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Average — Questions and Answers

Average questions are almost never about computing a mean — they are about how the mean shifts when an item is added, removed or replaced. The deviation method makes this instant: work with how far each value sits from an assumed average instead of with the raw numbers. Replacement questions in particular reduce to a single line: change in total = number of items × change in average.

26 solved questionsArithmetic AptitudeFree · no signup

Average— Concepts, Formulas & Shortcuts

  • Average = sum of observations / number of observations.
  • Average of the first n natural numbers = (n + 1)/2.
  • Average of n consecutive numbers = the middle term (for odd n) = (first + last)/2.
  • Replacement: new value = old value ± (count × change in average).
  • Adding a new member changes the average by (new value − old average)/(new count).
  • Average speed uses total distance / total time — never the average of the speeds.

Average Practice Questions with Answers

Attempt each question first, then open the explanation. All 26 questions below are free to read and require no signup.

  1. Q1.The average of the first 10 natural numbers is:

    Easy
    • A5
    • B5.5
    • C6
    • D6.5
    +Show Answer & Explanation

    Answer: B. 5.5

    Explanation: (1 + 10)/2 = 5.5, or 55/10 = 5.5.

    Average question 1 of 26

  2. Q2.The average of 20 numbers is zero. At most how many of them can be greater than zero?

    Moderate
    • A0
    • B1
    • C19
    • D20
    +Show Answer & Explanation

    Answer: C. 19

    Explanation: The sum must be zero, so at most 19 can be positive with one sufficiently large negative number balancing them.

    Average question 2 of 26

  3. Q3.The average age of 30 students is 15 years. When the teacher's age is included the average rises by 1 year. The teacher's age is:

    Moderate
    • A31 years
    • B41 years
    • C46 years
    • D51 years
    +Show Answer & Explanation

    Answer: C. 46 years

    Explanation: New total = 31 × 16 = 496; old total = 450 → teacher = 46 years.

    Average question 3 of 26

  4. Q4.The average of 5 consecutive even numbers is 24. The largest of them is:

    Easy
    • A26
    • B28
    • C30
    • D32
    +Show Answer & Explanation

    Answer: B. 28

    Explanation: The middle number is 24, so the set is 20, 22, 24, 26, 28 → largest = 28.

    Average question 4 of 26

  5. Q5.A cricketer averages 32 runs in 10 innings. How many runs must he score in the 11th innings to raise his average to 35?

    Moderate
    • A55
    • B60
    • C65
    • D70
    +Show Answer & Explanation

    Answer: C. 65

    Explanation: Required = 11 × 35 − 10 × 32 = 385 − 320 = 65 runs.

    Average question 5 of 26

  6. Q6.The average weight of 8 persons increases by 2.5 kg when a new person replaces one weighing 65 kg. The new person weighs:

    Moderate
    • A76 kg
    • B80 kg
    • C85 kg
    • D90 kg
    +Show Answer & Explanation

    Answer: C. 85 kg

    Explanation: Increase in total = 8 × 2.5 = 20 kg → new weight = 65 + 20 = 85 kg.

    Average question 6 of 26

  7. Q7.The average of 6 numbers is 8. If one number is removed the average becomes 7. The removed number is:

    Moderate
    • A11
    • B12
    • C13
    • D14
    +Show Answer & Explanation

    Answer: C. 13

    Explanation: Old total = 48, new total = 5 × 7 = 35 → removed = 13.

    Average question 7 of 26

  8. Q8.The average marks in three subjects is 60. If two of them are 55 and 65, the third is:

    Easy
    • A55
    • B58
    • C60
    • D62
    +Show Answer & Explanation

    Answer: C. 60

    Explanation: Total = 180; 180 − 55 − 65 = 60.

    Average question 8 of 26

  9. Q9.The average of 5, 10, 15, 20 and 25 is:

    Easy
    • A12
    • B15
    • C18
    • D20
    +Show Answer & Explanation

    Answer: B. 15

    Explanation: Sum = 75, and 75/5 = 15.

    Average question 9 of 26

  10. Q10.The average of the first 20 natural numbers is:

    Easy
    • A10
    • B10.5
    • C11
    • D11.5
    +Show Answer & Explanation

    Answer: B. 10.5

    Explanation: (n + 1)/2 = 21/2 = 10.5.

    Average question 10 of 26

  11. Q11.The average weight of 4 people is 60 kg. A fifth person joins and the average becomes 62 kg. The fifth person weighs:

    Moderate
    • A68 kg
    • B70 kg
    • C72 kg
    • D75 kg
    +Show Answer & Explanation

    Answer: B. 70 kg

    Explanation: New total = 5 × 62 = 310; old total = 240 → fifth person = 70 kg.

    Average question 11 of 26

  12. Q12.The average of 7 consecutive numbers is 20. The largest of them is:

    Moderate
    • A21
    • B22
    • C23
    • D24
    +Show Answer & Explanation

    Answer: C. 23

    Explanation: The middle (4th) term is 20, so the numbers run 17 to 23 → largest = 23.

    Average question 12 of 26

  13. Q13.The average marks of 40 students is 65. If the marks of one student are wrongly read as 45 instead of 85, the correct average is:

    Difficult
    • A65
    • B66
    • C67
    • D68
    +Show Answer & Explanation

    Answer: B. 66

    Explanation: The total was understated by 40, so the average rises by 40/40 = 1 → 66.

