Arithmetic Aptitude for Competitive Exam Success

Arithmetic Aptitude

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Q. A cone has a base radius of 4 cm and a height of 9 cm. What is the total surface area of the cone?

A. 50.24 cm²
B. 75.36 cm²
C. 100.48 cm²
D. 125.60 cm²

Solution

Total Surface Area = πr(r + l), where l = √(r² + h²) = √(4² + 9²) = √(16 + 81) = √97. Total Surface Area = π * 4 * (4 + √97).

Correct Answer: B — 75.36 cm²

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Q. A cone has a base radius of 4 cm and a slant height of 5 cm. What is the lateral surface area of the cone?

A. 40π cm²
B. 20π cm²
C. 30π cm²
D. 25π cm²

Solution

Lateral Surface Area = πrl = π * 4 * 5 = 20π cm².

Correct Answer: A — 40π cm²

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Q. A cone has a base radius of 5 cm and a height of 12 cm. What is the total surface area of the cone?

A. 130 cm²
B. 150 cm²
C. 180 cm²
D. 200 cm²

Solution

Total Surface Area = πr(r + l), where l = √(r² + h²) = √(5² + 12²) = √169 = 13. Total Surface Area = π * 5 * (5 + 13) = 90π cm².

Correct Answer: B — 150 cm²

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Q. A cone has a radius of 3 cm and a height of 4 cm. What is the volume of the cone?

A. 12 cm³
B. 36 cm³
C. 24 cm³
D. 18 cm³

Solution

Volume = (1/3)πr²h = (1/3) * π * 3² * 4 = (1/3) * 3.14 * 9 * 4 = 37.68 cm³.

Correct Answer: C — 24 cm³

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Q. A cone has a radius of 3 cm and a height of 4 cm. What is the volume of the cone? (Use π = 3.14)

A. 37.68 cm³
B. 12.56 cm³
C. 25.12 cm³
D. 18.84 cm³

Solution

Volume = (1/3)πr²h = (1/3) * 3.14 * 3² * 4 = 37.68 cm³

Correct Answer: A — 37.68 cm³

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Q. A container has 30 liters of a mixture of milk and water in the ratio 2:1. How much water is in the mixture?

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

Solution

In a 2:1 ratio, for every 3 parts, 1 part is water. Therefore, water = (1/3) * 30 = 10 liters.

Correct Answer: A — 10 liters

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Q. A container has 50 liters of a mixture of juice and water in the ratio 4:1. How much juice is in the mixture?

A. 30 liters
B. 35 liters
C. 40 liters
D. 45 liters

Solution

In a 4:1 ratio, total parts = 4 + 1 = 5. Juice = (4/5) * 50 = 40 liters.

Correct Answer: C — 40 liters

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Q. A container has 60 liters of a mixture of juice and water in the ratio 4:1. How much juice is in the mixture?

A. 48 liters
B. 12 liters
C. 36 liters
D. 24 liters

Solution

Juice = (4/5) * 60 = 48 liters.

Correct Answer: A — 48 liters

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Q. A container has 60 liters of a mixture of milk and water in the ratio of 2:1. If 12 liters of the mixture is replaced with water, what is the new ratio of milk to water?

A. 2:1
B. 1:2
C. 1:1
D. 3:2

Solution

Initially, milk = 40 liters, water = 20 liters. After removing 12 liters (8 liters milk and 4 liters water), we have 32 liters milk and 16 liters water. Adding 12 liters of water gives 32 liters milk and 28 liters water, resulting in a ratio of 32:28 or 8:7.

Correct Answer: D — 3:2

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Q. A container has 60 liters of a solution that is 15% acid. If 10 liters of this solution is replaced with water, what is the new percentage of acid in the solution?

A. 10%
B. 12%
C. 15%
D. 18%

Solution

Initial acid = 0.15 * 60 = 9 liters. After removing 10 liters, acid left = 9 - 0.15 * 10 = 7.5 liters. New volume = 60 liters. New percentage = (7.5/60) * 100 = 12.5%.

Correct Answer: A — 10%

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Q. A container has 80 liters of a mixture of milk and water in the ratio 3:1. If 20 liters of the mixture is replaced with water, what is the new ratio of milk to water?

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

Solution

Initially, there are 60 liters of milk and 20 liters of water. After removing 20 liters, 15 liters of milk and 5 liters of water are removed. Adding 20 liters of water gives 60 liters of milk and 25 liters of water. New ratio = 60:25 = 12:5.

Correct Answer: A — 2:1

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Q. A container has 80 liters of a solution that is 10% acid. If 20 liters of this solution is replaced with pure acid, what will be the new concentration of acid in the solution?

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

Solution

Initial acid = 10% of 80 = 8 liters. After removing 20 liters, acid left = 8 - 2 = 6 liters. Adding 20 liters of pure acid gives 6 + 20 = 26 liters of acid in 80 liters. New concentration = (26/80) * 100 = 32.5%.

Correct Answer: C — 25%

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Q. A container has a mixture of 80 liters of liquid, which is 25% acid. How much acid is in the container?

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

Solution

Acid = 25% of 80 liters = 0.25 * 80 = 20 liters.

Correct Answer: C — 20 liters

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Q. A container has a mixture of 80 liters of liquid, which is 25% alcohol. How much alcohol is in the container?

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

Solution

Alcohol = 25% of 80 liters = 0.25 * 80 = 20 liters.

