Arithmetic Aptitude for Competitive Exam Success

Arithmetic Aptitude

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Q. A box contains 5 white and 3 black balls. If one ball is drawn at random, what is the probability that it is black?

A. 0.25
B. 0.3
C. 0.5
D. 0.4

Solution

The total number of balls is 5 + 3 = 8. The probability of drawing a black ball is 3/8 = 0.375.

Correct Answer: B — 0.3

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Q. A building casts a shadow of 10 meters when the angle of elevation of the sun is 30 degrees. What is the height of the building?

A. 5√3 meters
B. 10 meters
C. 15 meters
D. 20 meters

Solution

Height = shadow * tan(angle) = 10 * √3 = 5√3 meters.

Correct Answer: A — 5√3 meters

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Q. A building casts a shadow of 10 meters when the angle of elevation of the sun is 45 degrees. What is the height of the building?

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

Solution

Height = shadow * tan(45) = 10 * 1 = 10 meters.

Correct Answer: A — 10 meters

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Q. A building casts a shadow of 12 meters when the angle of elevation of the sun is 30 degrees. What is the height of the building?

A. 6 meters
B. 12 meters
C. 18 meters
D. 24 meters

Solution

Using tan(30) = height/shadow length, height = shadow length * tan(30) = 12 * √3 = 12√3 meters.

Correct Answer: C — 18 meters

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Q. A building casts a shadow of 20 meters when the angle of elevation of the sun is 45 degrees. What is the height of the building?

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

Solution

Height = shadow * tan(45) = 20 * 1 = 20 meters

Correct Answer: A — 20 meters

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Q. A building casts a shadow of 20 meters when the angle of elevation of the sun is 45°. What is the height of the building?

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

Solution

Using tan(45°) = height/20, height = 20 * 1 = 20 meters.

Correct Answer: B — 20 meters

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Q. A building is 120 meters tall. From a point 80 meters away from the base of the building, what is the angle of elevation to the top of the building?

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

Solution

tan(θ) = height/distance = 120/80 = 1.5, θ = tan⁻¹(1.5) ≈ 60 degrees.

Correct Answer: C — 60 degrees

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Q. A building is 20 meters tall. If a person standing 15 meters away from the building sees the top at an angle of elevation of θ, what is sin(θ)?

A. 0.8
B. 0.6
C. 0.5
D. 0.75

Solution

sin(θ) = height / hypotenuse; hypotenuse = √(20^2 + 15^2) = √625 = 25; sin(θ) = 20/25 = 0.8

Correct Answer: A — 0.8

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Q. A building is 24 meters tall. If a person is standing 32 meters away from the base of the building, what is the angle of elevation to the top of the building?

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

Solution

tan(θ) = height/distance = 24/32 = 0.75; θ = tan^(-1)(0.75) ≈ 36.87 degrees.

Correct Answer: C — 60 degrees

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Q. A building is 25 meters tall. If a person is standing 20 meters away from the base of the building, what is the angle of elevation to the top of the building?

A. 36.87 degrees
B. 45 degrees
C. 53.13 degrees
D. 60 degrees

Solution

tan(θ) = height/distance = 25/20; θ = tan^(-1)(5/4) = 36.87 degrees.

Correct Answer: A — 36.87 degrees

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Q. A building is 80 meters tall. From a point 60 meters away from the base of the building, what is the angle of elevation to the top of the building?

A. 30 degrees
B. 36.87 degrees
C. 45 degrees
D. 53.13 degrees

Solution

tan(θ) = height/distance = 80/60, θ = tan⁻¹(4/3) ≈ 36.87 degrees.

Correct Answer: B — 36.87 degrees

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Q. A building is 80 meters tall. From a point 60 meters away from the base of the building, the angle of elevation to the top of the building is what?

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

Solution

Using tan(θ) = height/distance, tan(θ) = 80/60, θ = tan⁻¹(4/3) ≈ 53.13 degrees.

Correct Answer: B — 60 degrees

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Q. A building is 80 meters tall. From a point on the ground, the angle of elevation to the top of the building is 60 degrees. How far is the point from the base of the building?

A. 40√3 meters
B. 80 meters
C. 60 meters
D. 100 meters

Solution

Distance = height / tan(angle) = 80 / √3 = 80√3/3 meters.

Correct Answer: A — 40√3 meters

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Q. A bus travels at a speed of 60 km/h. How far can it travel in 4.5 hours?