    Average question 13 of 26

  14. Q14.The average age of 3 boys is 15 years. If their ages are in the ratio 3 : 5 : 7, the age of the youngest is:

    Moderate
    • A6 years
    • B9 years
    • C12 years
    • D15 years
    +Show Answer & Explanation

    Answer: B. 9 years

    Explanation: Total age = 45. Parts = 15, so 1 part = 3 → youngest = 3 × 3 = 9 years.

    Average question 14 of 26

  15. Q15.The average of 10 numbers is 23. If each number is increased by 4, the new average is:

    Easy
    • A23
    • B25
    • C27
    • D29
    +Show Answer & Explanation

    Answer: C. 27

    Explanation: Adding a constant to every value raises the average by the same constant: 23 + 4 = 27.

    Average question 15 of 26

  16. Q16.A batsman's average in 16 innings is 36. To raise it to 38, how many runs must he score in the 17th innings?

    Moderate
    • A60
    • B65
    • C70
    • D72
    +Show Answer & Explanation

    Answer: C. 70

    Explanation: Required = 17 × 38 − 16 × 36 = 646 − 576 = 70 runs.

    Average question 16 of 26

  17. Q17.The average of 8 numbers is 20. If two numbers, 15 and 25, are removed, the average of the rest is:

    Moderate
    • A19
    • B20
    • C21
    • D22
    +Show Answer & Explanation

    Answer: B. 20

    Explanation: Total = 160; removing 40 leaves 120 over 6 numbers → 20.

    Average question 17 of 26

  18. Q18.The average temperature for Monday, Tuesday and Wednesday was 28 °C, and for Tuesday, Wednesday and Thursday 30 °C. If Thursday was 33 °C, Monday's temperature was:

    Difficult
    • A25 °C
    • B26 °C
    • C27 °C
    • D28 °C
    +Show Answer & Explanation

    Answer: C. 27 °C

    Explanation: Mon+Tue+Wed = 84 and Tue+Wed+Thu = 90, so Thu − Mon = 6 → Mon = 33 − 6 = 27 °C.

    Average question 18 of 26

  19. Q19.The average of 10, 20 and 30 is:

    Easy
    • A15
    • B20
    • C25
    • D30
    +Show Answer & Explanation

    Answer: B. 20

    Explanation: Sum = 60, and 60/3 = 20.

    Average question 19 of 26

  20. Q20.The average of the first 5 even numbers is:

    Easy
    • A5
    • B6
    • C7
    • D8
    +Show Answer & Explanation

    Answer: B. 6

    Explanation: 2, 4, 6, 8, 10 sum to 30 → 30/5 = 6.

    Average question 20 of 26

  21. Q21.The average of 5 numbers is 18. Their sum is:

    Easy
    • A80
    • B85
    • C90
    • D95
    +Show Answer & Explanation

    Answer: C. 90

    Explanation: Sum = average × count = 18 × 5 = 90.

    Average question 21 of 26

  22. Q22.The average age of 4 boys is 12. If a boy aged 17 joins them, the new average is:

    Moderate
    • A12
    • B13
    • C14
    • D15
    +Show Answer & Explanation

    Answer: B. 13

    Explanation: New total = 48 + 17 = 65 over 5 boys → 13 years.

    Average question 22 of 26

  23. Q23.The average of 12 numbers is 15. If each is multiplied by 2, the new average is:

    Moderate
    • A15
    • B20
    • C25
    • D30
    +Show Answer & Explanation

    Answer: D. 30

    Explanation: Multiplying every value by 2 doubles the average: 15 × 2 = 30.

    Average question 23 of 26

  24. Q24.The average of 9 results is 50. If the average of the first 4 is 45 and of the last 4 is 52, the fifth result is:

    Difficult
    • A52
    • B54
    • C56
    • D62
    +Show Answer & Explanation

    Answer: D. 62

    Explanation: Total = 450. First four = 180, last four = 208 → fifth = 450 − 388 = 62.

    Average question 24 of 26

  25. Q25.A student's marks in 4 subjects average 72. To raise the average to 75 over 5 subjects, he must score:

    Moderate
    • A81
    • B84
    • C87
    • D90
    +Show Answer & Explanation

    Answer: C. 87

    Explanation: Required = 5 × 75 − 4 × 72 = 375 − 288 = 87 marks.

    Average question 25 of 26

  26. Q26.The average weight of 10 boxes is 12 kg. If the heaviest box of 20 kg is removed, the new average is:

    Moderate
    • A10.9 kg
    • B11.1 kg
    • C11.5 kg
    • D12 kg
    +Show Answer & Explanation

    Answer: B. 11.1 kg

    Explanation: Total = 120 kg; removing 20 leaves 100 kg over 9 boxes → 11.11 kg.

    Average question 26 of 26

Average — Frequently Asked Questions

What is the replacement shortcut in averages?+

If replacing one person changes the average of n people by d, the new person differs from the old one by exactly n × d. Replacing a 65 kg person among 8 people and raising the average 2.5 kg means the newcomer weighs 65 + 8 × 2.5 = 85 kg.

How do I find the required score to reach a target average?+

Required = (target average × new count) − current total. To lift a 32-run average over 10 innings to 35 in the 11th, you need 11 × 35 − 320 = 65 runs.

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