Arithmetic Aptitude for Competitive Exam Success

Arithmetic Aptitude

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Q. A tank can be filled by a pipe in 12 hours and emptied by another pipe in 18 hours. If both pipes are opened together, how long will it take to fill the tank?

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

Solution

The net rate is 1/12 - 1/18 = 1/36. Therefore, it will take 36 hours to fill the tank.

Correct Answer: C — 15 hours

Q. A tank can be filled by a pipe in 15 hours and emptied by another pipe in 10 hours. If both pipes are opened together, how long will it take to fill the tank?

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

Solution

The net rate is 1/15 - 1/10 = -1/30. Therefore, the tank will never fill.

Correct Answer: B — 20 hours

Q. A tank can be filled by a pipe in 15 hours and emptied by another pipe in 25 hours. If both pipes are opened together, how long will it take to fill the tank?

A. 10 hours
B. 12 hours
C. 15 hours
D. 20 hours

Solution

The net rate is 1/15 - 1/25 = 1/75. Therefore, it will take 75 hours to fill the tank.

Correct Answer: B — 12 hours

Q. A tank can be filled by a pipe in 25 hours and emptied by another pipe in 50 hours. If both pipes are opened together, how long will it take to fill the tank?

A. 16.67 hours
B. 20 hours
C. 25 hours
D. 30 hours

Solution

The net rate is 1/25 - 1/50 = 1/50. Therefore, it will take 50 hours to fill the tank.

Correct Answer: A — 16.67 hours

Q. A tank can be filled by a pipe in 25 minutes and emptied by another pipe in 50 minutes. If both pipes are opened together, how long will it take to fill the tank?

A. 16.67 minutes
B. 20 minutes
C. 25 minutes
D. 30 minutes

Solution

The net rate is 1/25 - 1/50 = 1/50. Therefore, it will take 50 minutes to fill the tank.

Correct Answer: A — 16.67 minutes

Q. A tank can be filled by a pipe in 4 hours and emptied by another pipe in 6 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 net rate is 1/4 - 1/6 = 1/12. Therefore, it will take 12 hours to fill the tank.

Correct Answer: C — 4 hours

Q. A tank can be filled by a pipe in 40 minutes and emptied by another pipe in 60 minutes. If both pipes are opened together, how long will it take to fill the tank?

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

Solution

The net rate is 1/40 - 1/60 = 1/120. Therefore, it will take 120 minutes to fill the tank.

Correct Answer: B — 30 minutes

Q. A tank can be filled by a pipe in 5 hours and emptied by another pipe in 10 hours. If both pipes are opened together, how long will it take to fill the tank?

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

Solution

The net rate is 1/5 - 1/10 = 1/10. Therefore, it will take 10 hours to fill the tank.

Correct Answer: D — 6 hours

Q. A tank can be filled by a pipe in 6 hours and emptied by another pipe in 4 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 net rate is 1/6 - 1/4 = -1/12. Therefore, the tank will never fill.

Correct Answer: C — 4 hours

Q. A tank can be filled by a pipe in 6 hours and emptied by another pipe in 9 hours. If both pipes are opened together, how long will it take to fill the tank?

A. 3.6 hours
B. 4 hours
C. 5 hours
D. 6 hours

Solution

The net rate is 1/6 - 1/9 = 1/18. Therefore, it will take 18 hours to fill the tank.

Correct Answer: A — 3.6 hours

Q. A tank can be filled by a pipe in 9 hours and emptied by another pipe in 18 hours. If both pipes are opened together, how long will it take to fill the tank?

A. 6 hours
B. 9 hours
C. 12 hours
D. 15 hours

Solution

The net rate is 1/9 - 1/18 = 1/18. Therefore, it will take 18 hours to fill the tank.

Correct Answer: C — 12 hours

Q. A tank has two pipes. Pipe A can fill the tank in 8 hours, and pipe B can empty it in 12 hours. If both pipes are opened together, how long will it take to fill the tank?

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

Solution

The net rate is 1/8 - 1/12 = 1/24. Therefore, it will take 24 hours to fill the tank.

Correct Answer: A — 4 hours

Q. A tank is filled by two pipes A and B in 12 hours and 16 hours respectively. If pipe A is opened for 4 hours and then pipe B is opened, how long will it take to fill the tank?

A. 8 hours
B. 10 hours
C. 12 hours
D. 14 hours

Solution

In 4 hours, A fills 1/3 of the tank. The remaining 2/3 can be filled by A and B together in 4 hours.

Correct Answer: B — 10 hours

Q. A tank is filled by two pipes A and B in 15 hours and 20 hours respectively. If both pipes are opened together, how long will it take to fill the tank?

A. 8 hours
B. 10 hours
C. 12 hours
D. 15 hours

Solution

The combined rate is 1/15 + 1/20 = 7/60. Therefore, it will take 60/7 hours to fill the tank.