A. 240 km
B. 270 km
C. 300 km
D. 330 km

Solution

Distance = Speed x Time = 60 km/h x 4.5 h = 270 km

Correct Answer: B — 270 km

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Q. A bus travels at a speed of 70 km/h. How far will it travel in 3.5 hours?

A. 210 km
B. 240 km
C. 250 km
D. 280 km

Solution

Distance = Speed * Time = 70 km/h * 3.5 h = 245 km.

Correct Answer: D — 280 km

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Q. A bus travels at a speed of 70 km/h. How far will it travel in 4.5 hours?

A. 280 km
B. 300 km
C. 320 km
D. 350 km

Solution

Distance = Speed * Time = 70 km/h * 4.5 h = 315 km.

Correct Answer: C — 320 km

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Q. A bus travels at a speed of 80 km/h. How long will it take to travel 320 km?

A. 3 hours
B. 4 hours
C. 5 hours
D. 6 hours

Solution

Time = Distance / Speed = 320 km / 80 km/h = 4 hours.

Correct Answer: B — 4 hours

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Q. A bus travels from city A to city B at a speed of 80 km/h and returns at a speed of 60 km/h. What is the average speed for the entire journey?

A. 70 km/h
B. 72 km/h
C. 75 km/h
D. 78 km/h

Solution

Average Speed = 2xy / (x + y) = 2(80)(60) / (80 + 60) = 72 km/h

Correct Answer: B — 72 km/h

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Q. A bus travels from City A to City B, a distance of 180 km, at a speed of 60 km/h. How long does the journey take?

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

Solution

Time = Distance / Speed = 180 km / 60 km/h = 3 hours.

Correct Answer: C — 3 hours

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Q. A bus travels from City A to City B, a distance of 180 km, at a speed of 90 km/h. How long does the journey take?

A. 1.5 hours
B. 2 hours
C. 2.5 hours
D. 3 hours

Solution

Time = Distance / Speed = 180 km / 90 km/h = 2 hours.

Correct Answer: B — 2 hours

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Q. A bus travels from city A to city B, a distance of 240 km, at a speed of 80 km/h. How long does it take?

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

Solution

Time = Distance / Speed = 240 km / 80 km/h = 3 hours

Correct Answer: B — 3 hours

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Q. A calendar is printed every year. If 5 calendars are printed in 5 years, how many are printed in 10 years?

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

Solution

If 5 calendars are printed in 5 years, then in 10 years, 10 calendars will be printed.

Correct Answer: A — 10

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Q. A calendar is printed in 2023. How many days until the next leap year?

A. 365
B. 366
C. 730
D. 731

Solution

The next leap year after 2023 is 2024, which is 1 year away, so 365 days.

Correct Answer: A — 365

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Q. A calendar is printed in 2023. How many Sundays will there be in the month of March 2023?

A. 4
B. 5
C. 6
D. 3

Solution

March 2023 has 31 days, starting from Wednesday. There are 5 Sundays in March 2023.

Correct Answer: B — 5

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Q. A calendar is sold for $30 after a discount of 10%. What was the original price?

A. $27
B. $33
C. $30
D. $25

Solution

Let the original price be x. Then, 90% of x = 30. So, x = 30 / 0.9 = $33.33

Correct Answer: B — $33

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Q. A calendar is sold for $45 after a 10% discount. What was the marked price?

A. $50
B. $55
C. $60
D. $45

Solution

Let the marked price be x. Then, 90% of x = 45. So, x = 45 / 0.9 = $50

Correct Answer: A — $50

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Q. A calendar is sold for $45 after a 10% increase in price. What was the original price?

A. $40
B. $41
C. $42
D. $43

Solution

Let the original price be x. Then, x + (10/100 * x) = 45. Solving gives x = $40.

Correct Answer: A — $40

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Q. A calendar is sold for $75 after a discount of 25%. What was the original price?

A. $90
B. $95
C. $100
D. $80

Solution

Let the original price be x. Then, x - (25/100 * x) = 75. Solving gives x = $100.

Correct Answer: A — $90

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Q. A can complete a race in 120 seconds, while B can complete it in 180 seconds. How much time will A be ahead of B when they finish the race?

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

Solution

A finishes in 120 seconds, B in 180 seconds. A is ahead by 180 - 120 = 60 seconds.

Correct Answer: B — 40 seconds

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Q. A can complete a work in 16 days, B in 24 days, and C in 32 days. If they all work together, how long will it take to complete the work?

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

Solution

Combined rate = (1/16 + 1/24 + 1/32) = 1/8. Therefore, they will complete the work in 8 days.

Correct Answer: A — 6 days

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Arithmetic Aptitude

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