Basic Numeracy (Class X Level) – Averages

Assam Public Service Commission (APSC)

Combined Competitive Examination (CCE)

Preliminary Examination – General Studies Paper II (Objective Type, 200 Marks)

Topic: Basic Numeracy (Class X Level)

Sub-Topic: Averages

Directions (Q1–Q30):

These questions test your understanding of arithmetic mean (average), combined average, weighted average, age problems, speed–time averages, and real-life applications. Choose the correct answer.

Averages – MCQs

MCQ 1

The average of 10, 20, and 30 is:
A. 15
B. 20
C. 25
D. 30

Correct Answer: B
Explanation: Average = (10 + 20 + 30) / 3 = 20.

MCQ 2

The average of the first 10 natural numbers is:
A. 5
B. 5.5
C. 6
D. 10

Correct Answer: B
Explanation: Average of first n natural numbers = (n + 1) / 2 = (10 + 1)/2 = 5.5.

MCQ 3

If the average of 5 numbers is 12, their sum is:
A. 12
B. 24
C. 60
D. 72

Correct Answer: C
Explanation: Sum = Average × Number = 12 × 5 = 60.

MCQ 4

The average age of 4 students is 16 years. What is their total age?
A. 32
B. 48
C. 64
D. 72

Correct Answer: C
Explanation: Total age = 16 × 4 = 64 years.

MCQ 5

If the average of 7 numbers is 20, and 6 of them have an average of 18, the 7th number is:
A. 26
B. 28
C. 30
D. 32

Correct Answer: B
Explanation:
Total of 7 numbers = 7 × 20 = 140
Total of 6 numbers = 6 × 18 = 108
7th number = 140 − 108 = 32 ❌
Correct recalculation: 140 − 108 = 32 → option D
✔ Correct Answer: D

MCQ 6

The average of even numbers from 2 to 20 is:
A. 10
B. 11
C. 12
D. 14

Correct Answer: B
Explanation: Average of evenly spaced numbers = (first + last)/2 = (2 + 20)/2 = 11.

MCQ 7

The average of 15 observations is 25. If one observation is 40, the average of the remaining 14 observations is:
A. 22
B. 23
C. 24
D. 25

Correct Answer: C
Explanation:
Total = 15 × 25 = 375
Remaining sum = 375 − 40 = 335
Average = 335/14 ≈ 23.93 ≈ 24

MCQ 8

The average of two numbers is 18. If one number is 10, the other is:
A. 8
B. 18
C. 26
D. 28

Correct Answer: C
Explanation: Sum = 18 × 2 = 36 → Other number = 36 − 10 = 26.

MCQ 9

The average of three consecutive integers is 15. The integers are:
A. 13, 14, 15
B. 14, 15, 16
C. 15, 16, 17
D. 12, 15, 18

Correct Answer: B
Explanation: Middle number of three consecutive integers equals the average.

MCQ 10

If the average of x and y is 20, then x + y equals:
A. 20
B. 30
C. 40
D. 50

Correct Answer: C
Explanation: (x + y)/2 = 20 → x + y = 40.

MCQ 11

The average marks of 30 students is 60. If the teacher’s marks are also included, the average becomes 61. The teacher’s marks are:
A. 60
B. 61
C. 90
D. 91

Correct Answer: D
Explanation:
Total of students = 30 × 60 = 1800
Total including teacher = 31 × 61 = 1891
Teacher’s marks = 1891 − 1800 = 91.

MCQ 12

The average of 5 consecutive odd numbers is 25. The smallest number is:
A. 19
B. 21
C. 23
D. 25

Correct Answer: B
Explanation: The middle number is the average → sequence = 21, 23, 25, 27, 29.

MCQ 13

If the average speed of a vehicle for a journey is 40 km/h, and the total distance is 120 km, the total time taken is:
A. 2 hours
B. 3 hours
C. 4 hours
D. 5 hours

Correct Answer: B
Explanation: Time = Distance / Speed = 120 / 40 = 3 hours.

MCQ 14

The average of first 20 natural numbers is:
A. 10
B. 10.5
C. 11
D. 20

Correct Answer: B
Explanation: Average = (20 + 1)/2 = 10.5.

MCQ 15

The average weight of 8 persons is 60 kg. If one person weighing 72 kg joins, the new average becomes:
A. 60 kg
B. 61 kg
C. 62 kg
D. 63 kg

Correct Answer: B
Explanation:
Original total = 8 × 60 = 480
New total = 480 + 72 = 552
New average = 552 / 9 = 61.33 ≈ 61 kg.

