Arithmetic Aptitude for Competitive Exam Success

Arithmetic Aptitude

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Q. A man earns $1200 after a 20% increase in his salary. What was his original salary?

A. $1000
B. $1100
C. $1200
D. $1300

Solution

Let the original salary be x. Then, x + 0.2x = 1200. Therefore, 1.2x = 1200, x = 1200/1.2 = 1000.

Correct Answer: A — $1000

Q. A man earns $1200 after a 25% increase in his salary. What was his original salary?

A. $800
B. $900
C. $1000
D. $1100

Solution

Let the original salary be x. Then, x + 0.25x = 1200. Therefore, 1.25x = 1200, x = 1200 / 1.25 = 960.

Correct Answer: C — $1000

Q. A man earns $1200 per month. If he spends 25% of his income on rent, how much does he spend on rent?

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

Solution

Rent = 25% of $1200 = (25/100)*1200 = $300.

Correct Answer: C — $300

Q. A man earns $1200 per month. If he spends 75% of his income, how much does he save?

A. $200
B. $300
C. $400
D. $500

Solution

Amount spent = 75% of 1200 = 0.75 * 1200 = $900. Savings = 1200 - 900 = $300.

Correct Answer: B — $300

Q. A man is 10 years older than his wife. If the sum of their ages is 70 years, how old is the wife?

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

Solution

Let the wife's age be x. Then the man's age is x + 10. The equation is x + (x + 10) = 70, which simplifies to 2x + 10 = 70, so 2x = 60, and x = 30.

Correct Answer: B — 25

Q. A man is 3 times as old as his son. If the sum of their ages is 48 years, how old is the son?

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

Solution

Let the son's age be x. Then the man's age is 3x. So, x + 3x = 48. Solving gives x = 12.

Correct Answer: C — 16

Q. A man is 50 meters away from a building. If he looks up at an angle of 60 degrees to see the top of the building, what is the height of the building?

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

Solution

Height = distance * tan(angle) = 50 * √3 = 50 * 1.732 = 86.6 meters.

Correct Answer: D — 40 meters

Q. A man is standing 15 meters away from a wall. If he looks up at an angle of 30 degrees to see the top of the wall, what is the height of the wall?

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

Solution

Height = distance * tan(angle) = 15 * (1/√3) ≈ 15 * 0.577 = 8.66 meters.

Correct Answer: B — 10 meters

Q. A man is standing 25 meters away from a vertical pole. If he looks up at an angle of 45 degrees, what is the height of the pole?

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

Solution

Height = distance * tan(angle) = 25 * 1 = 25 meters.

Correct Answer: A — 25 meters

Q. A man is standing 30 meters away from 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√3 meters
C. 45 meters
D. 60 meters

Solution

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

Correct Answer: A — 15√3 meters

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

A. 15 meters
B. 25 meters
C. 30 meters
D. 35 meters

Solution

Height = distance * tan(angle) = 30 * √3 = 30 * 1.732 = 51.96 meters.

Correct Answer: B — 25 meters

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

Solution

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

Correct Answer: A — 40 meters

Q. A man is standing 50 meters away from a building. If the angle of elevation to the top of the building is 60 degrees, what is the height of the building?

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

Solution

Height = distance * tan(angle) = 50 * √3 = 50 * 1.732 = 86.6 meters.

Correct Answer: D — 40 meters

Q. A man 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√3
B. 15√3
C. 20√3
D. 10√3

Solution

height = distance * tan(30) = 50 * (1/√3) = 50/√3 = 25√3 meters

Correct Answer: A — 25√3

Q. A man spends 25% of his salary on rent and 15% on groceries. If his salary is $4,000, how much does he spend on rent?

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

Solution

Rent = 25% of 4000 = (25/100) * 4000 = 1000.

Correct Answer: A — $800

Q. A man spends 25% of his salary on rent and 15% on groceries. What percentage of his salary does he spend on both?

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

Solution

Total percentage spent = 25% + 15% = 40%.

