Arithmetic Aptitude for Competitive Exam Success

Arithmetic Aptitude

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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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Q. The average of three consecutive integers is 20. What is the largest of these integers?

A. 19
B. 20
C. 21
D. 22

Solution

Let the integers be x, x+1, x+2. Average = (x + (x+1) + (x+2)) / 3 = 20. Solving gives x = 19, largest integer = 21.

Correct Answer: C — 21

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Q. The average of three numbers is 15. If one of the numbers is 12, what is the average of the other two numbers?

A. 14
B. 15
C. 16
D. 17

Solution

Total of three numbers = 3 * 15 = 45. Sum of other two numbers = 45 - 12 = 33. Average = 33 / 2 = 16.5.

Correct Answer: B — 15

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Q. The average of three numbers is 20. If one number is 10, what is the average of the other two numbers?

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

Solution

Total of three numbers = 20 * 3 = 60. The sum of the other two = 60 - 10 = 50. Average = 50 / 2 = 25.

Correct Answer: A — 15

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Q. The average of three numbers is 30. If one number is 20, what is the average of the other two numbers?

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

Solution

Total of three numbers = 3 * 30 = 90. Sum of other two numbers = 90 - 20 = 70. Average = 70 / 2 = 35.

Correct Answer: C — 25

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

A. 30
B. 32
C. 33
D. 35

Solution

Total of three numbers = 3 * 30 = 90. New total = 90 + 10 = 100. New average = 100 / 3 = 33.33.

Correct Answer: B — 32

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

A. 25
B. 30
C. 35
D. 40

Solution

Let the three numbers be a, b, and c. We have (a + b + c) / 3 = 30. Thus, a + b + c = 90. If c = 10, then a + b = 90 - 10 = 80. The average of a and b is 80 / 2 = 40.

Correct Answer: A — 25

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Q. The average of two numbers is 40. If one number is 30, what is the other number?

A. 50
B. 60
C. 70
D. 80

Solution

Let the other number be x. (30 + x) / 2 = 40. So, 30 + x = 80. Therefore, x = 50.

Correct Answer: A — 50

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

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

Solution

Total score = 30 * 75 = 2250. New total = 2250 - 90 = 2160. New average = 2160 / 29 = 74.55.

Correct Answer: A — 74

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Q. The average score of a student in 6 subjects is 75. If he scores 90 in the seventh subject, what will be his new average?

A. 76
B. 77
C. 78
D. 79

Solution

The total score in 6 subjects is 6 * 75 = 450. Adding the score of 90 gives a new total of 450 + 90 = 540. The new average is 540 / 7 = 77.14, which rounds to 77.

Correct Answer: B — 77

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Q. The average score of a team in 5 matches is 75. If they score 90 in the next match, what will be their new average?

A. 76
B. 77
C. 78
D. 79

Solution

Total score in 5 matches = 5 * 75 = 375. New total = 375 + 90 = 465. New average = 465 / 6 = 77.5.

Correct Answer: C — 78

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Q. The combined age of O and P is 80 years. If O is 10 years older than P, how old is O?

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

Solution

Let P's age be x. Then O's age is x + 10. So, x + (x + 10) = 80. Solving gives x = 35, hence O = 45.

Correct Answer: B — 40

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Q. The present age of a grandfather is 4 times that of his grandson. If the grandson is 5 years old, what is the grandfather's age?

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

Solution

If the grandson is 5 years old, then the grandfather is 4 * 5 = 20 years old.

Correct Answer: D — 30

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Q. The ratio of boys to girls in a class is 3:2. If there are 30 boys, how many girls are there?

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

Solution

If the ratio is 3:2, then for every 3 boys, there are 2 girls. Therefore, if there are 30 boys, the number of girls = (2/3) * 30 = 20

Correct Answer: B — 20

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Q. The ratio of the ages of G and H is 3:2. If G is 30 years old, how old is H?

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

Solution

If G is 30 years old, then H's age is (2/3) * 30 = 20 years.

Correct Answer: A — 20

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Q. The ratio of the ages of G and H is 3:4. If H is 32 years old, how old is G?

A. 24
B. 30
C. 28
D. 20

Solution

If H is 32 years, then G's age = (3/4) * 32 = 24 years.

Correct Answer: A — 24

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Q. The ratio of the ages of two friends is 2:3. If the sum of their ages is 50 years, what is the age of the older friend?

