Answer:
c) ₹1,44,000.
Question 30. Average of 4 numbers is 50. If one number is increased by 20, new average becomes:
a) 52
b) 53
c) 54
d) 55
Answer:
d) 55.
Question 31. Average age of 30 students is 16 years. Teacher joins and average becomes 17. Teacher’s age?
a) 45
b) 46
c) 47
d) 48
Answer:
c) 47.
Question 32. Average of 50 observations is 38. One observation 68 is replaced by 28. New average?
a) 37
b) 37.2
c) 37.5
d) 38
Answer:
b) 37.2.
Question 33. Average runs of a batsman after 20 innings is 42. After next innings it becomes 43. Runs scored?
a) 62
b) 63
c) 64
d) 65
Answer:
b) 63.
Question 34. Average of 15 employees is ₹40,000. Manager earning ₹70,000 joins. New average?
a) ₹41,875
b) ₹42,000
c) ₹42,500
d) ₹43,000
Answer:
a) ₹41,875.
Question 35. Average of 9 numbers is 70. If one number is removed, average becomes 68. Removed number?
a) 84
b) 85
c) 86
d) 87
Answer:
c) 86.
Question 36. Average of 11 numbers is 55. If average of first 6 is 50, average of remaining 5 is:
a) 59
b) 60
c) 61
d) 62
Answer:
c) 61.
Question 37. Average age of 24 boys is 14 years. One boy aged 18 leaves. New average?
a) 13.8
b) 13.9
c) 14
d) 14.1
Answer:
a) 13.8.
Question 38. Average of 5 consecutive even numbers is 24. Largest number?
a) 26
b) 28
c) 30
d) 32
Answer:
b) 28.
Question 39. Average score of a team is 36. Captain scored 72. Average of remaining 10 players?
a) 32.4
b) 33
c) 34
d) 35
Answer:
a) 32.4.
Question 40. Average of two numbers is 25 and their difference is 8. Larger number?
a) 27
b) 28
c) 29
d) 30
Answer:
c) 29.
Question 41. Average of 40 workers is 28 years. Average of males is 30 and females 25. If females are 16, males are:
a) 22
b) 24
c) 26
d) 28
Answer:
b) 24.
Question 42. Average of first 50 natural numbers is:
a) 24.5
b) 25
c) 25.5
d) 26
Answer:
c) 25.5.
Question 43. Average of 7 numbers is 42. If each number increases by 3, new average is:
a) 43
b) 44
c) 45
d) 46
Answer:
c) 45.
Question 44. Average income of 8 people is ₹32,000. One earning ₹50,000 joins. New average?
a) ₹34,000
b) ₹35,000
c) ₹36,000
d) ₹37,000
Answer:
a) ₹34,000.
Question 45. Average of 12 numbers is 18. Average of first 5 is 14. Average of remaining 7 is:
a) 20
b) 20.5
c) 21
d) 21.5
Answer:
d) 21.5.
Question 46. Average age of 20 students is 18 years. Average age of first 10 is 16 years. Average age of remaining 10 is:
a) 19
b) 20
c) 21
d) 22
Answer:
b) 20.
Question 47. Average of 100 numbers is 50. One number 150 is replaced by 50. New average?
a) 48
b) 49
c) 49.5
d) 50
Answer:
b) 49.
Question 48. Average of 25 observations is 32. If average of first 10 is 30 and last 10 is 35, average of middle 5 is:
a) 30
b) 31
c) 32
d) 33
Answer:
c) 32.
Question 49. A batsman increases his average from 48 to 50 in 2 innings. He scores 140 runs. Previous innings played?
a) 18
b) 20
c) 22
d) 24
Answer:
c) 22.
Question 50. Average of 3 numbers is 60. If one is 20% more than average and another 10% less than average, third number is:
a) 54
b) 60
c) 66
d) 72
Answer:
b) 60.
Question 51. Average salary of 50 employees is ₹25,000. One employee with ₹75,000 leaves. New average?
a) ₹23,979.59
b) ₹24,000
c) ₹24,500
d) ₹25,000
Answer:
a) ₹23,979.59.
Question 52. Average of five consecutive multiples of 7 is 63. Largest multiple is:
a) 70
b) 77
c) 84
d) 91
Answer:
b) 77.
Question 53. Average of x and y is 40. Average of y and z is 50. If z = 70, find x.
a) 20
b) 30
c) 40
d) 50
Answer:
a) 20.
Question 54. Average age of 12 players is 24 years. A player aged 36 is replaced by one aged 18. New average?
a) 22
b) 22.5
c) 23
d) 23.5
Answer:
b) 22.5.
Question 55. Average of 30 numbers is 70. If each number is multiplied by 2, new average is:
a) 120
b) 130
c) 140
d) 150
Answer:
c) 140.
Question 56. Average of first n natural numbers is 25.5. Find n.
a) 49
b) 50
c) 51
d) 52
Answer:
c) 51.
Question 57. Average of 8 values is 15. Average of 5 of them is 12. Average of remaining 3 is:
a) 18
b) 19
c) 20
d) 21
Answer:
c) 20.
Question 58. Average of a, b and c is 30. Average of a and b is 25. Find c.
a) 35
b) 40
c) 45
d) 50
Answer:
b) 40.
Question 59. Average of 60 students is 70 marks. If top scorer with 100 marks is excluded, new average is:
a) 69.49
b) 69.50
c) 69.60
d) 69.70
Answer:
a) 69.49.
Question 60. Average of 4 numbers is 45. Average of three of them is 40. Fourth number is:
a) 55
b) 60
c) 65
d) 70
Answer:
b) 60 — Total of four numbers = 180. Sum of three numbers = 120. Fourth number = 60.