Correct Answer: B — 15 liters

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Q. A container has a mixture of 80 liters of milk and water in the ratio 4:1. How much milk is in the container?

A. 64 liters
B. 16 liters
C. 32 liters
D. 48 liters

Solution

Total parts = 4 + 1 = 5. Milk = (4/5) * 80 = 64 liters.

Correct Answer: A — 64 liters

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Q. A cube has a side length of 4 cm. What is the volume of the cube?

A. 16 cm³
B. 64 cm³
C. 48 cm³
D. 32 cm³

Solution

Volume = side³ = 4³ = 64 cm³.

Correct Answer: B — 64 cm³

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Q. A cube has a volume of 27 cm³. What is the length of one side of the cube?

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

Solution

Side = ∛Volume = ∛27 = 3 cm.

Correct Answer: A — 3 cm

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Q. A cyclist covers a distance of 30 km in 1.5 hours. What is the cyclist's speed?

A. 18 km/h
B. 20 km/h
C. 22 km/h
D. 25 km/h

Solution

Speed = Distance / Time = 30 km / 1.5 h = 20 km/h.

Correct Answer: B — 20 km/h

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Q. A cyclist covers a distance of 45 km in 1.5 hours. What is the average speed of the cyclist?

A. 25 km/h
B. 30 km/h
C. 35 km/h
D. 40 km/h

Solution

Average Speed = Total Distance / Total Time = 45 km / 1.5 h = 30 km/h

Correct Answer: B — 30 km/h

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Q. A cyclist covers a distance of 45 km in 1.5 hours. What is the cyclist's speed?

A. 25 km/h
B. 30 km/h
C. 35 km/h
D. 40 km/h

Solution

Speed = Distance / Time = 45 km / 1.5 h = 30 km/h.

Correct Answer: B — 30 km/h

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Q. A cyclist covers a distance of 90 km in 3 hours. What is his average speed?

A. 25 km/h
B. 30 km/h
C. 20 km/h
D. 35 km/h

Solution

Average speed = Total distance / Total time = 90 km / 3 hours = 30 km/h.

Correct Answer: B — 30 km/h

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Q. A cyclist travels at a speed of 15 km/h. How long will it take to cover 45 km?

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

Solution

Time = Distance / Speed = 45 km / 15 km/h = 3 hours.

Correct Answer: B — 3 hours

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Q. A cylinder has a height of 10 cm and a radius of 2 cm. What is the lateral surface area of the cylinder?

A. 40π cm²
B. 20π cm²
C. 30π cm²
D. 10π cm²

Solution

Lateral Surface Area = 2πrh = 2 * π * 2 * 10 = 40π cm².

Correct Answer: A — 40π cm²

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Q. A cylinder has a height of 10 cm and a radius of 2 cm. What is the volume of the cylinder?

A. 40π cm³
B. 20π cm³
C. 30π cm³
D. 10π cm³

Solution

Volume = πr²h = π * 2² * 10 = π * 4 * 10 = 40π cm³.

Correct Answer: A — 40π cm³

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Q. A cylinder has a height of 10 cm and a radius of 2 cm. What is the volume of the cylinder? (Use π = 3.14)

A. 40 cm³
B. 60 cm³
C. 80 cm³
D. 100 cm³

Solution

Volume = πr²h = 3.14 * 2² * 10 = 125.6 cm³

Correct Answer: B — 60 cm³

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Q. A cylinder has a radius of 5 cm and a height of 10 cm. What is the total surface area of the cylinder?

A. 314 cm²
B. 150 cm²
C. 200 cm²
D. 250 cm²

Solution

Total Surface Area = 2πr(h + r) = 2 * π * 5 * (10 + 5) = 2 * 3.14 * 5 * 15 = 471 cm².

Correct Answer: A — 314 cm²

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Q. A cylinder has a radius of 5 cm and a height of 12 cm. What is the total surface area of the cylinder?

A. 340 cm²
B. 400 cm²
C. 380 cm²
D. 420 cm²

Solution

Total Surface Area = 2πr(h + r) = 2 * π * 5 * (12 + 5) = 2 * 3.14 * 5 * 17 = 530 cm².

Correct Answer: A — 340 cm²

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Q. A cylinder has a radius of 5 cm and a height of 7 cm. What is the total surface area of the cylinder?

A. 376.99 cm²
B. 314.16 cm²
C. 251.33 cm²
D. 157.08 cm²

Solution

Total Surface Area = 2πr(h + r) = 2 * π * 5 * (7 + 5) = 2 * 3.14 * 5 * 12 = 376.99 cm².

Correct Answer: A — 376.99 cm²

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Q. A cylindrical tank has a radius of 3 meters and a height of 5 meters. What is the surface area of the tank (including the top and bottom)?

A. 56.52 m²
B. 94.25 m²
C. 113.10 m²
D. 78.54 m²

Solution

Surface Area = 2πr(h + r) = 2 * π * 3 * (5 + 3) = 2 * 3.14 * 3 * 8 = 150.72 m².

Correct Answer: B — 94.25 m²

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Q. A cylindrical tank has a radius of 3 meters and a height of 5 meters. What is the surface area of the tank? (Use π = 3.14)

A. 56.52 m²
B. 94.2 m²
C. 94.5 m²
D. 47.1 m²

Solution

Surface Area = 2πr(h + r) = 2 * 3.14 * 3 * (5 + 3) = 94.2 m²

Correct Answer: B — 94.2 m²

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Arithmetic Aptitude

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