Arithmetic Aptitude for Competitive Exam Success

Arithmetic Aptitude

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Q. A tree is 30 meters tall. If the angle of elevation from a point 40 meters away from the base of the tree is θ, what is tan(θ)?

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

Solution

tan(θ) = height / distance = 30 / 40 = 0.75

Correct Answer: A — 0.75

Q. A triangle has a base of 10 m and a height of 6 m. What is its area?

A. 30 m²
B. 40 m²
C. 50 m²
D. 60 m²

Solution

Area = 1/2 × base × height = 1/2 × 10 m × 6 m = 30 m².

Correct Answer: A — 30 m²

Q. A triangle has a base of 8 m and a height of 5 m. What is its area?

A. 20 m²
B. 30 m²
C. 40 m²
D. 10 m²

Solution

Area = 1/2 × base × height = 1/2 × 8 m × 5 m = 20 m².

Correct Answer: A — 20 m²

Q. A woman is 3 years older than her brother. If the sum of their ages is 27 years, how old is the brother?

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

Solution

Let the brother's age be x. Then the woman's age is x + 3. The equation is x + (x + 3) = 27, which simplifies to 2x + 3 = 27, so 2x = 24, and x = 12.

Correct Answer: B — 10

Q. A woman is 5 years older than her sister. If the sister is 15 years old, how old is the woman?

A. 20
B. 25
C. 30
D. 35

Solution

If the sister is 15, then the woman is 15 + 5 = 20 years old.

Correct Answer: A — 20

Q. A's age is 2 years more than B's age. If the sum of their ages is 34, what is A's age?

A. 16
B. 18
C. 20
D. 22

Solution

Let B's age be x. Then A's age is x + 2. So, x + (x + 2) = 34, which gives 2x + 2 = 34, hence 2x = 32, x = 16. Therefore, A's age is 16 + 2 = 18.

Correct Answer: D — 22

Q. A's age is twice that of B's age. If the difference between their ages is 10 years, what is A's age?

A. 20
B. 25
C. 30
D. 35

Solution

Let B's age be x. Then A's age is 2x. The difference is 2x - x = 10, hence x = 10. So, A's age is 2 * 10 = 20.

Correct Answer: C — 30

Q. A, B, and C invest in a business in the ratio 1:2:3. If the total profit is $60,000, how much does B receive?

A. $10,000
B. $20,000
C. $30,000
D. $40,000

Solution

Total parts = 1 + 2 + 3 = 6. B's share = 2/6 * 60000 = $20,000.

Correct Answer: B — $20,000

Q. A, B, and C invest in a business in the ratio 1:2:3. If the total profit is $6000, how much does B receive?

A. $1,000
B. $2,000
C. $3,000
D. $4,000

Solution

Total parts = 1 + 2 + 3 = 6. B's share = 2/6 * 6000 = $2,000.

Correct Answer: B — $2,000

Q. A, B, and C invest in a business in the ratio 2:3:5. If the total profit is $10,000, how much does C receive?

A. $4,000
B. $5,000
C. $6,000
D. $7,000

Solution

Total parts = 2 + 3 + 5 = 10. C's share = (5/10) * 10000 = $5,000.

Correct Answer: B — $5,000

Q. A, B, and C invest in a business in the ratio 2:3:5. If the total profit is $40,000, how much does B receive?

A. $10,000
B. $12,000
C. $15,000
D. $18,000

Solution

Total parts = 2 + 3 + 5 = 10. B's share = (3/10) * 40000 = $12,000.

Correct Answer: B — $12,000

Q. A, B, and C invest in a business in the ratio 3:4:5. If the total profit is $24,000, how much does C receive?

A. $8,000
B. $10,000
C. $12,000
D. $14,000

Solution

Total parts = 3 + 4 + 5 = 12. C's share = (5/12) * 24000 = $10,000.

Correct Answer: C — $12,000

Q. A, B, and C invest in a business in the ratio 3:4:5. If the total profit is $2400, how much does C receive?

A. $800
B. $1000
C. $1200
D. $1400

Solution

The total parts = 3 + 4 + 5 = 12. C's share = 5/12 * 2400 = $1000.

Correct Answer: C — $1200

Q. A, B, and C invest in a business with investments of $5000, $7000, and $8000 respectively. If the total profit is $6000, how much does B receive?

A. $2000
B. $2400
C. $2800
D. $3000

Solution

Total investment = 5000 + 7000 + 8000 = 20000. B's share = (7000/20000) * 6000 = $2100.

