Arithmetic Aptitude for Competitive Exam Success

Arithmetic Aptitude

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Q. A mixture of two types of fruit juice is made in the ratio 4:1. If the total volume of the mixture is 100 liters, how much of the first type of juice is there?

A. 80 liters
B. 70 liters
C. 60 liters
D. 50 liters

Solution

Total parts = 4 + 1 = 5. First type juice = (4/5) * 100 = 80 liters.

Correct Answer: A — 80 liters

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Q. A mixture of two types of nuts contains 40% cashews and 60% almonds. If 50 kg of the mixture is prepared, how many kilograms of cashews are there?

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

Solution

Cashews in the mixture = 40% of 50 kg = 0.4 * 50 = 20 kg.

Correct Answer: C — 25 kg

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Q. A mixture of two types of tea contains 40% of tea A and 60% of tea B. If 20 liters of tea B is added, what will be the new percentage of tea A if the total mixture becomes 100 liters?

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

Solution

Initial volume of tea A = 0.4 * 80 = 32 liters. Total volume after adding tea B = 100 liters. New percentage of tea A = (32/100) * 100 = 32%.

Correct Answer: C — 40%

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Q. A mother is 21 years older than her daughter. If the daughter is 9 years old now, how old will the mother be in 5 years?

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

Solution

The mother is currently 9 + 21 = 30 years old. In 5 years, she will be 30 + 5 = 35.

Correct Answer: C — 35

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Q. A mother is 4 times as old as her daughter. After 8 years, the mother will be twice as old as her daughter. How old is the daughter now?

A. 4
B. 8
C. 12
D. 16

Solution

Let the daughter's age be x. Then the mother's age is 4x. In 8 years, 4x + 8 = 2(x + 8). Solving gives x = 8.

Correct Answer: B — 8

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Q. A mother is 4 times as old as her daughter. After 8 years, the mother will be twice as old as her daughter. What is the present age of the daughter?

A. 4
B. 8
C. 12
D. 16

Solution

Let the daughter's age be x. Then the mother's age is 4x. In 8 years, 4x + 8 = 2(x + 8). Solving gives x = 8.

Correct Answer: B — 8

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Q. A number is increased by 20% and then decreased by 20%. What is the net change in the number?

A. 0%
B. 4%
C. 5%
D. 10%

Solution

Let the original number be 100. After a 20% increase, it becomes 120. After a 20% decrease, it becomes 120 - 24 = 96. The net change is (96 - 100)/100 * 100% = -4%.

Correct Answer: B — 4%

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Q. A number is increased by 20% and then decreased by 20%. What is the net change?

A. 0%
B. 4%
C. 5%
D. 10%

Solution

Let the number be 100. After a 20% increase, it becomes 120. After a 20% decrease, it becomes 120 - 24 = 96. The net change is (96 - 100)/100 * 100% = -4%.

Correct Answer: A — 0%

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Q. A parallelogram has a base of 12 cm and a height of 5 cm. What is its area?

A. 60 cm²
B. 50 cm²
C. 70 cm²
D. 40 cm²

Solution

Area = base × height = 12 cm × 5 cm = 60 cm².

Correct Answer: A — 60 cm²

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Q. A parallelogram has a base of 15 meters and a height of 10 meters. What is the area of the parallelogram in square meters?

A. 100
B. 120
C. 150
D. 180

Solution

Area = base × height = 15 × 10 = 150 square meters.

Correct Answer: C — 150

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Q. A person bought a bicycle for $200 and sold it for $180. What is the percentage loss?

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

Solution

Loss = Cost Price - Selling Price = 200 - 180 = 20. Percentage Loss = (Loss/Cost Price) * 100 = (20/200) * 100 = 10%.

Correct Answer: A — 10%

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Q. A person bought a bicycle for $300 and sold it for $360. What is the percentage profit?

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

Solution

Profit = Selling Price - Cost Price = 360 - 300 = $60. Percentage profit = (Profit / Cost Price) × 100 = (60 / 300) × 100 = 20%.

Correct Answer: B — 25%

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Q. A person bought a watch for $500 and sold it for $600. What is the percentage profit?

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

Solution

Profit = Selling Price - Cost Price = 600 - 500 = $100. Percentage Profit = (Profit / Cost Price) × 100 = (100 / 500) × 100 = 20%.

Correct Answer: B — 25%

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Q. A person can complete a work in 12 days. If he works for 4 days, what fraction of the work is left?

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

Solution

Work done in 4 days = 4/12 = 1/3. Work left = 1 - 1/3 = 2/3.

Correct Answer: D — 2/3

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Q. A person invests $1,000 at an interest rate of 5% per annum. How much interest will he earn in one year?

A. $40
B. $50
C. $60
D. $70

Solution

Interest = 5% of 1,000 = 50.

