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30 Averages Questions and Answers

30 solved Averages questions with step-by-step explanations. Includes formulas, shortcuts, and tips for placement tests and competitive exams.

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Advanced averages questions for experienced learners. These medium-to-hard questions test deeper understanding and are ideal for those who have already mastered the basics. Each question includes a detailed explanation.

Key Formulas

Average = Sum of values / Number of values Sum = Average × Number of values Missing value = (Average × N) - Sum of known values Weighted Avg = (W₁V₁ + W₂V₂ + ...) / (W₁ + W₂ + ...)
Q1 Medium

Average of 7 numbers is 46. 6 numbers are 46, 35, 33, 78, 92, 43. Find the missing number.

  • A. 5
  • B. -5 ✓
  • C. 1
  • D. 4
Explanation: Average = Sum of all values ÷ Number of values. To find the total sum, multiply the average by the number of items. This simple formula solves most average problems. Total sum = 7x46 = 322. Missing = Total - Known sum = -5.
Q2 Medium

Class A has 29 students with average marks 64. Class B has 29 students with average 64. Find combined average.

  • A. 64 ✓
  • B. 61
  • C. 66
  • D. 62
Explanation: Average = Sum of all values ÷ Number of values. To find the total sum, multiply the average by the number of items. This simple formula solves most average problems. Combined average = (29x64+29x64)/(58) = 64.
Q3 Medium

Average of 5 numbers is 44. 4 numbers are 39, 72, 88, 63. Find the missing number.

  • A. -34
  • B. -38
  • C. -44
  • D. -42 ✓
Explanation: Average = Sum of all values ÷ Number of values. To find the total sum, multiply the average by the number of items. This simple formula solves most average problems. Total sum = 5x44 = 220. Missing = Total - Known sum = -42.
Q4 Medium

Average of 8 numbers is 49. 7 numbers are 83, 51, 69, 55, 84, 21, 91. Find the missing number.

  • A. -64
  • B. -55
  • C. -49
  • D. -62 ✓
Explanation: Average = Sum of all values ÷ Number of values. To find the total sum, multiply the average by the number of items. This simple formula solves most average problems. Total sum = 8x49 = 392. Missing = Total - Known sum = -62.
Q5 Medium

Average of 9 numbers is 37. After adding 117, what is the new average?

  • A. 43
  • B. 42
  • C. 47
  • D. 45 ✓
Explanation: Average = Sum of all values ÷ Number of values. To find the total sum, multiply the average by the number of items. This simple formula solves most average problems. New average = (9x37+117)/10 = 45.
Q6 Medium

Class A has 26 students with average marks 66. Class B has 26 students with average 68. Find combined average.

  • A. 69
  • B. 65
  • C. 64
  • D. 67 ✓
Explanation: Average = Sum of all values ÷ Number of values. To find the total sum, multiply the average by the number of items. This simple formula solves most average problems. Combined average = (26x66+26x68)/(52) = 67.
Q7 Medium

Average of 7 numbers is 56. After adding 96, what is the new average?

  • A. 59
  • B. 58
  • C. 61 ✓
  • D. 63
Explanation: Average = Sum of all values ÷ Number of values. To find the total sum, multiply the average by the number of items. This simple formula solves most average problems. New average = (7x56+96)/8 = 61.
Q8 Medium

Class A has 21 students with average marks 59. Class B has 21 students with average 55. Find combined average.

  • A. 54
  • B. 59
  • C. 57 ✓
  • D. 55
Explanation: Average = Sum of all values ÷ Number of values. To find the total sum, multiply the average by the number of items. This simple formula solves most average problems. Combined average = (21x59+21x55)/(42) = 57.
Q9 Medium

Average of 6 numbers is 56. 5 numbers are 56, 20, 74, 51, 70. Find the missing number.

  • A. 59
  • B. 65 ✓
  • C. 61
  • D. 69
Explanation: Average = Sum of all values ÷ Number of values. To find the total sum, multiply the average by the number of items. This simple formula solves most average problems. Total sum = 6x56 = 336. Missing = Total - Known sum = 65.
Q10 Medium

Average of 5 numbers is 56. 4 numbers are 49, 30, 32, 78. Find the missing number.