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

Solution

Let their ages be 2x and 3x. Then, 2x + 3x = 50, 5x = 50, x = 10. Older friend's age = 3x = 3*10 = 30.

Correct Answer: A — 30

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Q. The ratio of the lengths of two sides of a triangle is 3:4. If the perimeter is 70 cm, what is the length of the shorter side?

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

Solution

Let the sides be 3x and 4x. Then, 3x + 4x = 70, 7x = 70, x = 10. Shorter side = 3x = 3*10 = 30.

Correct Answer: B — 20

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Q. The ratio of the speeds of two cars is 5:7. If the faster car travels 140 km in 2 hours, how far does the slower car travel in the same time?

A. 100
B. 120
C. 140
D. 160

Solution

Speed of faster car = 140 km / 2 hours = 70 km/h. Speed of slower car = (5/7) * 70 = 50 km/h. Distance traveled by slower car in 2 hours = 50 * 2 = 100 km.

Correct Answer: B — 120

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Q. The sum of the ages of A and B is 50 years. If A is 10 years older than B, how old is A?

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

Solution

Let B's age be x. Then A's age is x + 10. So, x + (x + 10) = 50. Solving gives x = 20, hence A = 30.

Correct Answer: C — 30

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Q. The sum of the ages of A and B is 50 years. If A is 10 years older than B, what is B's age?

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

Solution

Let B's age be x. Then A's age is x + 10. So, x + (x + 10) = 50. Solving gives x = 20.

Correct Answer: B — 25

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Q. The sum of the ages of a father and his son is 50 years. If the father is 30 years older than the son, how old is the son?

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

Solution

Let the son's age be x. Then the father's age is x + 30. So, x + (x + 30) = 50. Solving gives x = 10.

Correct Answer: C — 20

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Q. The sum of the ages of a father and his son is 50 years. If the father is 40 years old, how old is the son?

A. 10
B. 15
C. 20
D. 30

Solution

If the father is 40 years old, then the son is 50 - 40 = 10 years old.

Correct Answer: C — 20

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Q. The sum of the ages of a mother and her daughter is 50 years. If the mother is 4 times as old as her daughter, how old is the daughter?

A. 10
B. 8
C. 12
D. 6

Solution

Let the daughter's age be x. Then the mother's age is 4x. The equation is x + 4x = 50, which simplifies to 5x = 50, so x = 10.

Correct Answer: A — 10

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Q. The sum of the ages of a mother and her daughter is 60 years. If the mother is 4 times as old as her daughter, how old is the daughter?

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

Solution

Let the daughter's age be x. Then the mother's age is 4x. So, x + 4x = 60. Solving gives x = 12.

Correct Answer: B — 10

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Q. Three pipes can fill a tank in 6, 8, and 12 hours respectively. If all three pipes are opened together, how long will it take to fill the tank?

A. 2 hours
B. 3 hours
C. 4 hours
D. 5 hours

Solution

The combined rate is 1/6 + 1/8 + 1/12 = 1/3. Therefore, it will take 3 hours to fill the tank.

Correct Answer: B — 3 hours

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Q. Three years ago, a man was 5 times as old as his son. If the man is currently 38 years old, how old is his son now?

A. 6
B. 7
C. 8
D. 9

Solution

Let the son's age be x. Three years ago, the man was 35 and the son was x - 3. So, 35 = 5(x - 3). Solving gives x = 8.

Correct Answer: C — 8

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Q. Three years ago, A was 2 times as old as B. If B is currently 12 years old, how old is A now?

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

Solution

Three years ago, B was 12 - 3 = 9 years old. A was 2 * 9 = 18 years old. Now, A is 18 + 3 = 21 years old.

Correct Answer: B — 20

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Q. Three years ago, A was 5 times as old as B. If B is now 10 years old, how old is A now?

A. 25
B. 30
C. 35
D. 40

Solution

Three years ago, B was 7 years old. Therefore, A was 5 * 7 = 35 years old. Now, A is 35 + 3 = 38 years old.

Correct Answer: B — 30

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Q. Three years ago, A was 5 times as old as B. If B is now 7 years old, how old is A now?

A. 25
B. 30
C. 35
D. 40

Solution

Three years ago, B was 4 years old. Therefore, A was 5 * 4 = 20 years old. Now, A is 20 + 3 = 23 years old.

Correct Answer: B — 30

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Arithmetic Aptitude

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