MCQ 16

The average of numbers a, b, c is 12. If a = 10 and b = 14, then c is:
A. 10
B. 12
C. 14
D. 16

Correct Answer: B
Explanation:
(a + b + c)/3 = 12 → (10 + 14 + c) = 36 → c = 12.

MCQ 17

The average age of a family of 5 members is 30 years. If a new baby is born, the average age becomes 25 years. The age of the baby is:
A. 0
B. 5
C. 10
D. 15

Correct Answer: A
Explanation:
Old total = 5 × 30 = 150
New total = 6 × 25 = 150
Baby’s age = 0.

MCQ 18

The average of 10 numbers is 50. If each number is increased by 5, the new average is:
A. 50
B. 52
C. 55
D. 60

Correct Answer: C
Explanation: Increase in average = 5 → New average = 55.

MCQ 19

The average of numbers from 1 to 99 is:
A. 49
B. 49.5
C. 50
D. 50.5

Correct Answer: C
Explanation: Average = (first + last)/2 = (1 + 99)/2 = 50.

MCQ 20

If the average of x, y, z is 15 and z = 21, then the average of x and y is:
A. 9
B. 12
C. 15
D. 18

Correct Answer: B
Explanation:
(x + y + 21)/3 = 15 → x + y = 24 → average = 12.

MCQ 21

The average marks of a student in 5 subjects is 72. If he scores 80 in the sixth subject, the new average is:
A. 72
B. 73
C. 74
D. 75

Correct Answer: B
Explanation:
Total = 5 × 72 = 360
New total = 360 + 80 = 440
Average = 440/6 ≈ 73.33 ≈ 73.

MCQ 22

The average of 7 numbers is 21. If the average of the first 3 numbers is 15, the average of the remaining 4 numbers is:
A. 24
B. 25
C. 26
D. 27

Correct Answer: B
Explanation:
Total = 7 × 21 = 147
First 3 total = 3 × 15 = 45
Remaining total = 102
Average = 102/4 = 25.5 ≈ 25.

MCQ 23

If the average of n numbers is x, their sum is:
A. x/n
B. n/x
C. n × x
D. x − n

Correct Answer: C
Explanation: Sum = n × x.

MCQ 24

The average of five consecutive integers is 40. The largest integer is:
A. 40
B. 41
C. 42
D. 43

Correct Answer: D
Explanation: Sequence: 38, 39, 40, 41, 42 ❌
Correct: 5 consecutive integers → middle = 40 → numbers = 38, 39, 40, 41, 42
✔ Largest = 42 → option C

MCQ 25

The average of first n natural numbers is:
A. n
B. (n + 1)/2
C. n/2
D. (n − 1)/2

Correct Answer: B
Explanation: Standard formula.

MCQ 26

If the average of 4 numbers is 18 and one number is 30, the average of the remaining 3 numbers is:
A. 14
B. 15
C. 16
D. 18

Correct Answer: B
Explanation:
Total = 4 × 18 = 72
Remaining sum = 72 − 30 = 42
Average = 42/3 = 14 ❌
Correct calculation: 42/3 = 14 → option A
✔ Correct Answer: A

MCQ 27

The average salary of 20 workers is ₹10,000. If one worker earning ₹20,000 leaves, the new average is:
A. ₹9,000
B. ₹9,500
C. ₹10,000
D. ₹10,500

Correct Answer: B
Explanation:
Total = 20 × 10,000 = 2,00,000
Remaining total = 1,80,000
New average = 1,80,000 / 19 ≈ 9,474 ≈ 9,500.

MCQ 28

The average of numbers 2, 4, 6, …, 20 is:
A. 10
B. 11
C. 12
D. 14

Correct Answer: B
Explanation: Average = (2 + 20)/2 = 11.

MCQ 29

The average of two numbers is 15. If one number is 9, the other number is:
A. 18
B. 21
C. 24
D. 30

Correct Answer: B
Explanation: Sum = 30 → Other number = 21.

MCQ 30

Average-based questions mainly test:
A. Memorization
B. Approximation only
C. Logical numerical reasoning
D. Language skills

Correct Answer: C
Explanation: Averages test conceptual understanding and numerical relationships.

✅ APSC Exam Relevance

These MCQs comprehensively cover basic averages, combined averages, age problems, speed–time applications, and real-life numeracy, fully aligned with APSC CCE GS Paper II – Basic Numeracy (Class X level).

• Average problems for competitive exams

• Basic numeracy averages MCQs GS Paper II

• Arithmetic mean questions APSC CCE

• Combined average problems Class X

• Average age and speed MCQs