Correct Answer: B — $50

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Q. A person invests $1000 at a simple interest rate of 5% per annum. How much interest will he earn in 3 years?

A. $100
B. $150
C. $200
D. $250

Solution

Simple Interest = Principal * Rate * Time = $1000 * 5% * 3 = $1000 * 0.05 * 3 = $150.

Correct Answer: A — $100

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Q. A person invests $2500 at a simple interest rate of 10% per annum. How much interest will he earn in 6 years?

A. $150
B. $200
C. $300
D. $400

Solution

Simple Interest = 2500 × 10 × 6 / 100 = $1500.

Correct Answer: C — $300

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Q. A person invests $5000 in a stock that gives a simple interest of 6% per annum. What will be the interest earned in 3 years?

A. $900
B. $800
C. $600
D. $700

Solution

Simple Interest = Principal * Rate * Time / 100 = 5000 * 6 * 3 / 100 = $900

Correct Answer: A — $900

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Q. A person is looking at the top of a 40-meter tall building from a distance of 50 meters. What is the angle of elevation?

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

Solution

tan(θ) = height/distance = 40/50, θ = tan⁻¹(0.8) ≈ 38.66 degrees.

Correct Answer: B — 36.87 degrees

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Q. A person is looking at the top of a hill from a distance of 50 meters. If the angle of elevation is 30 degrees, what is the height of the hill?

A. 25 meters
B. 50 meters
C. 75 meters
D. 100 meters

Solution

Height = distance * tan(30) = 50 * (1/√3) = 50/√3 ≈ 28.87 meters.

Correct Answer: A — 25 meters

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Q. A person is standing 10 meters away from a vertical pole. If the angle of elevation to the top of the pole is 60 degrees, what is the height of the pole?

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

Solution

Height = distance * tan(60) = 10 * √3 = 10√3 meters.

Correct Answer: A — 5√3 meters

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Q. A person is standing 15 meters away from a building. If the angle of elevation to the top of the building is 30 degrees, what is the height of the building?

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

Solution

Height = distance * tan(angle) = 15 * (1/√3) = 15/√3 = 15√3 meters.

Correct Answer: A — 15√3 meters

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Q. A person is standing 15 meters away from a tree. If the angle of elevation to the top of the tree is 45 degrees, what is the height of the tree?

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

Solution

Height = distance * tan(angle) = 15 * 1 = 15 meters.

Correct Answer: B — 15 meters

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Q. A person is standing 15 meters away from a vertical pole. If the angle of elevation to the top of the pole is 60 degrees, what is the height of the pole?

A. 15√3 meters
B. 10√3 meters
C. 20 meters
D. 25 meters

Solution

Height = distance * tan(60) = 15 * √3 = 15√3 meters

Correct Answer: A — 15√3 meters

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Q. A person is standing 25 meters away from a building. If the angle of elevation to the top of the building is 60 degrees, what is the height of the building?

A. 25√3 meters
B. 30 meters
C. 35 meters
D. 40 meters

Solution

Height = distance * tan(60) = 25 * √3 = 25√3 meters.

Correct Answer: A — 25√3 meters

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Q. A person is standing 25 meters away from a hill. If the angle of elevation to the top of the hill is 37 degrees, what is the height of the hill?

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

Solution

Height = distance * tan(37) = 25 * 0.7536 ≈ 18.84 meters, rounded to 20 meters.

Correct Answer: B — 20 meters

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Q. A person is standing 25 meters away from a vertical pole. If the angle of elevation to the top of the pole is 30 degrees, what is the height of the pole?

A. 12.5 meters
B. 25 meters
C. 15√3 meters
D. 20 meters

Solution

Height = distance * tan(angle) = 25 * (1/√3) = 25/√3 ≈ 12.5 meters.

Correct Answer: A — 12.5 meters

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Q. A person is standing 25 meters away from a vertical pole. If the angle of elevation to the top of the pole is 53 degrees, what is the height of the pole?

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

Solution

Height = distance * tan(angle) = 25 * tan(53°) ≈ 25 * 1.327 = 20.68 meters.

Correct Answer: B — 20 meters

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Q. A person is standing 25 meters away from a wall. If the angle of elevation to the top of the wall is 75 degrees, what is the height of the wall?

A. 24.5 meters
B. 25 meters
C. 26.5 meters
D. 27.5 meters

Solution

Height = distance * tan(75) = 25 * 3.732 = 93.3 meters.

Correct Answer: D — 27.5 meters

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Q. A person is standing 30 meters away from a building. If the angle of elevation to the top of the building is 45 degrees, what is the height of the building?

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

Solution

Height = distance * tan(45) = 30 * 1 = 30 meters.

Correct Answer: A — 30 meters

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Arithmetic Aptitude

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