Hey there! If you’re looking to get a solid handle on averages, you’ve come to the right place. I remember when I first started tutoring math, this was one of the topics where students often knew the formula but would get tripped up on the word problems. Over the years, I’ve found that practicing with clear, step-by-step solutions is the best way to build confidence. That’s exactly what we’re going to do here.
Think of this as a friendly study session. We’ll walk through 25 common average problems, the kind you might see on a test or in your homework. I’ll explain the reasoning behind each answer, sharing the little tricks and checks I teach my own students. Let’s dive in and make sense of averages together.
25 Practice Problems on Averages (With Answers & Explanations)
Q1. What is the arithmetic mean of the numbers 4, 8, 12, 16, and 20?
(a) 10
(b) 12
(c) 14
(d) 16
Answer: (b)
Explanation: The mean is the sum of all numbers divided by the count. So, Mean = (4 + 8 + 12 + 16 + 20) / 5 = 60 / 5 = 12.
Q2. The average of five numbers is 18. If one of the numbers is 24, what is the sum of the remaining four numbers?
(a) 66
(b) 72
(c) 78
(d) 84
Answer: (a)
Explanation: If the average of 5 numbers is 18, their total sum is 18 × 5 = 90. If one number is 24, the sum of the other four is 90 – 24 = 66.
Q3. The average weight of 6 children is 28 kg. If a seventh child joins and the new average becomes 30 kg, what is the weight of the seventh child?
(a) 34 kg
(b) 36 kg
(c) 38 kg
(d) 42 kg
Answer: (d)
Explanation: Total weight of 6 children = 6 × 28 = 168 kg. Total weight of 7 children = 7 × 30 = 210 kg. The seventh child’s weight is the difference: 210 – 168 = 42 kg.
Q4. Find the mean of the first 10 odd natural numbers.
(a) 9
(b) 10
(c) 11
(d) 12
Answer: (b)
Explanation: The numbers are 1, 3, 5, 7, 9, 11, 13, 15, 17, 19. A quick way: they form an arithmetic series. The sum is (10/2) × (1 + 19) = 5 × 20 = 100. Mean = 100 / 10 = 10.
Q5. The average score of a student in 4 tests is 75. If the scores in three tests are 68, 80, and 72, what is the score in the fourth test?
(a) 78
(b) 80
(c) 82
(d) 84
Answer: (b)
Explanation: Total score needed for a 75 average over 4 tests is 75 × 4 = 300. Sum of the three known scores = 68 + 80 + 72 = 220. The fourth score must be 300 – 220 = 80.
Q6. The mean of five numbers is 24. If each number is increased by 3, what is the new mean?
(a) 24
(b) 27
(c) 30
(d) 33
Answer: (b)
Explanation: This is a key concept: if you add (or subtract) the same constant from every number, the mean changes by that same constant. So, new mean = 24 + 3 = 27.
Q7. The average of 8 numbers is 45. If one number, 60, is removed, what is the average of the remaining 7 numbers?
(a) 42
(b) 43
(c) 44
(d) 45
Answer: (b)
Explanation: Total of 8 numbers = 8 × 45 = 360. After removing 60, the new sum is 360 – 60 = 300. The new average for 7 numbers is 300 / 7 ≈ 42.857, which rounds closest to 43.
Q8. The average monthly income of a family of 4 members is ₹15,000. If the income of one member is ₹18,000, what is the average income of the other three members?
(a) ₹12,500
(b) ₹13,000
(c) ₹13,500
(d) ₹14,000
Answer: (d)
Explanation: Total family income = 4 × ₹15,000 = ₹60,000. Income of the other three = ₹60,000 – ₹18,000 = ₹42,000. Their average is ₹42,000 / 3 = ₹14,000.
Q9. The average of numbers 2, 4, 6, 8, …, 20 (even numbers up to 20) is:
(a) 9
(b) 10
(c) 11
(d) 12
Answer: (c)
Explanation: There are 10 terms here (2, 4, 6…20). The sum of an arithmetic series is (number of terms/2) × (first + last). So, Sum = (10/2) × (2 + 20) = 5 × 22 = 110. Mean = 110 / 10 = 11.
Q10. The mean of 12 observations is 50. If two observations, 30 and 70, are discarded, the mean of the remaining observations is:
(a) 48
(b) 50
(c) 52
(d) 54
Answer: (b)
Explanation: Original total sum = 12 × 50 = 600. Removing 30 and 70 (sum 100) leaves a sum of 500. There are now 10 observations left. New mean = 500 / 10 = 50. Notice the average stayed the same because the two numbers we removed averaged to 50 themselves.
Q11. In a class of 20 students, the average marks in Mathematics is 68. If 5 students scored 80 each, what is the average marks of the remaining 15 students?
