Q1): The average marks of 18 students is 64 and of 12 students is 70. What is the average marks of all 30 students?
A) 65.2
B) 66.0
C) 66.4
D) 67.0
Answer: C) 66.4
Explanation:
- Step 1: Combined average = (Total marks of both groups) ÷ (Total students)
- Step 2: Total marks = (18×64) + (12×70) = 1152 + 840 = 1992
- Step 3: Total students = 18 + 12 = 30
- Step 4: Average = 1992 ÷ 30 = 66.4
- Final: Option C is correct
Q2): The average of 7 numbers is 23. If 29 is replaced by 41, what is the new average?
A) 24
B) 24 5/7
C) 25
D) 25 1/7
Answer: B) 24 5/7
Explanation:
- Step 1: Total of 7 numbers = 23 × 7 = 161
- Step 2: Replacement increases total by (41 − 29) = 12
- Step 3: New total = 161 + 12 = 173
- Step 4: New average = 173 ÷ 7 = 24 5/7
- Final: Option B is correct
Q3): The average of 9 numbers is 16. One number is 7 less than the average and another is 5 more than the average. Find the sum of the remaining 7 numbers.
A) 110
B) 112
C) 114
D) 116
Answer: C) 114
Explanation:
- Step 1: Total sum of 9 numbers = 16 × 9 = 144
- Step 2: Two given numbers = (16 − 7) and (16 + 5) = 9 and 21
- Step 3: Sum of these two = 9 + 21 = 30
- Step 4: Remaining sum = 144 − 30 = 114
- Final: Option C is correct
Q4): A student gets 80 in assignments (30% weight) and 60 in final exam (70% weight). What is the overall score?
A) 64
B) 65
C) 66
D) 68
Answer: C) 66
Explanation:
- Step 1: Weighted score = (0.30×80) + (0.70×60)
- Step 2: Assignment part = 24
- Step 3: Exam part = 42
- Step 4: Total = 24 + 42 = 66
- Final: Option C is correct
Q5): A person travels equal distances at 30 km/h and 45 km/h. What is the average speed for the whole journey?
A) 35 km/h
B) 36 km/h
C) 37.5 km/h
D) 40 km/h
Answer: B) 36 km/h
Explanation:
- Step 1: For equal distances, average speed = (2ab) ÷ (a + b)
- Step 2: Here a = 30, b = 45
- Step 3: Average speed = (2×30×45) ÷ (30+45) = 2700 ÷ 75
- Step 4: 2700 ÷ 75 = 36
- Final: Option B is correct
Q6): A vehicle travels 120 km at 40 km/h and then 80 km at 60 km/h. What is the average speed for the entire trip?
A) 45 km/h
B) 46.15 km/h
C) 48 km/h
D) 50 km/h
Answer: B) 46.15 km/h
Explanation:
- Step 1: Average speed = (Total distance) ÷ (Total time)
- Step 2: Total distance = 120 + 80 = 200 km
- Step 3: Total time = (120/40) + (80/60) = 3 + 4/3 = 13/3 hours
- Step 4: Average speed = 200 ÷ (13/3) = 600/13 ≈ 46.15
- Final: Option B is correct
Q7): The average of 5 numbers is 18. Three numbers are 12, 19, 23 and the remaining two numbers are x and (x+4). Find x.
A) 14
B) 15
C) 16
D) 17
Answer: C) 16
Explanation:
- Step 1: Total of 5 numbers = 18 × 5 = 90
- Step 2: Sum of known three = 12 + 19 + 23 = 54
- Step 3: Sum of remaining two = 90 − 54 = 36
- Step 4: x + (x+4) = 36 ⇒ 2x = 32 ⇒ x = 16
- Final: Option C is correct
Q8): The average of 8 numbers is 25. If each number is increased by 20%, what is the new average?
A) 28
B) 29
C) 30
D) 31
Answer: C) 30
Explanation:
- Step 1: If every value increases by 20%, average also increases by 20%
- Step 2: New average = 25 × 1.20
- Step 3: 25 × 1.20 = 30
- Step 4: Match with options
- Final: Option C is correct
Q9): The average of the first n even natural numbers is 41. Find n.
A) 39
B) 40
C) 41
D) 42
Answer: B) 40
Explanation:
- Step 1: First n even numbers are 2, 4, 6, …, 2n
- Step 2: Average = (First + Last) ÷ 2 = (2 + 2n) ÷ 2 = n + 1
- Step 3: Given n + 1 = 41
- Step 4: n = 40
- Final: Option B is correct
Q10): In a class, average age of boys is 21 years and girls is 18 years. The overall average is 19.2 years. What is the ratio of boys to girls?
A) 1 : 2
B) 2 : 3
C) 3 : 2
D) 4 : 5
Answer: B) 2 : 3
Explanation:
- Step 1: Let boys = b, girls = g
- Step 2: (21b + 18g) ÷ (b + g) = 19.2
- Step 3: 21b + 18g = 19.2b + 19.2g ⇒ 1.8b = 1.2g
- Step 4: b : g = 1.2 : 1.8 = 2 : 3
- Final: Option B is correct
Q11): The average of 10 numbers is 35. The average of the first 4 numbers is 32 and the average of the last 3 numbers is 40. Find the average of the middle 3 numbers.
