Average: Essential Concepts for Competitive Exam Success

Average

Q. In a class of 30 students, the average age is 15 years. If 5 new students aged 16 years join, what will be the new average age?

A. 15.5
B. 15.8
C. 16
D. 16.2

Solution

Total age of 30 students = 30 * 15 = 450. Total age of 5 new students = 5 * 16 = 80. New total age = 450 + 80 = 530. New average = 530 / 35 = 15.14.

Correct Answer: B — 15.8

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Q. In a class of 40 students, the average height is 150 cm. If 10 new students with an average height of 160 cm join, what will be the new average height?

A. 152
B. 154
C. 156
D. 158

Solution

The total height of the original students is 40 * 150 = 6000 cm. The total height of the new students is 10 * 160 = 1600 cm. The new total height is 6000 + 1600 = 7600 cm. The new average height is 7600 / 50 = 152 cm.

Correct Answer: C — 156

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Q. In a class of 40 students, the average height is 150 cm. If 10 new students with an average height of 160 cm join, what is the new average height?

A. 152
B. 154
C. 156
D. 158

Solution

Total height of 40 students = 40 * 150 = 6000 cm. Total height of 10 new students = 10 * 160 = 1600 cm. New total height = 6000 + 1600 = 7600 cm. New average = 7600 / 50 = 152 cm.

Correct Answer: B — 154

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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

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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

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Q. In a group of 5 friends, the average age is 25 years. If one friend leaves and the average age becomes 26 years, what is the age of the friend who left?

A. 24
B. 25
C. 26
D. 27

Solution

Total age of 5 friends = 5 * 25 = 125. Total age of 4 friends = 4 * 26 = 104. Age of friend who left = 125 - 104 = 21.

Correct Answer: D — 27

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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

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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

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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

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Q. The average age of a group of 5 people is 30 years. If a new person joins the group, making the average age 32 years, what is the age of the new person?

A. 35
B. 40
C. 45
D. 50

Solution

Total age of 5 people = 5 * 30 = 150. New total age = 6 * 32 = 192. Age of new person = 192 - 150 = 42.

Correct Answer: B — 40

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Q. The average of 10 numbers is 40. If one number is removed, the average becomes 38. What is the removed number?

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

Solution

Total of 10 numbers = 10 * 40 = 400. Total of 9 numbers = 9 * 38 = 342. Removed number = 400 - 342 = 58.

Correct Answer: A — 42

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Q. The average of 10 numbers is 50. If one number is increased by 10, what will be the new average?

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

Solution

The total of the 10 numbers is 10 * 50 = 500. If one number is increased by 10, the new total becomes 500 + 10 = 510. The new average is 510 / 10 = 51.

Correct Answer: B — 51

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Q. The average of 10 numbers is 50. If one number is replaced by 70, what will be the new average?

A. 50
B. 52
C. 54
D. 56

Solution

The sum of the 10 numbers is 10 * 50 = 500. Replacing one number with 70 gives a new sum of 500 - x + 70. The new average is (500 - x + 70) / 10. Since x is 50, the new average is (500 - 50 + 70) / 10 = 52.

Correct Answer: B — 52

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Q. The average of 12 numbers is 15. If one number is increased by 5, what will be the new average?

A. 15
B. 15.5
C. 16
D. 16.5

Solution

Total of 12 numbers = 12 * 15 = 180. New total = 180 + 5 = 185. New average = 185 / 12 = 15.42.

Correct Answer: C — 16

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Q. The average of 12 numbers is 25. If one number is increased by 5, what will be the new average?

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

Solution

Total of 12 numbers = 12 * 25 = 300. New total = 300 + 5 = 305. New average = 305 / 12 = 25.42.

Correct Answer: B — 26

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Q. The average of 4 consecutive integers is 25. What is the largest of these integers?

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

Solution

Let the integers be x, x+1, x+2, x+3. Average = (4x + 6) / 4 = 25. Solving gives x = 24. Largest integer = x + 3 = 27.

Correct Answer: C — 28

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Q. The average of 4 consecutive integers is 25. What is the smallest of these integers?

A. 23
B. 24
C. 25
D. 26

Solution

Let the integers be x, x+1, x+2, x+3. Average = (4x + 6) / 4 = 25. So, 4x + 6 = 100. Therefore, x = 23.