  • A. 87
  • B. 91 ✓
  • C. 95
  • D. 85
Explanation: Average = Sum of all values ÷ Number of values. To find the total sum, multiply the average by the number of items. This simple formula solves most average problems. Total sum = 5x56 = 280. Missing = Total - Known sum = 91.
Q11 Medium

Average of 6 numbers is 70. 5 numbers are 45, 64, 72, 68, 92. Find the missing number.

  • A. 73
  • B. 75
  • C. 83
  • D. 79 ✓
Explanation: Average = Sum of all values ÷ Number of values. To find the total sum, multiply the average by the number of items. This simple formula solves most average problems. Total sum = 6x70 = 420. Missing = Total - Known sum = 79.
Q12 Medium

Class A has 41 students with average marks 63. Class B has 41 students with average 47. Find combined average.

  • A. 55 ✓
  • B. 53
  • C. 52
  • D. 57
Explanation: Average = Sum of all values ÷ Number of values. To find the total sum, multiply the average by the number of items. This simple formula solves most average problems. Combined average = (41x63+41x47)/(82) = 55.
Q13 Medium

Average of 9 numbers is 37. After adding 77, what is the new average?

  • A. 39
  • B. 38
  • C. 43
  • D. 41 ✓
Explanation: Average = Sum of all values ÷ Number of values. To find the total sum, multiply the average by the number of items. This simple formula solves most average problems. New average = (9x37+77)/10 = 41.
Q14 Medium

Average of 7 numbers is 65. 6 numbers are 90, 31, 43, 84, 75, 21. Find the missing number.

  • A. 111 ✓
  • B. 105
  • C. 115
  • D. 107
Explanation: Average = Sum of all values ÷ Number of values. To find the total sum, multiply the average by the number of items. This simple formula solves most average problems. Total sum = 7x65 = 455. Missing = Total - Known sum = 111.
Q15 Medium

Average of 5 numbers is 70. 4 numbers are 71, 90, 75, 49. Find the missing number.

  • A. 61
  • B. 65 ✓
  • C. 69
  • D. 59
Explanation: Average = Sum of all values ÷ Number of values. To find the total sum, multiply the average by the number of items. This simple formula solves most average problems. Total sum = 5x70 = 350. Missing = Total - Known sum = 65.
Q16 Medium

Average of 7 numbers is 43. 6 numbers are 87, 52, 32, 36, 30, 24. Find the missing number.

  • A. 34
  • B. 40 ✓
  • C. 44
  • D. 36
Explanation: Average = Sum of all values ÷ Number of values. To find the total sum, multiply the average by the number of items. This simple formula solves most average problems. Total sum = 7x43 = 301. Missing = Total - Known sum = 40.
Q17 Medium

Average of 6 numbers is 40. 5 numbers are 83, 45, 26, 29, 86. Find the missing number.

  • A. -29 ✓
  • B. -24
  • C. -22
  • D. -16
Explanation: Average = Sum of all values ÷ Number of values. To find the total sum, multiply the average by the number of items. This simple formula solves most average problems. Total sum = 6x40 = 240. Missing = Total - Known sum = -29.
Q18 Medium

Class A has 36 students with average marks 70. Class B has 36 students with average 54. Find combined average.

  • A. 59
  • B. 60
  • C. 64
  • D. 62 ✓
Explanation: Average = Sum of all values ÷ Number of values. To find the total sum, multiply the average by the number of items. This simple formula solves most average problems. Combined average = (36x70+36x54)/(72) = 62.
Q19 Medium

Average of 5 numbers is 62. 4 numbers are 87, 41, 49, 53. Find the missing number.

  • A. 80 ✓
  • B. 74
  • C. 84
  • D. 76
Explanation: Average = Sum of all values ÷ Number of values. To find the total sum, multiply the average by the number of items. This simple formula solves most average problems. Total sum = 5x62 = 310. Missing = Total - Known sum = 80.
Q20 Medium

Average of 6 numbers is 61. 5 numbers are 56, 93, 86, 45, 27. Find the missing number.

  • A. 55
  • B. 63
  • C. 53
  • D. 59 ✓
Explanation: Average = Sum of all values ÷ Number of values. To find the total sum, multiply the average by the number of items. This simple formula solves most average problems. Total sum = 6x61 = 366. Missing = Total - Known sum = 59.
Q21 Medium

Class A has 32 students with average marks 56. Class B has 32 students with average 58. Find combined average.

