Arithmetic Aptitude for Competitive Exam Success

Arithmetic Aptitude

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Q. A car's value depreciates by 20% each year. If the current value is $10,000, what will be its value after one year?

A. $7,500
B. $8,000
C. $8,500
D. $9,000

Solution

Depreciation = 20% of 10000 = 0.2 * 10000 = 2000; Value after one year = 10000 - 2000 = 8000.

Correct Answer: A — $7,500

Q. A car's value depreciates by 20% each year. If the current value is $25,000, what will be its value after one year?

A. $20,000
B. $22,000
C. $24,000
D. $25,000

Solution

Depreciation = 20% of 25,000 = 5,000. Value after one year = 25,000 - 5,000 = 20,000.

Correct Answer: B — $22,000

Q. A card is drawn from a standard deck of 52 cards. What is the probability that it is a heart?

A. 1/4
B. 1/13
C. 1/2
D. 1/3

Solution

There are 13 hearts in a deck of 52 cards. The probability is 13/52 = 1/4.

Correct Answer: A — 1/4

Q. A circular garden has a diameter of 10 m. What is its area? (Use π = 3.14)

A. 78.5 m²
B. 31.4 m²
C. 50 m²
D. 100 m²

Solution

Radius = diameter/2 = 10 m/2 = 5 m. Area = πr² = 3.14 × (5 m)² = 78.5 m².

Correct Answer: A — 78.5 m²

Q. A circular garden has a diameter of 14 m. What is its area (use π ≈ 3.14)?

A. 153.86 m²
B. 154 m²
C. 150 m²
D. 160 m²

Solution

Radius = diameter/2 = 14 m/2 = 7 m. Area = π × radius² = 3.14 × (7 m)² = 153.86 m².

Correct Answer: A — 153.86 m²

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 clock gains 5 minutes every hour. If it shows 10:00 AM now, what will be the actual time when it shows 12:00 PM?

A. 11:30 AM
B. 11:50 AM
C. 12:10 PM
D. 12:20 PM

Solution

In 2 hours, the clock will gain 10 minutes (5 minutes/hour * 2 hours). So, when the clock shows 12:00 PM, the actual time will be 12:00 PM - 10 minutes = 11:50 AM.

Correct Answer: B — 11:50 AM

Q. A clock shows 8:00. What will be the angle between the hour and minute hands at 8:30?

A. 180 degrees
B. 165 degrees
C. 150 degrees
D. 135 degrees

Solution

At 8:30, the hour hand is at 255 degrees (8 * 30 + 30 * 0.5) and the minute hand is at 180 degrees (30 * 6). The angle between them is |255 - 180| = 75 degrees.

Correct Answer: B — 165 degrees

Q. A company increased the salary of its employees by 12%. If an employee's current salary is $1,500, what will be the new salary?

A. $1,620
B. $1,680
C. $1,700
D. $1,800

Solution

New salary = 1500 + (12/100)*1500 = 1500 + 180 = $1,680.

Correct Answer: B — $1,680

Q. A company increased the salary of its employees by 15%. If an employee's current salary is $2000, what will be the new salary after the increase?

A. $2200
B. $2300
C. $2400
D. $2500

Solution

New salary = Current salary + (15% of Current salary) = 2000 + (0.15 * 2000) = 2000 + 300 = 2300.

Correct Answer: A — $2200

Q. A container has 30 liters of a mixture of milk and water in the ratio 2:1. How much water is in the mixture?

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

Solution

In a 2:1 ratio, for every 3 parts, 1 part is water. Therefore, water = (1/3) * 30 = 10 liters.

Correct Answer: A — 10 liters

Q. A container has 50 liters of a mixture of juice and water in the ratio 4:1. How much juice is in the mixture?

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

Solution

In a 4:1 ratio, total parts = 4 + 1 = 5. Juice = (4/5) * 50 = 40 liters.

Correct Answer: C — 40 liters

Q. A container has 60 liters of a mixture of juice and water in the ratio 4:1. How much juice is in the mixture?

A. 48 liters
B. 12 liters
C. 36 liters
D. 24 liters

Solution

Juice = (4/5) * 60 = 48 liters.

Correct Answer: A — 48 liters

Q. A die is rolled. What is the probability of rolling a number greater than 4?

A. 1/6
B. 1/3
C. 1/2
D. 1/4

Solution

The numbers greater than 4 are 5 and 6. So, the probability is 2/6 = 1/3.

Correct Answer: B — 1/3

Q. A family has 3 children. What is the probability that at least one of them is a girl?

A. 1/8
B. 1/4
C. 3/4
D. 7/8

Solution

The only scenario where there are no girls is if all are boys. The probability of all boys is (1/2)^3 = 1/8. Therefore, the probability of at least one girl is 1 - 1/8 = 7/8.

Correct Answer: D — 7/8

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 father is 4 times as old as his son. If the sum of their ages is 50 years, how old is the father?

A. 40
B. 30
C. 20
D. 10

Solution

Let the son's age be x. Then the father's age is 4x. So, x + 4x = 50. Solving gives the father is 40.

Correct Answer: A — 40

Q. A father is three times as old as his son. If the father is 36 years old, how old is the son?

A. 12
B. 10
C. 15
D. 9

Solution

If the father is 36 years old and he is three times as old as his son, then the son's age is 36 / 3 = 12.

Correct Answer: A — 12

Q. A grandfather is 4 times as old as his grandson. If the grandson is 5 years old, how old is the grandfather?

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

Solution

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

Correct Answer: A — 20

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 is 3 times as old as B. If the sum of their ages is 48 years, how old is A?

A. 36
B. 24
C. 12
D. 18

Solution

Let B's age be x. Then A's age is 3x. So, x + 3x = 48, which gives 4x = 48, hence x = 12. Therefore, A is 3 * 12 = 36 years old.

Correct Answer: A — 36

Q. A is 3 years older than B. If the sum of their ages is 27, how old is A?

A. 12
B. 15
C. 18
D. 21

Solution

Let B's age be x. Then A's age is x + 3. So, x + (x + 3) = 27. Solving gives x = 12. Therefore, A is 15.

Correct Answer: B — 15

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