Average: Essential Concepts for Competitive Exam Success

Average

Q. A bag contains 5 red balls and 3 blue balls. If the average weight of the red balls is 200 grams and the blue balls is 150 grams, what is the average weight of all the balls?

A. 175
B. 180
C. 185
D. 190

Solution

Total weight of red balls = 5 * 200 = 1000 grams. Total weight of blue balls = 3 * 150 = 450 grams. Total weight = 1000 + 450 = 1450 grams. Average weight = 1450 / 8 = 181.25.

Correct Answer: B — 180

Q. A class has 30 students with an average score of 75. If one student scores 90, what will be the new average?

A. 75.5
B. 76
C. 76.5
D. 77

Solution

New total = (75 * 30 + 90) / 31 = (2250 + 90) / 31 = 2340 / 31 = 76.5.

Correct Answer: C — 76.5

Q. A class has 30 students. If the average score of the class is 75 and one student scored 90, what will be the new average if that student is removed?

A. 74
B. 75
C. 76
D. 77

Solution

Total score = 30 * 75 = 2250. New total = 2250 - 90 = 2160. New average = 2160 / 29 = 74.48, approximately 74.

Correct Answer: C — 76

Q. A class has 30 students. If the average score of the class is 75 and one student scores 90, what is the average score of the remaining students?

A. 74
B. 75
C. 76
D. 77

Solution

Total score of 30 students = 30 * 75 = 2250. Total score of remaining 29 students = 2250 - 90 = 2160. Average = 2160 / 29 = 74.48, approximately 74.

Correct Answer: C — 76

Q. A class has 30 students. If the average score of the class is 75 and one student scored 90, what is the average score of the remaining students?

A. 72
B. 74
C. 76
D. 78

Solution

Total score of 30 students = 30 * 75 = 2250. Total score of remaining 29 students = 2250 - 90 = 2160. Average of remaining = 2160 / 29 = 74.48, approximately 74.

Correct Answer: B — 74

Q. A class of 30 students has an average score of 75. If a new student joins and the average becomes 76, what is the score of the new student?

A. 80
B. 85
C. 90
D. 95

Solution

The total score of 30 students is 30 * 75 = 2250. After the new student joins, the total score becomes 31 * 76 = 2356. Therefore, the new student's score is 2356 - 2250 = 106.

Correct Answer: B — 85

Q. A family has 4 members with an average age of 25 years. If the youngest member is 10 years old, what will be the average age if the youngest member turns 20?

A. 26
B. 27
C. 28
D. 29

Solution

Total age of family = 4 * 25 = 100. New total age after youngest turns 20 = 100 - 10 + 20 = 110. New average = 110 / 4 = 27.5, approximately 27.

Correct Answer: B — 27

Q. A family has 4 members with an average income of $3000. If the father earns $4000, what is the average income of the other three members?

A. 2500
B. 3000
C. 3500
D. 4000

Solution

Total income of 4 members = 4 * 3000 = 12000. Income of other 3 members = 12000 - 4000 = 8000. Average = 8000 / 3 = 2666.67, approximately 2500.

Correct Answer: A — 2500

Q. A family has an average income of $5000. If the father earns $7000, what is the average income of the mother and child?

A. 4000
B. 4500
C. 5000
D. 5500

Solution

Total income = 5000 * 3 = 15000. Income of mother and child = 15000 - 7000 = 8000. Average = 8000 / 2 = 4000.

Correct Answer: B — 4500

Q. A group of 6 people has an average weight of 70 kg. If one person weighing 80 kg leaves, what is the new average weight?

A. 68
B. 69
C. 70
D. 71

Solution

The total weight of the group is 6 * 70 = 420 kg. After the 80 kg person leaves, the total weight becomes 420 - 80 = 340 kg. The new average is 340 / 5 = 68 kg.

Correct Answer: B — 69

Q. A group of friends has an average age of 25 years. If one friend aged 30 joins, what is the new average age of the group of 4 friends?

A. 25
B. 26
C. 27
D. 28

Solution

Total age of 3 friends = 25 * 3 = 75. New total = 75 + 30 = 105. New average = 105 / 4 = 26.25.

Correct Answer: B — 26

Q. A group of friends has an average age of 25 years. If one friend leaves and the average age becomes 26, how many friends were there originally?

A. 5
B. 6
C. 7
D. 8

Solution

Let the number of friends be x. Then, (25x - age of friend) / (x - 1) = 26. Solving gives x = 6.

Correct Answer: B — 6

Q. A person scores 80, 90, and 70 in three exams. What score does he need in the fourth exam to achieve an average of 85?

A. 90
B. 95
C. 100
D. 85

Solution

Let the fourth score be x. (80 + 90 + 70 + x) / 4 = 85. Solving gives x = 100.

Correct Answer: B — 95

Q. A student scores 60, 70, and 80 in three subjects. If he wants an average of 75, what score does he need in the fourth subject?

A. 70
B. 75
C. 80
D. 85

Solution

Let the fourth score be x. (60 + 70 + 80 + x) / 4 = 75. Solving gives x = 90.

Correct Answer: D — 85

Q. A student scores 80, 85, and 90 in three tests. What score does he need in the fourth test to have an average of 85?

A. 80
B. 85
C. 90
D. 95

Solution

Let the fourth score be x. (80 + 85 + 90 + x) / 4 = 85. Solving gives x = 95.

