Arithmetic Aptitude for Competitive Exam Success

Arithmetic Aptitude

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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

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

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

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

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

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

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

Q. A population of a town increased from 20,000 to 25,000 in a year. What is the percentage increase in the population?

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

Solution

Percentage increase = ((25000 - 20000) / 20000) * 100 = (5000 / 20000) * 100 = 25%.

Correct Answer: B — 25%

Q. A population of a town increased from 20,000 to 25,000 in a year. What is the percentage increase?

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

Solution

Percentage increase = ((25000 - 20000) / 20000) * 100 = 25%.

Correct Answer: B — 25%

Q. A population of a town increased from 20,000 to 25,000 in a year. What is the percentage increase in population?

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

Solution

Percentage increase = ((25000 - 20000) / 20000) * 100 = 25%.

Correct Answer: B — 25%

Q. A population of a town increased from 20,000 to 25,000. What is the percentage increase?

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

Solution

Percentage increase = ((25000 - 20000) / 20000) * 100 = 25%

Correct Answer: B — 25%

Q. A principal amount of $2500 is invested at a compound interest rate of 7% per annum. What will be the amount after 5 years?

A. $3500
B. $3502.50
C. $3520.25
D. $3525.00

Solution

Amount = P(1 + r)^n = 2500(1 + 0.07)^5 = 2500(1.402552) = $3506.38.

Correct Answer: C — $3520.25

Q. A principal of $2500 is invested at a compound interest rate of 3% per annum. What will be the amount after 6 years?

A. $2925.00
B. $3000.00
C. $2800.00
D. $2700.00

Solution

Total Amount = 2500(1 + 0.03)^6 = 2500(1.191016) = 2977.54

Correct Answer: A — $2925.00

Q. A product is marked at $120 and is sold at a 25% discount. What is the selling price of the product?

A. $80
B. $85
C. $90
D. $95

Solution

Discount = 25% of 120 = 30. Selling price = 120 - 30 = $90.

Correct Answer: C — $90

Q. A product is marked at $120 and is sold at a discount of 25%. What is the selling price of the product?

A. $80
B. $85
C. $90
D. $95

Solution

Discount = 25% of 120 = 0.25 * 120 = 30; Selling price = Marked price - Discount = 120 - 30 = 90.

Correct Answer: A — $80

Q. A product is marked at $200 and is sold at a 15% discount. What is the selling price?

A. $170
B. $180
C. $190
D. $200

Solution

Selling price = 200 - (15/100 * 200) = 200 - 30 = $170.

Correct Answer: A — $170

Q. A product is marked at $500 and is sold at a 10% discount. What is the selling price?

A. $450
B. $475
C. $500
D. $550

Solution

Discount = 10% of 500 = 50. Selling price = 500 - 50 = 450.

Correct Answer: B — $475

Q. A product is marked at $500 and is sold at a 15% discount. What is the selling price?

A. $425
B. $450
C. $475
D. $500

Solution

Discount = 15% of 500 = 0.15 * 500 = 75. Selling price = 500 - 75 = 425.

Correct Answer: A — $425

Q. A product's price increased from $150 to $180. What is the percentage increase in price?

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

Solution

Percentage increase = ((180 - 150) / 150) * 100 = (30 / 150) * 100 = 20%.

Correct Answer: B — 20%

Q. A product's price increased from $200 to $250. What is the percentage increase in the price?

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

Solution

Percentage increase = ((250 - 200)/200)*100 = (50/200)*100 = 25%.

Correct Answer: B — 25%

Q. A product's price increased from $200 to $250. What is the percentage increase in price?

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

Solution

Percentage increase = ((250 - 200) / 200) * 100 = (50 / 200) * 100 = 25%.

Correct Answer: B — 25%

Q. A product's price increased from $50 to $65. What is the percentage increase in the price?

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

Solution

Increase = 65 - 50 = 15; Percentage increase = (15/50) * 100 = 30%.

Correct Answer: B — 30%

Q. A product's price increased from $80 to $100. What is the percentage increase?

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

Solution

Percentage increase = ((100 - 80) / 80) * 100 = (20 / 80) * 100 = 25%.

Correct Answer: B — 25%

Q. A rectangle has an area of 72 cm² and a length of 12 cm. What is its width?

A. 6 cm
B. 8 cm
C. 4 cm
D. 10 cm

Solution

Area = length × width. Therefore, width = Area/length = 72 cm²/12 cm = 6 cm.

Correct Answer: B — 8 cm

Q. A rectangle has an area of 72 m² and a length of 12 m. What is its width?

A. 6 m
B. 8 m
C. 4 m
D. 10 m

Solution

Area = length × width; width = Area / length = 72 m² / 12 m = 6 m.

Correct Answer: B — 8 m

Q. A rectangular garden is 15 m long and 10 m wide. If a path of 1 m width is built around it, what is the area of the path?

A. 80 m²
B. 100 m²
C. 60 m²
D. 120 m²

Solution

Total area with path = (15+2) × (10+2) = 17 × 12 = 204 m². Area of garden = 15 × 10 = 150 m². Area of path = 204 - 150 = 54 m².

Correct Answer: A — 80 m²

Q. A rhombus has diagonals of lengths 10 cm and 24 cm. What is its area?

A. 120 cm²
B. 140 cm²
C. 160 cm²
D. 180 cm²

Solution

Area = (d1 × d2)/2 = (10 cm × 24 cm)/2 = 120 cm².

Correct Answer: A — 120 cm²

Q. A shirt is sold for $240 after a discount of 20%. What was the original price of the shirt?

A. $200
B. $220
C. $240
D. $300

Solution

Let the original price be x. After a 20% discount, the selling price is x - 0.2x = 0.8x. Given 0.8x = 240, we find x = 240 / 0.8 = 300.

Correct Answer: A — $200

Q. A shirt is sold for $30 after a discount of 25%. What was the original price of the shirt?

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

Solution

Let the original price be x. Then, 0.75x = 30. Therefore, x = 30 / 0.75 = 40.

Correct Answer: B — $40

Q. A solution contains 40% salt. If you have 60 liters of this solution, how much salt is present?

A. 20 liters
B. 24 liters
C. 30 liters
D. 36 liters

Solution

Salt = 40% of 60 liters = 0.4 * 60 = 24 liters.

Correct Answer: B — 24 liters

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