Q1): Find the average of 12, 15, 13, 10, and 20.
A) 13
B) 14
C) 15
D) 16
Answer: B) 14
Explanation:
- Step 1: Average = (Sum of values) ÷ (Number of values)
- Step 2: Sum = 12 + 15 + 13 + 10 + 20 = 70
- Step 3: Average = 70 ÷ 5 = 14
- Step 4: Match with options
- Final: Option B is correct
Q2): What is the average of the first 9 natural numbers (1 to 9)?
A) 4
B) 5
C) 6
D) 7
Answer: B) 5
Explanation:
- Step 1: Sum of 1 to 9 = 1 + 2 + … + 9 = 45
- Step 2: Number of terms = 9
- Step 3: Average = 45 ÷ 9 = 5
- Step 4: Match with options
- Final: Option B is correct
Q3): The average age of 4 students is 17 years. One student is 20 years old. Find the average age of the remaining 3 students.
A) 15
B) 16
C) 17
D) 18
Answer: B) 16
Explanation:
- Step 1: Total age of 4 students = 17 × 4 = 68
- Step 2: Remove the 20-year-old student: 68 − 20 = 48
- Step 3: Average of remaining 3 = 48 ÷ 3 = 16
- Step 4: Match with options
- Final: Option B is correct
Q4): The average of 6 numbers is 11. What is their total sum?
A) 60
B) 62
C) 66
D) 72
Answer: C) 66
Explanation:
- Step 1: Sum = Average × Number of terms
- Step 2: Average = 11, Number = 6
- Step 3: Sum = 11 × 6 = 66
- Step 4: Match with options
- Final: Option C is correct
Q5): The average of 5 numbers is 24. If a new number 30 is added, what is the new average?
A) 24
B) 25
C) 26
D) 27
Answer: B) 25
Explanation:
- Step 1: Total of 5 numbers = 24 × 5 = 120
- Step 2: Add the new number: 120 + 30 = 150
- Step 3: New count = 6, so new average = 150 ÷ 6 = 25
- Step 4: Match with options
- Final: Option B is correct
Q6): The average age of 8 boys is 15 years. A teacher joins them and the average becomes 16 years. Find the teacher’s age.
A) 22
B) 24
C) 26
D) 28
Answer: B) 24
Explanation:
- Step 1: Total age of 8 boys = 15 × 8 = 120
- Step 2: Total age of 9 people now = 16 × 9 = 144
- Step 3: Teacher’s age = 144 − 120 = 24
- Step 4: Match with options
- Final: Option B is correct
Q7): The average marks of 10 students is 50. One student who scored 59 leaves. What is the new average of the remaining 9 students?
A) 48
B) 49
C) 50
D) 51
Answer: B) 49
Explanation:
- Step 1: Total marks of 10 students = 50 × 10 = 500
- Step 2: Remove the student’s marks: 500 − 59 = 441
- Step 3: New average = 441 ÷ 9 = 49
- Step 4: Match with options
- Final: Option B is correct
Q8): The average of 7 numbers is 18. Six numbers are 16, 20, 18, 15, 19, 17. Find the 7th number.
A) 20
B) 21
C) 22
D) 23
Answer: B) 21
Explanation:
- Step 1: Total of 7 numbers = 18 × 7 = 126
- Step 2: Sum of given six = 16 + 20 + 18 + 15 + 19 + 17 = 105
- Step 3: 7th number = 126 − 105 = 21
- Step 4: Match with options
- Final: Option B is correct
Q9): The average of 5 numbers is 12. If two numbers are 9 and 15, what is the sum of the remaining 3 numbers?
A) 34
B) 35
C) 36
D) 37
Answer: C) 36
Explanation:
- Step 1: Total of 5 numbers = 12 × 5 = 60
- Step 2: Sum of two known numbers = 9 + 15 = 24
- Step 3: Sum of remaining 3 = 60 − 24 = 36
- Step 4: Match with options
- Final: Option C is correct
Q10): The average of 3 numbers is 24. If two numbers are 20 and 25, find the third number.
A) 26
B) 27
C) 28
D) 29
Answer: B) 27
Explanation:
- Step 1: Total of 3 numbers = 24 × 3 = 72
- Step 2: Sum of two known numbers = 20 + 25 = 45
- Step 3: Third number = 72 − 45 = 27
- Step 4: Match with options
- Final: Option B is correct
Q11): The average marks of 40 students is 55. The average of top 10 students is 70. Find the average of the remaining 30 students.
