Arithmetic Aptitude for Competitive Exam Success

Arithmetic Aptitude

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Q. In how many ways can 7 different books be arranged on a shelf if 3 specific books must be in the middle?

A. 720
B. 1440
C. 5040
D. 840

Solution

Arrange the 3 specific books in the middle (3!) and the remaining 4 books (4!): 3! * 4! = 1440.

Correct Answer: B — 1440

Q. In how many ways can the letters of the word 'BANANA' be arranged?

A. 60
B. 30
C. 20
D. 10

Solution

The number of arrangements of the letters in 'BANANA' is 6! / (3!) = 20.

Correct Answer: B — 30

Q. In how many ways can the letters of the word 'MATH' be arranged?

A. 24
B. 12
C. 6
D. 4

Solution

The number of ways to arrange the letters of 'MATH' is 4! = 24.

Correct Answer: A — 24

Q. Pipe A can fill a tank in 15 hours, and pipe B can fill the same tank in 20 hours. If both pipes are opened together, how long will it take to fill the tank?

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

Solution

The combined rate is 1/15 + 1/20 = 7/60. Therefore, it will take 60/7 hours, approximately 8.57 hours to fill the tank.

Correct Answer: B — 8 hours

Q. Pipe A can fill a tank in 15 hours, while pipe B can fill it in 10 hours. If both pipes are opened together, how long will it take to fill the tank?

A. 4 hours
B. 5 hours
C. 6 hours
D. 7 hours

Solution

The combined rate is 1/15 + 1/10 = 1/6. Therefore, it will take 6 hours to fill the tank.

Correct Answer: B — 5 hours

Q. Pipe A can fill a tank in 6 hours, and pipe B can fill the same tank in 9 hours. If both 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 + 1/9 = 5/18. Therefore, it will take 18/5 = 3.6 hours to fill the tank.

Correct Answer: B — 3 hours

Q. Pipe A can fill a tank in 6 hours, while pipe B can empty it in 4 hours. If both 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 net rate is 1/6 - 1/4 = -1/12. Therefore, the tank will never fill.

Correct Answer: C — 4 hours

Q. Pipe A can fill a tank in 6 hours, while pipe B can fill it in 4 hours. If both pipes are opened together, how long will it take to fill the tank?

A. 2.4 hours
B. 3 hours
C. 3.6 hours
D. 4 hours

Solution

The combined rate is 1/6 + 1/4 = 5/12. Therefore, time taken = 12/5 = 2.4 hours.

Correct Answer: B — 3 hours

Q. Pipe A can fill a tank in 6 hours, while pipe B can fill it in 9 hours. If both 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 + 1/9 = 5/18. Therefore, it will take 18/5 = 3.6 hours to fill the tank.

Correct Answer: B — 3 hours

Q. Ten years ago, a man was twice as old as his son. If the man is currently 40 years old, how old is his son now?

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

Solution

Ten years ago, the man was 30 years old. If he was twice as old as his son then, the son was 30 / 2 = 15 years old. Now, the son is 15 + 10 = 25 years old.

Correct Answer: B — 20

Q. Ten years ago, a woman was 3 times as old as her son. If the son is now 10 years old, how old is the woman now?

A. 30
B. 40
C. 50
D. 60

Solution

Ten years ago, the son was 0 years old. Therefore, the woman was 3 * 0 = 0 years old. Now, she is 10 + 10 = 20 years old.

Correct Answer: B — 40

Q. Ten years ago, the age of a man was 3 times the age of his son. If the son is now 10 years old, how old is the man now?

A. 30
B. 40
C. 50
D. 60

Solution

Ten years ago, the son was 10 - 10 = 0 years old. The man was 3 * 0 = 0 years old then, so now he is 10 + 30 = 40 years old.

Correct Answer: B — 40

Q. Ten years ago, the age of A was three times the age of B. If B is now 15 years old, how old is A now?

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

Solution

Ten years ago, B was 15 - 10 = 5 years old. A was 3 * 5 = 15 years old then, so A is now 15 + 10 = 25.

Correct Answer: B — 30

Q. Ten years ago, the age of A was twice the age of B. If A is now 30 years old, how old is B now?

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

Solution

Ten years ago, A was 30 - 10 = 20 years old. Therefore, B was 20 / 2 = 10 years old then. Now, B is 10 + 10 = 20 years old.

Correct Answer: D — 25

Q. Ten years ago, the age of G was half of H's age. If H is now 30 years old, how old is G now?

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

Solution

Ten years ago, H was 20 years old. Therefore, G was 10 years old. Now, G is 10 + 10 = 20 years old.

Correct Answer: C — 25

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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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