Arithmetic Aptitude for Competitive Exam Success

Arithmetic Aptitude

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Q. A person is standing 30 meters away from a tree. If the angle of elevation to the top of the tree is 60 degrees, what is the height of the tree?

A. 30√3
B. 20√3
C. 10√3
D. 40√3

Solution

height = distance * tan(60) = 30 * √3 = 30√3 meters

Correct Answer: A — 30√3

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Q. A person is standing 30 meters away from the base of a building. If the angle of elevation to the top of the building is 60 degrees, what is the height of the building?

A. 15√3 meters
B. 30 meters
C. 20√3 meters
D. 25 meters

Solution

Height = distance * tan(60) = 30 * √3 = 15√3 meters.

Correct Answer: A — 15√3 meters

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Q. A person is standing 40 meters away from a building. If the angle of elevation to the top of the building is 30 degrees, what is the height of the building?

A. 20 meters
B. 23 meters
C. 30 meters
D. 35 meters

Solution

Height = distance * tan(angle) = 40 * (1/√3) = 40 / 1.732 = 23.09 meters.

Correct Answer: A — 20 meters

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Q. A person is standing 40 meters away from a building. If the angle of elevation to the top of the building is 45 degrees, what is the height of the building?

A. 20 meters
B. 30 meters
C. 40 meters
D. 45 meters

Solution

Height = distance * tan(angle) = 40 * 1 = 40 meters.

Correct Answer: C — 40 meters

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Q. A person is standing 40 meters away from a tower. If the angle of elevation to the top of the tower is 45 degrees, what is the height of the tower?

A. 20 meters
B. 30 meters
C. 40 meters
D. 45 meters

Solution

Height = distance * tan(angle) = 40 * 1 = 40 meters.

Correct Answer: C — 40 meters

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Q. A person is standing 45 meters away from a building. If the angle of elevation to the top of the building is 45 degrees, what is the height of the building?

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

Solution

Height = distance * tan(angle) = 45 * 1 = 45 meters.

Correct Answer: B — 45 meters

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Q. A person is standing 50 meters away from a building. If the angle of elevation to the top of the building is 30 degrees, what is the height of the building?

A. 25 meters
B. 50 meters
C. 75 meters
D. 100 meters

Solution

Height = distance * tan(angle) = 50 * (1/√3) = 50/√3 meters.

Correct Answer: A — 25 meters

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Q. A person is standing 50 meters away from a hill. If the angle of elevation to the top of the hill is 37 degrees, what is the height of the hill?

A. 30 meters
B. 40 meters
C. 50 meters
D. 20 meters

Solution

Height = distance * tan(angle) = 50 * tan(37°) ≈ 30 meters.

Correct Answer: A — 30 meters

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Q. A person is standing 50 meters away from a hill. If the angle of elevation to the top of the hill is 30 degrees, what is the height of the hill?

A. 25√3 meters
B. 50 meters
C. 30 meters
D. 40 meters

Solution

Height = distance * tan(angle) = 50 * (1/√3) = 50/√3 = 25√3 meters.

Correct Answer: A — 25√3 meters

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Q. A person is standing 50 meters away from a statue. If the angle of elevation to the top of the statue is 45 degrees, what is the height of the statue?

A. 25 meters
B. 50 meters
C. 35 meters
D. 45 meters

Solution

Height = distance * tan(angle) = 50 * 1 = 50 meters.

Correct Answer: B — 50 meters

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Q. A person looks at the top of a building from a distance of 50 meters. If the angle of elevation is 30 degrees, what is the height of the building?

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

Solution

Height = distance * tan(30) = 50 * (1/√3) ≈ 25 meters.

Correct Answer: A — 25 meters

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Q. A person looks at the top of a tree from a distance of 40 meters. If the angle of elevation is 30 degrees, what is the height of the tree?

A. 20 meters
B. 30 meters
C. 40 meters
D. 50 meters

Solution

Height = distance * tan(angle) = 40 * (1/√3) ≈ 20 meters.

Correct Answer: A — 20 meters

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Q. A person received a 15% raise in his salary. If his new salary is $1,150, what was his old salary?

A. $1,000
B. $1,050
C. $1,100
D. $1,200

Solution

Let the old salary be x. Then, x + 0.15x = 1150. Therefore, 1.15x = 1150, x = 1150 / 1.15 = 1000.

Correct Answer: A — $1,000

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Q. A person scores 80, 90, and 70 in three exams. What score does he need in the fourth exam to achieve an average of 85?

A. 90
B. 95
C. 100
D. 85

Solution

Let the fourth score be x. (80 + 90 + 70 + x) / 4 = 85. Solving gives x = 100.