Correct Answer: C — 90

Q. A student scores 80, 90, and 70 in three subjects. If he wants an average of 85 after scoring in a fourth subject, what should he score?

A. 90
B. 95
C. 100
D. 85

Solution

Total score needed for average of 85 = 4 * 85 = 340. Current total = 80 + 90 + 70 = 240. Required score = 340 - 240 = 100.

Correct Answer: B — 95

Q. A student scores 80, 90, and 70 in three subjects. What score does he need in the fourth subject to have an average of 85?

A. 90
B. 95
C. 100
D. 85

Solution

Let the score in the fourth subject be x. The average is (80 + 90 + 70 + x) / 4 = 85. Thus, 240 + x = 340, so x = 100.

Correct Answer: B — 95

Q. A student scores 80, 90, and 70 in three subjects. What score does he need in the fourth subject to achieve an average of 85?

A. 90
B. 95
C. 100
D. 85

Solution

Total score needed for average of 85 = 4 * 85 = 340. Current total = 80 + 90 + 70 = 240. Score needed = 340 - 240 = 100.

Correct Answer: B — 95

Q. If the average of 10 numbers is 50 and the average of another 10 numbers is 60, what is the average of all 20 numbers?

A. 55
B. 56
C. 57
D. 58

Solution

Total of first 10 numbers = 10 * 50 = 500. Total of second 10 numbers = 10 * 60 = 600. Combined total = 500 + 600 = 1100. Average = 1100 / 20 = 55.

Correct Answer: A — 55

Q. If the average of 4 numbers is 15, what is the sum of those numbers?

A. 45
B. 60
C. 75
D. 90

Solution

The sum of the numbers is 4 * 15 = 60.

Correct Answer: A — 45

Q. If the average of 6 numbers is 12 and the average of 4 other numbers is 15, what is the average of all 10 numbers?

A. 13
B. 14
C. 15
D. 16

Solution

Total of first 6 numbers = 6 * 12 = 72. Total of next 4 numbers = 4 * 15 = 60. Combined total = 72 + 60 = 132. Average = 132 / 10 = 13.2.

Correct Answer: B — 14

Q. If the average of 8 numbers is 50, what is the average if one number is removed and it was 60?

A. 48
B. 49
C. 50
D. 51

Solution

Total = 50 * 8 = 400. New total = 400 - 60 = 340. New average = 340 / 7 = 48.57.

Correct Answer: B — 49

Q. If the average of 8 numbers is 50, what is the average if one number is removed and the new average is 52?

A. 50
B. 51
C. 52
D. 53

Solution

Total of 8 numbers = 50 * 8 = 400. New total = 52 * 7 = 364. The removed number = 400 - 364 = 36.

Correct Answer: B — 51

Q. If the average of five numbers is 12, what is their total sum?

A. 48
B. 60
C. 72
D. 84

Solution

Total sum = Average * Number of items = 12 * 5 = 60.

Correct Answer: A — 48

Q. If the average of three numbers is 15 and the first two numbers are 10 and 20, what is the third number?

A. 10
B. 15
C. 20
D. 25

Solution

Total of three numbers = 3 * 15 = 45. Sum of first two numbers = 10 + 20 = 30. Third number = 45 - 30 = 15.

Correct Answer: D — 25

Q. In a group of 10 people, the average age is 30 years. If two new members join the group and the average age becomes 32 years, what is the average age of the new members?

A. 34
B. 36
C. 38
D. 40

Solution

Total age of 10 people = 10 * 30 = 300. New total age = 12 * 32 = 384. Age of new members = 384 - 300 = 84. Average age of new members = 84 / 2 = 42.

Correct Answer: B — 36

Q. In a group of 5 friends, the average age is 24 years. If the age of one friend is 30 years, what is the average age of the remaining friends?

A. 22
B. 23
C. 24
D. 25

Solution

The total age of the 5 friends is 5 * 24 = 120. The total age of the remaining 4 friends is 120 - 30 = 90. The average age of the remaining friends is 90 / 4 = 22.5.

Correct Answer: B — 23

Q. In a group of 6 friends, the average age is 22 years. If one friend leaves and the average age becomes 23 years, what is the age of the friend who left?

A. 20
B. 22
C. 24
D. 26

Solution

Total age of 6 friends = 6 * 22 = 132. Total age of 5 friends = 5 * 23 = 115. Age of friend who left = 132 - 115 = 17.

Correct Answer: C — 24

Q. In a race, the average speed of a runner is 10 km/h. If he runs for 2 hours and then increases his speed to 15 km/h for the next 3 hours, what is his average speed for the entire race?

A. 12
B. 13
C. 14
D. 15

Solution

Total distance = (10 * 2) + (15 * 3) = 20 + 45 = 65 km. Total time = 2 + 3 = 5 hours. Average speed = 65 / 5 = 13 km/h.

Correct Answer: B — 13

Q. The average age of a group of 10 people is 30 years. If two new members join the group, increasing the average age to 32 years, what is the average age of the new members?

A. 36
B. 38
C. 40
D. 42

Solution

Total age of 10 people = 10 * 30 = 300. New total age = 12 * 32 = 384. Age of new members = 384 - 300 = 84. Average age of new members = 84 / 2 = 42.

Correct Answer: C — 40

Showing 1 to 30 of 48 (2 Pages)