(a) 60
(b) 62
(c) 64
(d) 66
Answer: (c)
Explanation: Total marks for the class = 20 × 68 = 1360. Marks from the 5 students = 5 × 80 = 400. Marks for the remaining 15 students = 1360 – 400 = 960. Their average = 960 / 15 = 64.
Q12. The average of five consecutive integers is 15. What is the largest integer?
(a) 16
(b) 17
(c) 18
(d) 19
Answer: (b)
Explanation: For an odd set of consecutive numbers, the average is the middle number. So if the average is 15, the five numbers are 13, 14, 15, 16, 17. The largest is 17.
Q13. The average salary of 9 workers is ₹22,000. If one worker’s salary is ₹30,000, what is the average salary of the other 8 workers?
(a) ₹20,000
(b) ₹20,500
(c) ₹21,000
(d) ₹21,500
Answer: (c)
Explanation: Total salary for all 9 = 9 × ₹22,000 = ₹1,98,000. Salary for the other 8 = ₹1,98,000 – ₹30,000 = ₹1,68,000. Their average = ₹1,68,000 / 8 = ₹21,000.
Q14. The mean of the data set {5, 10, 15, 20, 25, 30} is:
(a) 15
(b) 17.5
(c) 20
(d) 22.5
Answer: (b)
Explanation: Sum = 5 + 10 + 15 + 20 + 25 + 30 = 105. Number of items = 6. Mean = 105 / 6 = 17.5.
Q15. If the average of x, x+2, x+4, x+6 is 19, find x.
(a) 14
(b) 16
(c) 18
(d) 20
Answer: (b)
Explanation: The numbers are evenly spaced. Their sum is 4x + (0+2+4+6) = 4x + 12. The average is (4x + 12)/4 = x + 3. We are told this equals 19. So, x + 3 = 19, therefore x = 16.
Q16. The average of 7 numbers is 24. If each number is multiplied by 3, what is the new average?
(a) 24
(b) 48
(c) 72
(d) 96
Answer: (c)
Explanation: Another core concept: if you multiply every number in a set by a constant, the average is also multiplied by that constant. New mean = 24 × 3 = 72.
Q17. The average age of a father and his two sons is 30 years. If the father’s age is 45 years, what is the average age of the two sons?
(a) 20
(b) 22.5
(c) 25
(d) 27.5
Answer: (b)
Explanation: Total age of all three = 3 × 30 = 90 years. Combined age of the two sons = 90 – 45 = 45 years. Their average age = 45 / 2 = 22.5 years.
Q18. The mean of 10 numbers is 50. If one number is changed from 40 to 90, what is the new mean?
(a) 55
(b) 60
(c) 65
(d) 70
Answer: (a)
Explanation: Original total = 10 × 50 = 500. The change increases the total by (90 – 40) = 50. New total = 500 + 50 = 550. New mean = 550 / 10 = 55.
Q19. The average of the first n natural numbers is 21. Find n.
(a) 40
(b) 41
(c) 42
(d) 43
Answer: (b)
Explanation: There’s a handy formula: the average of the first ‘n’ natural numbers is (n + 1)/2. So, we set (n + 1)/2 = 21. Multiplying both sides by 2 gives n + 1 = 42, so n = 41.
Q20. In a data set of 6 numbers, the mean is 18. If five of the numbers are 12, 15, 18, 20, and 13, what is the sixth number?
(a) 28
(b) 30
(c) 32
(d) 34
Answer: (b)
Explanation: Total sum for all 6 numbers = 6 × 18 = 108. Sum of the five given numbers = 12 + 15 + 18 + 20 + 13 = 78. The sixth number is 108 – 78 = 30.
Q21. The average of 9 observations is 40. If three observations, each equal to 52, are removed, what is the average of the remaining observations?
(a) 30
(b) 32
(c) 34
(d) 36
Answer: (c)
Explanation: Original total sum = 9 × 40 = 360. Sum of the three removed observations = 3 × 52 = 156. Remaining sum = 360 – 156 = 204. Number of observations left = 6. New average = 204 / 6 = 34.
Q22. The average of 5 numbers is 28. If one number is 20, what is the average of the other four numbers?
(a) 29
(b) 30
(c) 31
(d) 32
Answer: (b)
Explanation: Total of 5 numbers = 5 × 28 = 140. Sum of the other four = 140 – 20 = 120. Their average = 120 / 4 = 30.
Q23. The mean of the numbers 3, 6, 9, 12, …, 30 (multiples of 3 up to 30) is:
(a) 15
(b) 16.5
(c) 18
(d) 19.5
Answer: (b)
Explanation: These are 10 terms: 3, 6, 9,…30. Using the series sum formula: Sum = (