Correct Answer: B — $2400

Q. C, D, and E invest in a business in the ratio 1:2:3. If the total profit is $12,000, how much does D receive?

A. $2,000
B. $4,000
C. $6,000
D. $8,000

Solution

Total parts = 1 + 2 + 3 = 6. D's share = (2/6) * 12000 = $4,000.

Correct Answer: C — $6,000

Q. Calculate the area of a circle with a radius of 7 cm (use π = 22/7).

A. 154 cm²
B. 44 cm²
C. 77 cm²
D. 88 cm²

Solution

Area = πr² = (22/7) × (7 cm)² = 154 cm².

Correct Answer: A — 154 cm²

Q. Calculate the area of a circle with a radius of 7 cm (use π ≈ 3.14).

A. 38.48 cm²
B. 43.96 cm²
C. 153.86 cm²
D. 154 cm²

Solution

Area = π × radius² = 3.14 × (7 cm)² = 3.14 × 49 cm² = 153.86 cm².

Correct Answer: C — 153.86 cm²

Q. Calculate the area of a rectangle with a length of 15 m and a width of 10 m.

A. 150 m²
B. 140 m²
C. 160 m²
D. 130 m²

Solution

Area = length × width = 15 m × 10 m = 150 m².

Correct Answer: A — 150 m²

Q. Calculate the area of a sector with a radius of 5 cm and a central angle of 60 degrees.

A. 13.09 cm²
B. 15.71 cm²
C. 20.93 cm²
D. 25.00 cm²

Solution

Area = (θ/360) × π × r² = (60/360) × 3.14 × (5 cm)² = 13.09 cm².

Correct Answer: A — 13.09 cm²

Q. Calculate the Banker's Discount on a loan of $1200 for 6 months at an interest rate of 5%.

A. $30.00
B. $25.00
C. $20.00
D. $15.00

Solution

Banker's Discount = (1200 x 5 x 6/12) / 100 = $30.00

Correct Answer: B — $25.00

Q. Calculate the maturity value of a bill of $4000 with a Banker's Discount of $200 for 6 months.

A. $3800
B. $4000
C. $4200
D. $4400

Solution

Maturity Value = Principal + BD = 4000 + 200 = $4200

Correct Answer: C — $4200

Q. Convert 0.125 to a fraction.

A. 1/8
B. 1/4
C. 1/2
D. 3/8

Solution

0.125 = 125/1000 = 1/8 after simplification.

Correct Answer: A — 1/8

Q. Convert 0.2 to a fraction.

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

Solution

0.2 = 2/10 = 1/5 after simplification.

Correct Answer: A — 1/5

Q. Find the area of a parallelogram with a base of 12 cm and a height of 5 cm.

A. 50 cm²
B. 60 cm²
C. 70 cm²
D. 80 cm²

Solution

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

Correct Answer: B — 60 cm²

Q. Find the area of a rectangle with a length of 15 m and a width of 10 m.

A. 100 m²
B. 120 m²
C. 150 m²
D. 160 m²

Solution

Area = length × width = 15 m × 10 m = 150 m².

Correct Answer: C — 150 m²

Q. Find the Banker's Discount on a sum of $2000 due in 1 year at a rate of 10%.

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

Solution

Banker's Discount = (2000 x 10 x 1) / 100 = $200

Correct Answer: A — $200

Q. From a group of 8 people, how many ways can a committee of 3 be formed?

A. 56
B. 24
C. 8
D. 12

Solution

The number of ways to form a committee of 3 from 8 is C(8, 3) = 56.

Correct Answer: A — 56

Q. From a group of 8 people, how many ways can a committee of 4 be formed?

A. 70
B. 56
C. 80
D. 90

Solution

The number of ways to form a committee of 4 from 8 is C(8, 4) = 70.

Correct Answer: A — 70

Q. From a point 40 meters away from the base of a tower, the angle of elevation to the top of the tower is 30 degrees. What is the height of the tower?

A. 20√3 meters
B. 30 meters
C. 40 meters
D. 50 meters

Solution

Height = distance * tan(30) = 40 * (1/√3) = 40/√3 = 20√3 meters

Correct Answer: A — 20√3 meters

Q. From a point 60 meters away from the base of a hill, the angle of elevation to the top of the hill is 30 degrees. What is the height of the hill?

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

Solution

Height = distance * tan(angle) = 60 * (1/√3) = 60 / 1.732 = 34.64 meters.

Correct Answer: B — 30 meters

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