A) 33
B) 34
C) 35
D) 36
Answer: B) 34
Explanation:
- Step 1: Total of 10 numbers = 35 × 10 = 350
- Step 2: Sum of first 4 = 32 × 4 = 128
- Step 3: Sum of last 3 = 40 × 3 = 120
- Step 4: Middle 3 sum = 350 − (128 + 120) = 102 ⇒ average = 102 ÷ 3 = 34
- Final: Option B is correct
Q12): The average of 12 numbers is 50. If 60 and 70 are removed, what is the average of the remaining 10 numbers?
A) 45
B) 46
C) 47
D) 48
Answer: C) 47
Explanation:
- Step 1: Total of 12 numbers = 50 × 12 = 600
- Step 2: Removed sum = 60 + 70 = 130
- Step 3: Remaining sum = 600 − 130 = 470
- Step 4: New average = 470 ÷ 10 = 47
- Final: Option C is correct
Q13): The average age of 6 people is 28. Two more people join and the average becomes 29.5. What is the average age of the two new people?
A) 32
B) 33
C) 34
D) 35
Answer: C) 34
Explanation:
- Step 1: Total age of 6 people = 28 × 6 = 168
- Step 2: Total age of 8 people = 29.5 × 8 = 236
- Step 3: Sum of ages of new 2 people = 236 − 168 = 68
- Step 4: Average of new 2 = 68 ÷ 2 = 34
- Final: Option C is correct
Q14): The average of 5 numbers is 26. If one number is 14, what is the average of the remaining 4 numbers?
A) 28
B) 29
C) 30
D) 31
Answer: B) 29
Explanation:
- Step 1: Total of 5 numbers = 26 × 5 = 130
- Step 2: Remove the known number: 130 − 14 = 116
- Step 3: Remaining count = 4
- Step 4: Average of remaining 4 = 116 ÷ 4 = 29
- Final: Option B is correct
Q15): The prices of 3 items are ₹120, ₹150 and ₹180. If the average price of 4 items should be ₹160, what should be the price of the 4th item?
A) ₹180
B) ₹190
C) ₹200
D) ₹210
Answer: B) ₹190
Explanation:
- Step 1: Required total for 4 items = 160 × 4 = 640
- Step 2: Current total of 3 items = 120 + 150 + 180 = 450
- Step 3: Price of 4th item = 640 − 450 = 190
- Step 4: Match with options
- Final: Option B is correct
Q16): The average of x, (x+2), (x+4) and (x+6) is 27. Find x.
A) 22
B) 23
C) 24
D) 25
Answer: C) 24
Explanation:
- Step 1: Sum = x + (x+2) + (x+4) + (x+6) = 4x + 12
- Step 2: Average = (4x + 12) ÷ 4 = x + 3
- Step 3: Given x + 3 = 27
- Step 4: x = 24
- Final: Option C is correct
Q17): The average of 9 numbers is 22. Three of the numbers are 18, 20 and 25. What is the average of the remaining 6 numbers?
A) 21.5
B) 22
C) 22.5
D) 23
Answer: C) 22.5
Explanation:
- Step 1: Total of 9 numbers = 22 × 9 = 198
- Step 2: Sum of given three = 18 + 20 + 25 = 63
- Step 3: Remaining sum = 198 − 63 = 135
- Step 4: Remaining average = 135 ÷ 6 = 22.5
- Final: Option C is correct
Q18): A player’s average score after 19 matches is 45. If he scores 55 in the 20th match, what is his new average?
A) 45.0
B) 45.5
C) 46.0
D) 46.5
Answer: B) 45.5
Explanation:
- Step 1: Total after 19 matches = 45 × 19 = 855
- Step 2: Add 20th match score: 855 + 55 = 910
- Step 3: Total matches now = 20
- Step 4: New average = 910 ÷ 20 = 45.5
- Final: Option B is correct
Q19): The average of 5 tests is 70. What marks are needed in the 6th test to make the overall average 72?
A) 78
B) 80
C) 82
D) 84
Answer: C) 82
Explanation:
- Step 1: Total needed for 6-test average 72 = 72 × 6 = 432
- Step 2: Total of first 5 tests = 70 × 5 = 350
- Step 3: Required marks in 6th test = 432 − 350 = 82
- Step 4: Match with options
- Final: Option C is correct
Q20): Three numbers are in the ratio 2 : 3 : 5. Their average is 40. Find the largest number.
A) 48
B) 56
C) 60
D) 64
Answer: C) 60
Explanation:
- Step 1: Let numbers be 2k, 3k, 5k
- Step 2: Average = (2k + 3k + 5k) ÷ 3 = 10k ÷ 3
- Step 3: Given 10k/3 = 40 ⇒ 10k = 120 ⇒ k = 12
- Step 4: Largest number = 5k = 5×12 = 60
- Final: Option C is correct