Correct Answer: A — 23

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Q. The average of 4 numbers is 30. If one number is 10, what is the average of the other three numbers?

A. 28
B. 30
C. 32
D. 34

Solution

Total of 4 numbers = 4 * 30 = 120. Total of other three numbers = 120 - 10 = 110. Average of other three = 110 / 3 = 36.67, approximately 36.

Correct Answer: A — 28

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Q. The average of 4 numbers is 30. If one number is increased by 10, what will be the new average?

A. 30
B. 32.5
C. 35
D. 37.5

Solution

Total = 30 * 4 = 120. New total = 120 + 10 = 130. New average = 130 / 4 = 32.5.

Correct Answer: B — 32.5

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Q. The average of 5 numbers is 12. If one number is removed, the average becomes 10. What is the removed number?

A. 8
B. 10
C. 12
D. 14

Solution

Total of 5 numbers = 5 * 12 = 60. Total of 4 numbers = 4 * 10 = 40. Removed number = 60 - 40 = 20.

Correct Answer: D — 14

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Q. The average of 5 numbers is 15. If one number is 25, what is the average of the remaining numbers?

A. 10
B. 12
C. 15
D. 18

Solution

Total of 5 numbers = 5 * 15 = 75. Total of remaining 4 numbers = 75 - 25 = 50. New average = 50 / 4 = 12.5.

Correct Answer: A — 10

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Q. The average of 5 numbers is 40. If the largest number is 60, what is the average of the other four numbers?

A. 35
B. 40
C. 45
D. 50

Solution

The total of the 5 numbers is 5 * 40 = 200. The sum of the other four numbers is 200 - 60 = 140. The average of the other four numbers is 140 / 4 = 35.

Correct Answer: A — 35

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Q. The average of 5 numbers is 40. If the largest number is removed, the average of the remaining numbers is 35. What is the largest number?

A. 45
B. 50
C. 55
D. 60

Solution

Total of 5 numbers = 5 * 40 = 200. Total of 4 numbers = 4 * 35 = 140. Largest number = 200 - 140 = 60.

Correct Answer: B — 50

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Q. The average of 8 numbers is 12. If one number is removed, the average becomes 10. What is the removed number?

A. 16
B. 18
C. 20
D. 22

Solution

The total of the 8 numbers is 8 * 12 = 96. The total of the remaining 7 numbers is 7 * 10 = 70. Therefore, the removed number is 96 - 70 = 26.

Correct Answer: C — 20

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Q. The average of 8 numbers is 24. If one number is added which is 36, what will be the new average?

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

Solution

Total of 8 numbers = 8 * 24 = 192. New total = 192 + 36 = 228. New average = 228 / 9 = 25.33.

Correct Answer: B — 26

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Q. The average of 8 numbers is 24. If one number is removed, the average becomes 22. What is the removed number?

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

Solution

Total of 8 numbers = 8 * 24 = 192. Total of 7 numbers = 7 * 22 = 154. Removed number = 192 - 154 = 38.

Correct Answer: D — 26

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Q. The average of 8 numbers is 40. If one number is removed, the average becomes 35. What is the removed number?

A. 45
B. 40
C. 35
D. 30

Solution

Total of 8 numbers = 8 * 40 = 320. Total of 7 numbers = 7 * 35 = 245. Removed number = 320 - 245 = 75.

Correct Answer: A — 45

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Q. The average of 8 numbers is 40. If one number is removed, the average becomes 38. What is the removed number?

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

Solution

Total of 8 numbers = 8 * 40 = 320. Total of 7 numbers = 7 * 38 = 266. Removed number = 320 - 266 = 54.

Correct Answer: A — 42

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Q. The average of 8 numbers is 50. If one number is increased by 10, what will be the new average?

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

Solution

Total of 8 numbers = 8 * 50 = 400. New total = 400 + 10 = 410. New average = 410 / 8 = 51.25, approximately 51.

Correct Answer: B — 51

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Q. The average of five numbers is 20. If one number is excluded, the average becomes 18. What is the excluded number?

A. 22
B. 20
C. 18
D. 16

Solution

Total of five numbers = 5 * 20 = 100. Total of four numbers = 4 * 18 = 72. Excluded number = 100 - 72 = 28.

Correct Answer: A — 22

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