Arithmetic Aptitude for Competitive Exam Success

Arithmetic Aptitude

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Q. The age of a father is twice the age of his son. If the sum of their ages is 60 years, how old is the son?

A. 20
B. 25
C. 30
D. 15

Solution

Let the son's age be x. Then the father's age is 2x. The equation is x + 2x = 60, which simplifies to 3x = 60, so x = 20.

Correct Answer: B — 25

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Q. The age of a grandfather is 3 times the age of his grandson. If the grandfather is 60 years old, how old is the grandson?

A. 15
B. 20
C. 25
D. 30

Solution

If the grandfather is 60 years old, then the grandson is 60 / 3 = 20 years old.

Correct Answer: B — 20

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Q. The age of a grandfather is 3 times the age of his grandson. If the grandson is 15 years old, how old is the grandfather?

A. 30
B. 45
C. 60
D. 75

Solution

If the grandson is 15 years old, then the grandfather is 3 * 15 = 45 years old.

Correct Answer: C — 60

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Q. The age of a grandfather is 4 times the age of his grandson. If the grandson is 8 years old, what is the grandfather's age?

A. 24
B. 32
C. 36
D. 40

Solution

If the grandson is 8 years old, then the grandfather is 4 * 8 = 32 years old.

Correct Answer: B — 32

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Q. The age of a grandfather is 4 times the age of his grandson. If the grandson is 8 years old, how old is the grandfather?

A. 24
B. 32
C. 36
D. 40

Solution

If the grandson is 8 years old, then the grandfather is 4 * 8 = 32 years old.

Correct Answer: B — 32

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Q. The age of a grandfather is three times the age of his grandson. If the grandson is 12 years old, what is the grandfather's age?

A. 30
B. 36
C. 40
D. 42

Solution

If the grandson is 12, then the grandfather is 3 * 12 = 36 years old.

Correct Answer: B — 36

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Q. The age of a man is 5 years more than twice the age of his son. If the son is 10 years old, how old is the man?

A. 20
B. 25
C. 30
D. 35

Solution

If the son is 10 years old, then the man's age is 2 * 10 + 5 = 25 years.

Correct Answer: C — 30

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Q. The age of a mother is 4 times that of her daughter. If the daughter is 8 years old, what is the mother's age?

A. 24
B. 32
C. 36
D. 40

Solution

If the daughter is 8 years old, then the mother is 4 * 8 = 32 years old.

Correct Answer: A — 24

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Q. The age of a mother is 4 times the age of her daughter. If the daughter is 5 years old, how old is the mother?

A. 15
B. 20
C. 25
D. 30

Solution

If the daughter is 5 years old, then the mother is 4 * 5 = 20 years old.

Correct Answer: B — 20

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Q. The age of a mother is 4 times the age of her daughter. If the daughter is 6 years old, how old is the mother?

A. 18
B. 20
C. 24
D. 30

Solution

If the daughter is 6 years old, then the mother is 4 * 6 = 24 years old.

Correct Answer: C — 24

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Q. The age of a mother is 5 times the age of her daughter. If the daughter is 6 years old, what is the mother's age?

A. 24
B. 30
C. 36
D. 40

Solution

If the daughter is 6 years old, then the mother is 5 * 6 = 30 years old.

Correct Answer: A — 24

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Q. The age of I is three times the age of J. If the difference in their ages is 24 years, how old is J?

A. 8
B. 12
C. 16
D. 20

Solution

Let J's age be x. Then I's age is 3x. The difference is 3x - x = 24, hence 2x = 24, x = 12. Therefore, J is 12 years old.

Correct Answer: C — 16

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Q. The ages of M and N are in the ratio 5:3. If the sum of their ages is 64 years, what is M's age?

A. 30
B. 32
C. 34
D. 36

Solution

Let M's age be 5x and N's age be 3x. Then 5x + 3x = 64. Solving gives x = 8, thus M = 40.

Correct Answer: B — 32

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Q. The ages of O and P are in the ratio 5:3. If the sum of their ages is 64, what is O's age?

A. 40
B. 32
C. 36
D. 28

Solution

Let O's age be 5x and P's age be 3x. Then, 5x + 3x = 64. Solving gives x = 8, O's age = 5 * 8 = 40.

Correct Answer: A — 40

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Q. The area of a circle is 78.5 square meters. What is the radius of the circle? (Use π = 3.14)

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

Solution

Area = π × radius²; 78.5 = 3.14 × radius²; radius² = 78.5 / 3.14 = 25; radius = √25 = 5 meters.

Correct Answer: B — 6

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Q. The area of a triangle is 60 square meters and its base is 12 meters. What is the height of the triangle in meters?

A. 8
B. 10
C. 12
D. 15

Solution

Area = (1/2) × base × height; 60 = (1/2) × 12 × height; height = (60 × 2) / 12 = 10 meters.

Correct Answer: B — 10

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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 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 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 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, 10, 15, 20, and x is 12. What is the value of x?

A. 5
B. 10
C. 15
D. 20

Solution

Average = (5 + 10 + 15 + 20 + x) / 5 = 12. Therefore, 50 + x = 60, so x = 10.

Correct Answer: B — 10

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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 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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Arithmetic Aptitude

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