  • A. 57 ✓
  • B. 59
  • C. 54
  • D. 55
Explanation: Average = Sum of all values ÷ Number of values. To find the total sum, multiply the average by the number of items. This simple formula solves most average problems. Combined average = (32x56+32x58)/(64) = 57.
Q22 Medium

Average of 8 numbers is 38. After adding 56, what is the new average?

  • A. 42
  • B. 38
  • C. 40 ✓
  • D. 37
Explanation: Average = Sum of all values ÷ Number of values. To find the total sum, multiply the average by the number of items. This simple formula solves most average problems. New average = (8x38+56)/9 = 40.
Q23 Medium

Class A has 28 students with average marks 71. Class B has 28 students with average 47. Find combined average.

  • A. 57
  • B. 59 ✓
  • C. 56
  • D. 61
Explanation: Average = Sum of all values ÷ Number of values. To find the total sum, multiply the average by the number of items. This simple formula solves most average problems. Combined average = (28x71+28x47)/(56) = 59.
Q24 Medium

Average of 6 numbers is 62. 5 numbers are 45, 65, 66, 71, 72. Find the missing number.

  • A. 49
  • B. 47
  • C. 53 ✓
  • D. 57
Explanation: Average = Sum of all values ÷ Number of values. To find the total sum, multiply the average by the number of items. This simple formula solves most average problems. Total sum = 6x62 = 372. Missing = Total - Known sum = 53.
Q25 Medium

Class A has 40 students with average marks 69. Class B has 40 students with average 37. Find combined average.

  • A. 51
  • B. 50
  • C. 53 ✓
  • D. 55
Explanation: Average = Sum of all values ÷ Number of values. To find the total sum, multiply the average by the number of items. This simple formula solves most average problems. Combined average = (40x69+40x37)/(80) = 53.
Q26 Medium

Average of 7 numbers is 68. 6 numbers are 80, 58, 56, 24, 95, 39. Find the missing number.

  • A. 120
  • B. 124 ✓
  • C. 128
  • D. 118
Explanation: Average = Sum of all values ÷ Number of values. To find the total sum, multiply the average by the number of items. This simple formula solves most average problems. Total sum = 7x68 = 476. Missing = Total - Known sum = 124.
Q27 Medium

Class A has 46 students with average marks 57. Class B has 46 students with average 43. Find combined average.

  • A. 47
  • B. 48
  • C. 52
  • D. 50 ✓
Explanation: Average = Sum of all values ÷ Number of values. To find the total sum, multiply the average by the number of items. This simple formula solves most average problems. Combined average = (46x57+46x43)/(92) = 50.
Q28 Medium

Average of 8 numbers is 54. After adding 54, what is the new average?

  • A. 51
  • B. 52
  • C. 56
  • D. 54 ✓
Explanation: Average = Sum of all values ÷ Number of values. To find the total sum, multiply the average by the number of items. This simple formula solves most average problems. New average = (8x54+54)/9 = 54.
Q29 Medium

Average of 6 numbers is 62. 5 numbers are 92, 49, 20, 95, 95. Find the missing number.

  • A. 17
  • B. 21 ✓
  • C. 25
  • D. 15
Explanation: Average = Sum of all values ÷ Number of values. To find the total sum, multiply the average by the number of items. This simple formula solves most average problems. Total sum = 6x62 = 372. Missing = Total - Known sum = 21.
Q30 Medium

Average of 7 numbers is 43. 6 numbers are 87, 79, 47, 88, 84, 77. Find the missing number.

  • A. -149
  • B. -161 ✓
  • C. -150
  • D. -148
Explanation: Average = Sum of all values ÷ Number of values. To find the total sum, multiply the average by the number of items. This simple formula solves most average problems. Total sum = 7x43 = 301. Missing = Total - Known sum = -161.

Key Takeaways

  • Sum = Average × Count — this is the most useful formula for average problems.
  • When values are added/removed: update the sum first, then recalculate average.
  • Weighted average = (w1×v1 + w2×v2) / (w1 + w2) for different weights.

Frequently Asked Questions

What is the formula for average?

Average = Sum of all values ÷ Number of values. The reverse is equally useful: Sum = Average × Number of values.

How do I find a missing value when average is known?

Missing value = (Average × Total count) - Sum of known values. This single formula solves most average-based problems.

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