Correct Answer: B — 10 hours

Q. A tank is filled by two pipes A and B in 15 hours and 25 hours respectively. If both pipes are opened together, how long will it take to fill the tank?

A. 9 hours
B. 10 hours
C. 12 hours
D. 15 hours

Solution

The combined rate is 1/15 + 1/25 = 2/15. Therefore, it will take 15/2 = 7.5 hours to fill the tank.

Correct Answer: B — 10 hours

Q. A tank is filled by two pipes in 10 hours and 15 hours respectively. If the first pipe is opened for 5 hours and then the second pipe is opened, how long will it take to fill the tank?

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

Solution

The first pipe fills 1/10 * 5 = 1/2 of the tank. The remaining 1/2 can be filled by both pipes together in 2 hours.

Correct Answer: B — 3 hours

Q. A tank is filled by two pipes in 12 hours and 15 hours respectively. If the first pipe is opened for 5 hours and then the second pipe is opened, how long will it take to fill the tank completely?

A. 6 hours
B. 7 hours
C. 8 hours
D. 9 hours

Solution

In 5 hours, the first pipe fills 5/12 of the tank. The remaining is 1 - 5/12 = 7/12. The combined rate of both pipes is 1/12 + 1/15 = 7/60. Therefore, it will take (7/12) / (7/60) = 60/12 = 5 hours to fill the remaining part.

Correct Answer: C — 8 hours

Q. A tank is filled by two pipes in 12 hours and 16 hours respectively. 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 combined rate is 1/12 + 1/16 = 7/48. Therefore, it will take 48/7 hours to fill the tank.

Correct Answer: C — 7 hours

Q. A tank is filled by two pipes in 15 and 20 minutes respectively. If both pipes are opened together, how long will it take to fill the tank?

A. 8 minutes
B. 10 minutes
C. 12 minutes
D. 15 minutes

Solution

The combined rate is 1/15 + 1/20 = 7/60. Therefore, time taken = 60/7 ≈ 8.57 minutes.

Correct Answer: B — 10 minutes

Q. A tank is filled by two pipes in 8 hours and 12 hours respectively. If both pipes are opened together, how long will it take to fill the tank?

A. 4.8 hours
B. 5 hours
C. 6 hours
D. 7 hours

Solution

The combined rate is 1/8 + 1/12 = 5/24. Therefore, it will take 24/5 = 4.8 hours to fill the tank.

Correct Answer: A — 4.8 hours

Q. A tower is 100 meters high. From a point 80 meters away from the base of the tower, what is the angle of elevation to the top of the tower?

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

Solution

tan(θ) = height/distance = 100/80, θ = tan⁻¹(1.25) ≈ 51.34 degrees.

Correct Answer: B — 60 degrees

Q. A tower is 100 meters high. From a point on the ground, the angle of elevation to the top of the tower is 45 degrees. How far is the point from the base of the tower?

A. 50 meters
B. 100 meters
C. 75 meters
D. 125 meters

Solution

Distance = height / tan(angle) = 100 / 1 = 100 meters.

Correct Answer: B — 100 meters

Q. A tower is 50 meters high. From a point 30 meters away from the base of the tower, what is the angle of elevation to the top of the tower?

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

Solution

tan(θ) = height / distance = 50 / 30; θ = tan^(-1)(5/3) ≈ 60 degrees

Correct Answer: C — 60 degrees

Q. A tower is 50 meters high. From a point 40 meters away from the base of the tower, what is the angle of elevation to the top of the tower?

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

Solution

tan(θ) = height/distance = 50/40, θ = tan⁻¹(1.25) ≈ 51.34 degrees.

Correct Answer: A — 36.87 degrees

Q. A tower is 50 meters high. From a point on the ground, the angle of elevation to the top of the tower is 45 degrees. How far is the point from the base of the tower?

A. 25 meters
B. 35 meters
C. 50 meters
D. 70 meters

Solution

Distance = height / tan(angle) = 50 / 1 = 50 meters.

Correct Answer: C — 50 meters

Q. A trapezoid has bases of 10 m and 6 m, and a height of 4 m. What is its area?

A. 32 m²
B. 36 m²
C. 40 m²
D. 44 m²

Solution

Area = 1/2 × (base1 + base2) × height = 1/2 × (10 m + 6 m) × 4 m = 32 m².

Correct Answer: A — 32 m²

Q. A tree casts a shadow of 10 meters long. If the angle of elevation of the sun is 30 degrees, what is the height of the tree?

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

Solution

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

Correct Answer: A — 5√3 meters

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

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

Solution

Height = shadow * tan(angle) = 10 * √3 = 10 * 1.732 = 17.32 meters.

Correct Answer: C — 15 meters

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

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

Q. A tree is 15 meters tall. If the angle of elevation from a point 20 meters away from the base of the tree is θ, what is tan(θ)?

A. 0.75
B. 1.25
C. 1.5
D. 2

Solution

tan(θ) = height / distance = 15 / 20 = 0.75

Correct Answer: A — 0.75

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