Arithmetic Aptitude for Competitive Exam Success

Arithmetic Aptitude

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Q. A boat travels 30 km downstream in 2 hours. If the speed of the stream is 5 km/h, what is the speed of the boat in still water?

A. 10 km/h
B. 15 km/h
C. 20 km/h
D. 25 km/h

Solution

Let the speed of the boat in still water be y km/h. Downstream speed = y + 5 km/h. Therefore, (y + 5) * 2 = 30. Solving gives y = 10 km/h.

Correct Answer: B — 15 km/h

Q. A boat travels 40 km upstream in 5 hours. If the speed of the boat in still water is 8 km/h, what is the speed of the current?

A. 1 km/h
B. 2 km/h
C. 3 km/h
D. 4 km/h

Solution

Speed upstream = Distance/Time = 40/5 = 8 km/h. Thus, 8 - x = 8, so x = 0. The current speed is 0 km/h.

Correct Answer: D — 4 km/h

Q. A boat travels 50 km downstream in 5 hours and returns upstream in 10 hours. What is the speed of the stream?

A. 2 km/h
B. 3 km/h
C. 4 km/h
D. 5 km/h

Solution

Let the speed of the stream be x km/h. Downstream speed = (y + x) and upstream speed = (y - x). From the equations, we can derive that x = 4 km/h.

Correct Answer: C — 4 km/h

Q. A boat travels 50 km downstream in 5 hours. If the speed of the current is 5 km/h, what is the speed of the boat in still water?

A. 8 km/h
B. 10 km/h
C. 12 km/h
D. 14 km/h

Solution

Speed downstream = Distance/Time = 50 km / 5 h = 10 km/h. Speed of boat in still water = Speed downstream - Speed of current = 10 km/h - 5 km/h = 5 km/h.

Correct Answer: B — 10 km/h

Q. A box contains 10 balls, 7 of which are white. If one ball is drawn at random, what is the probability that it is not white?

A. 1/10
B. 3/10
C. 7/10
D. 1/3

Solution

There are 3 non-white balls. Probability = 3/10.

Correct Answer: B — 3/10

Q. A box contains 10 balls: 3 are blue, 4 are red, and 3 are green. What is the probability of drawing a blue ball?

A. 1/3
B. 3/10
C. 1/4
D. 2/5

Solution

The total number of balls is 10. The probability of drawing a blue ball is 3/10.

Correct Answer: B — 3/10

Q. A box contains 10 balls: 3 are red, 4 are blue, and 3 are green. What is the probability of drawing a blue ball?

A. 1/3
B. 2/5
C. 4/10
D. 3/10

Solution

The total number of balls is 10. The probability of drawing a blue ball is 4/10 = 2/5.

Correct Answer: B — 2/5

Q. A box contains 10 balls: 4 are blue, 3 are green, and 3 are red. What is the probability of drawing a red ball?

A. 1/3
B. 3/10
C. 1/4
D. 2/5

Solution

The total number of balls is 10. The probability of drawing a red ball is 3/10.

Correct Answer: B — 3/10

Q. A box contains 10 balls: 4 blue, 3 green, and 3 red. What is the probability of drawing a red ball?

A. 1/3
B. 1/4
C. 3/10
D. 3/5

Solution

The total number of balls is 10. The probability of drawing a red ball is 3/10.

Correct Answer: C — 3/10

Q. A box contains 10 balls: 4 red, 3 blue, and 3 green. What is the probability of drawing a blue ball?

A. 1/3
B. 3/10
C. 2/5
D. 1/5

Solution

The probability of drawing a blue ball is 3/10.

Correct Answer: B — 3/10

Q. A box contains 10 balls: 6 white and 4 black. If one ball is drawn at random, what is the probability that it is not black?

A. 1/5
B. 2/5
C. 3/5
D. 4/5

Solution

The probability of not drawing a black ball = 6/10 = 3/5.

Correct Answer: D — 4/5

Q. A box contains 10 chocolates, 4 of which are dark chocolate. What is the probability of selecting a dark chocolate?

A. 2/5
B. 1/3
C. 1/2
D. 4/10

Solution

Probability of selecting dark chocolate = 4/10 = 2/5.

Correct Answer: A — 2/5

Q. A box contains 10 chocolates, 4 of which are dark chocolate. What is the probability of randomly selecting a dark chocolate?

A. 0.4
B. 0.5
C. 0.3
D. 0.2

Solution

The probability of selecting a dark chocolate is 4/10 = 0.4.

Correct Answer: A — 0.4

Q. A box contains 4 white and 6 black balls. If one ball is drawn at random, what is the probability that it is black?

A. 2/5
B. 3/5
C. 4/5
D. 1/5

Solution

The total number of balls is 4 + 6 = 10. The probability of drawing a black ball is 6/10 = 3/5.

Correct Answer: B — 3/5

Q. A box contains 4 white, 5 black, and 6 red balls. What is the probability of picking a black ball?

A. 1/3
B. 5/15
C. 1/4
D. 5/15

Solution

Total balls = 4 + 5 + 6 = 15. Probability of black ball = 5/15 = 1/3.

Correct Answer: B — 5/15

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

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

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

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

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

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

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

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

Q. A car's value depreciates by 10% each year. If its current value is $18,000, what will be its value after one year?

A. $16,200
B. $15,000
C. $14,400
D. $17,000

Solution

Depreciation = 10% of 18000 = 0.1 * 18000 = 1800. Value after one year = 18000 - 1800 = 16200.

Correct Answer: A — $16,200

Q. A car's value depreciates by 10% each year. If its current value is $20,000, what will be its value after one year?

A. $18,000
B. $19,000
C. $17,500
D. $16,000

Solution

Value after one year = 20000 - (10/100 * 20000) = 20000 - 2000 = $18,000.

Correct Answer: A — $18,000

Q. A car's value depreciates by 10% each year. If its current value is $9000, what will be its value after one year?

A. $8100
B. $8200
C. $8300
D. $8400

Solution

Depreciation = 10% of 9000 = 0.1 * 9000 = 900. Value after one year = 9000 - 900 = 8100.

Correct Answer: A — $8100

Q. A car's value depreciates by 10% each year. If the current value is $20,000, what will be its value after one year?

A. $18,000
B. $19,000
C. $20,000
D. $21,000

Solution

Value after one year = 20000 - (0.1 * 20000) = 20000 - 2000 = $18,000.

Correct Answer: A — $18,000

Q. A car's value depreciates by 15% each year. If its current value is $20,000, what will be its value after one year?

A. $15,000
B. $16,500
C. $17,000
D. $18,000

Solution

Value after one year = 20000 - (0.15 * 20000) = 20000 - 3000 = 17000

Correct Answer: B — $16,500

Q. A car's value depreciates by 15% each year. If its current value is $8500, what will be its value after one year?

A. $7225
B. $7500
C. $8000
D. $8500

Solution

Value after one year = 8500 - (15% of 8500) = 8500 - 1275 = 7225.

Correct Answer: A — $7225

Q. A car's value depreciates by 15% each year. If the current value is $20,000, what will be its value after one year?

A. $17,000
B. $18,000
C. $19,000
D. $16,500

Solution

Depreciation = 15% of 20000 = 3000; Value after one year = 20000 - 3000 = 17000.

Correct Answer: A — $17,000

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