Correct Answer: B — 95

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Q. A person spends 30% of his salary on rent and 20% on groceries. If his salary is $1,000, how much does he spend on rent?

A. $200
B. $250
C. $300
D. $350

Solution

Rent = 30% of 1000 = 0.3 * 1000 = 300.

Correct Answer: C — $300

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Q. A person spends 40% of his income on rent and 30% on food. If his income is $2000, how much does he spend on rent?

A. $600
B. $700
C. $800
D. $900

Solution

Rent = 40% of 2000 = 0.4 * 2000 = 800.

Correct Answer: A — $600

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Q. A person standing 100 meters away from a hill observes the top of the hill at an angle of elevation of 60 degrees. What is the height of the hill?

A. 100√3
B. 50√3
C. 75√3
D. 25√3

Solution

height = distance * tan(60) = 100 * √3 = 100√3 meters

Correct Answer: A — 100√3

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Q. A person standing 15 meters away from a building observes the top of the building at an angle of elevation of 45 degrees. What is the height of the building?

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

Solution

Height = distance * tan(45) = 15 * 1 = 15 m

Correct Answer: B — 15 m

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Q. A person standing 20 meters away from a building observes the top of the building at an angle of elevation of 45 degrees. What is the height of the building?

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

Solution

Height = distance * tan(angle) = 20 * 1 = 20 meters.

Correct Answer: A — 20 meters

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Q. A person standing 20 meters away from a wall sees the top of the wall at an angle of elevation of 30 degrees. What is the height of the wall?

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

Solution

Height = distance * tan(angle) = 20 * (1/√3) = 20 / 1.732 = 11.55 meters.

Correct Answer: B — 10 meters

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Q. A person standing 25 meters away from a building observes the top of the building at an angle of elevation of 53 degrees. What is the height of the building?

A. 15 meters
B. 20 meters
C. 30 meters
D. 40 meters

Solution

Height = distance * tan(angle) = 25 * tan(53) ≈ 25 * 1.327 = 33.175 meters.

Correct Answer: C — 30 meters

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Q. A person standing 40 meters away from a building observes the top of the building at an angle of elevation of 30 degrees. What is the height of the building?

A. 20 meters
B. 10√3 meters
C. 30 meters
D. 40 meters

Solution

Height = distance * tan(angle) = 40 * (1/√3) = 40/√3 = 10√3 meters.

Correct Answer: B — 10√3 meters

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Q. A person standing 50 meters away from a building observes the top of the building at an angle of elevation of 30 degrees. What is the height of the building?

A. 25 meters
B. 15√3 meters
C. 10√3 meters
D. 20 meters

Solution

Height = distance * tan(30) = 50 * (1/√3) = 50/√3 = 15√3 meters

Correct Answer: B — 15√3 meters

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Q. A person standing 50 meters away from a building observes the top of the building at an angle of elevation of 60 degrees. What is the height of the building?

A. 25√3 meters
B. 50 meters
C. 75 meters
D. 100 meters

Solution

Height = distance * tan(angle) = 50 * √3 = 25√3 meters.

Correct Answer: A — 25√3 meters

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Q. A person travels 60 km at a speed of 20 km/h. How long will it take?

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

Solution

Time = Distance / Speed = 60 km / 20 km/h = 3 hours.

Correct Answer: B — 3 hours

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Q. A person walks at a speed of 4 km/h. How long will it take to walk 10 km?

A. 2 hours
B. 2.5 hours
C. 3 hours
D. 3.5 hours

Solution

Time = Distance / Speed = 10 km / 4 km/h = 2.5 hours.

Correct Answer: B — 2.5 hours

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

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

Solution

The net rate of filling the tank is 1/10 - 1/15 = 1/30. Therefore, it will take 30 hours to fill the tank.

Correct Answer: B — 6 hours

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Q. A pipe can fill a tank in 12 hours, and another pipe can empty it in 8 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 net rate is 1/12 - 1/8 = 1/24. Therefore, it will take 24 hours to fill the tank.

Correct Answer: C — 6 hours

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Q. A pipe can fill a tank in 5 hours, and a second pipe can fill the same tank in 10 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 1/5 + 1/10 = 3/10. Therefore, it will take 10/3 hours or 3.33 hours to fill the tank.

Correct Answer: A — 2 hours

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Q. A population of a town increased from 10,000 to 12,000. What is the percentage increase?

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

Solution

Percentage increase = ((12,000 - 10,000) / 10,000) * 100 = 20%.

Correct Answer: A — 20%

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Arithmetic Aptitude

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