A) 49
B) 50
C) 51
D) 52
Answer: B) 50
Explanation:
- Step 1: Total marks of 40 students = 55 × 40 = 2200
- Step 2: Total marks of top 10 = 70 × 10 = 700
- Step 3: Remaining total = 2200 − 700 = 1500, remaining students = 30
- Step 4: Average = 1500 ÷ 30 = 50
- Final: Option B is correct
Q12): The average age of 12 men is 30 years and of 8 women is 25 years. Find the average age of all 20 people.
A) 27
B) 28
C) 29
D) 30
Answer: B) 28
Explanation:
- Step 1: Total age of men = 30 × 12 = 360
- Step 2: Total age of women = 25 × 8 = 200
- Step 3: Combined average = (360 + 200) ÷ 20 = 560 ÷ 20 = 28
- Step 4: Match with options
- Final: Option B is correct
Q13): A student scores 70 in Theory (60% weight) and 80 in Practical (40% weight). What is the overall score?
A) 73
B) 74
C) 75
D) 76
Answer: B) 74
Explanation:
- Step 1: Weighted average = (Weight₁×Score₁) + (Weight₂×Score₂)
- Step 2: Weights: 60% = 0.6, 40% = 0.4
- Step 3: Overall = (0.6×70) + (0.4×80) = 42 + 32 = 74
- Step 4: Match with options
- Final: Option B is correct
Q14): The average of 9 numbers is 20. If each number is increased by 3, what is the new average?
A) 22
B) 23
C) 24
D) 25
Answer: B) 23
Explanation:
- Step 1: If each value increases by k, average also increases by k
- Step 2: Old average = 20
- Step 3: New average = 20 + 3 = 23
- Step 4: Match with options
- Final: Option B is correct
Q15): The average of 4 numbers is 15. One number 10 is replaced by 18. What is the new average?
A) 16
B) 17
C) 18
D) 19
Answer: B) 17
Explanation:
- Step 1: Total of 4 numbers = 15 × 4 = 60
- Step 2: Replace 10 with 18 → total increases by (18 − 10) = 8
- Step 3: New total = 60 + 8 = 68, new average = 68 ÷ 4 = 17
- Step 4: Match with options
- Final: Option B is correct
Q16): The average of 6 numbers is 14. If one number is 9, find the average of the remaining 5 numbers.
A) 14
B) 15
C) 16
D) 17
Answer: B) 15
Explanation:
- Step 1: Total of 6 numbers = 14 × 6 = 84
- Step 2: Remove the known number: 84 − 9 = 75
- Step 3: Average of remaining 5 = 75 ÷ 5 = 15
- Step 4: Match with options
- Final: Option B is correct
Q17): The average sales for 7 days is ₹360 per day. The average sales for the first 3 days is ₹320 per day. Find the average sales for the remaining 4 days.
A) 385
B) 390
C) 395
D) 400
Answer: B) 390
Explanation:
- Step 1: Total sales for 7 days = 360 × 7 = 2520
- Step 2: Total sales for first 3 days = 320 × 3 = 960
- Step 3: Remaining total = 2520 − 960 = 1560 for 4 days
- Step 4: Remaining average = 1560 ÷ 4 = 390
- Final: Option B is correct
Q18): The average of 8 numbers is 25. The average of the first 5 numbers is 22. Find the average of the last 3 numbers.
A) 29
B) 30
C) 31
D) 32
Answer: B) 30
Explanation:
- Step 1: Total of 8 numbers = 25 × 8 = 200
- Step 2: Sum of first 5 = 22 × 5 = 110
- Step 3: Sum of last 3 = 200 − 110 = 90
- Step 4: Average of last 3 = 90 ÷ 3 = 30
- Final: Option B is correct
Q19): The average weight of 5 bags is 19 kg. One bag weighs 23 kg. Find the average weight of the remaining 4 bags.
A) 17
B) 18
C) 19
D) 20
Answer: B) 18
Explanation:
- Step 1: Total weight of 5 bags = 19 × 5 = 95
- Step 2: Remove the 23 kg bag: 95 − 23 = 72
- Step 3: Average of remaining 4 = 72 ÷ 4 = 18
- Step 4: Match with options
- Final: Option B is correct
Q20): The average marks in 4 subjects is 75. The average marks in 5 subjects is 78. Find the marks in the 5th subject.
A) 88
B) 89
C) 90
D) 91
Answer: C) 90
Explanation:
- Step 1: Total of 4 subjects = 75 × 4 = 300
- Step 2: Total of 5 subjects = 78 × 5 = 390
- Step 3: Marks in 5th subject = 390 − 300 = 90
- Step 4: Match with options
- Final: Option C is correct