Correct Answer: B — 40%

Q. A man spends 25% of his salary on rent. If his salary is $4,000, how much does he spend on rent?

A. $800
B. $1,000
C. $1,200
D. $1,500

Solution

Rent = 0.25 * 4000 = 1000

Correct Answer: B — $1,000

Q. A man spends 30% of his salary on rent and 20% on groceries. If his salary is $1000, how much does he spend on rent?

A. $300
B. $200
C. $400
D. $500

Solution

Amount spent on rent = 30% of 1000 = 0.3 * 1000 = $300.

Correct Answer: A — $300

Q. A man spends 30% of his salary on rent, 20% on food, and saves the rest. If his salary is $1000, how much does he save?

A. $500
B. $400
C. $300
D. $200

Solution

Rent = 30% of 1000 = 300; Food = 20% of 1000 = 200; Total expenditure = 300 + 200 = 500; Savings = 1000 - 500 = 500.

Correct Answer: C — $300

Q. A man spends 30% of his salary on rent, 20% on food, and saves the rest. If his salary is $2000, how much does he save?

A. $1000
B. $1200
C. $1400
D. $1500

Solution

Rent = 30% of 2000 = 600. Food = 20% of 2000 = 400. Total expenses = 600 + 400 = 1000. Savings = 2000 - 1000 = $1000.

Correct Answer: C — $1400

Q. A man spends 40% of his income on rent and 30% on food. If his income is $1,000, how much does he spend on rent?

A. $300
B. $400
C. $500
D. $600

Solution

Rent = 0.4 * 1000 = $400.

Correct Answer: B — $400

Q. A man spends 40% of his income on rent and 30% on food. If his income is $1,000, how much does he spend on food?

A. $200
B. $300
C. $400
D. $500

Solution

Spending on food = 30% of 1000 = 0.3 * 1000 = 300.

Correct Answer: B — $300

Q. A man spends 40% of his income on rent. If his income is $5000, how much does he spend on rent?

A. $1800
B. $2000
C. $2200
D. $2400

Solution

Rent = 0.4 * 5000 = $2000.

Correct Answer: B — $2000

Q. A man spends 40% of his salary on rent and 25% on food. What percentage of his salary is left?

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

Solution

Total spent = 40% + 25% = 65%. Salary left = 100% - 65% = 35%.

Correct Answer: B — 30%

Q. A mixture contains 30% vinegar. If you have 90 liters of this mixture, how much vinegar is present?

A. 20 liters
B. 25 liters
C. 27 liters
D. 30 liters

Solution

Vinegar = 30% of 90 liters = 0.3 * 90 = 27 liters.

Correct Answer: C — 27 liters

Q. A mixture of 40 liters contains 25% sugar. How much sugar is in the mixture?

A. 5 liters
B. 8 liters
C. 10 liters
D. 12 liters

Solution

Sugar = 25% of 40 liters = 0.25 * 40 = 10 liters.

Correct Answer: A — 5 liters

Q. A mixture of 80 liters contains 10% oil. How much oil is in the mixture?

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

Solution

Oil = 10% of 80 liters = 0.1 * 80 = 8 liters.

Correct Answer: D — 8 liters

Q. A mother is 21 years older than her daughter. If the daughter is 9 years old now, how old will the mother be in 5 years?

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

Solution

The mother is currently 9 + 21 = 30 years old. In 5 years, she will be 30 + 5 = 35.

Correct Answer: C — 35

Q. A mother is 4 times as old as her daughter. After 8 years, the mother will be twice as old as her daughter. How old is the daughter now?

A. 4
B. 8
C. 12
D. 16

Solution

Let the daughter's age be x. Then the mother's age is 4x. In 8 years, 4x + 8 = 2(x + 8). Solving gives x = 8.

Correct Answer: B — 8

Q. A mother is 4 times as old as her daughter. After 8 years, the mother will be twice as old as her daughter. What is the present age of the daughter?

A. 4
B. 8
C. 12
D. 16

Solution

Let the daughter's age be x. Then the mother's age is 4x. In 8 years, 4x + 8 = 2(x + 8). Solving gives x = 8.

Correct Answer: B — 8

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