Arithmetic Aptitude for Competitive Exam Success

Arithmetic Aptitude

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Q. A 10-meter tall pole casts a shadow of 5 meters long. What is the angle of elevation of the sun?

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

Solution

tan(angle) = height/shadow = 10/5 = 2, angle = 60 degrees.

Correct Answer: C — 60 degrees

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Q. A and B are of different ages. If A is 5 years older than B and the sum of their ages is 45, what is A's age?

A. 20
B. 22
C. 25
D. 27

Solution

Let B's age be x. Then A's age is x + 5. So, x + (x + 5) = 45. Solving gives A = 25.

Correct Answer: C — 25

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Q. A and B are of different ages. If A is 5 years older than B and the sum of their ages is 45, how old is A?

A. 20
B. 22
C. 25
D. 27

Solution

Let B's age be x. Then A's age is x + 5. So, x + (x + 5) = 45. Solving gives A = 25.

Correct Answer: C — 25

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Q. A and B can complete a task in 10 days and 15 days respectively. If they work together for 5 days, how much of the task is left?

A. 1/3
B. 1/4
C. 1/5
D. 1/6

Solution

A's rate = 1/10, B's rate = 1/15. Combined rate = 1/10 + 1/15 = 1/6. Work done in 5 days = 5/6. Remaining = 1 - 5/6 = 1/6.

Correct Answer: A — 1/3

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Q. A and B can complete a work in 12 days and 15 days respectively. If they work together, how long will it take them to complete the work?

A. 6 days
B. 8 days
C. 10 days
D. 5 days

Solution

A's work rate = 1/12, B's work rate = 1/15. Combined rate = 1/12 + 1/15 = 5/60 = 1/12. Time taken = 12 days.

Correct Answer: B — 8 days

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Q. A and B can complete a work in 12 days and 15 days respectively. If they work together, how many days will they take to complete the work?

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

Solution

A's work rate = 1/12, B's work rate = 1/15. Combined work rate = 1/12 + 1/15 = 5/60 = 1/12. Time taken = 12 days.

Correct Answer: C — 8 days

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Q. A and B can complete a work in 12 days and 15 days respectively. In how many days can they complete the work together?

A. 6
B. 8
C. 10
D. 5

Solution

A's work rate = 1/12, B's work rate = 1/15. Together, they work at the rate of 1/12 + 1/15 = 5/60 + 4/60 = 9/60 = 3/20. Therefore, they complete the work in 20/3 days = 6.67 days.

Correct Answer: B — 8

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Q. A and B invest in a business in the ratio 3:2. If A's investment is $9000, what is B's investment?

A. $6000
B. $4500
C. $3000
D. $7500

Solution

If A's investment is $9000 and the ratio is 3:2, then B's investment = (2/3) * 9000 = $6000.

Correct Answer: A — $6000

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Q. A and B invest in a business in the ratio 3:4. If B's investment is $2800, what is A's investment?

A. $2100
B. $2400
C. $3000
D. $3200

Solution

Let A's investment be 3x and B's be 4x. 4x = 2800, so x = 700. A's investment = 3x = 3 * 700 = $2100.

Correct Answer: B — $2400

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

A. $15,000
B. $18,000
C. $20,000
D. $25,000

Solution

Total parts = 3 + 5 = 8. A's share = 3/8 * 40000 = $15,000.

Correct Answer: B — $18,000

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Q. A and B invest in a business in the ratio 4:5. If A's profit is $8,000, what is B's profit?

A. $6,000
B. $10,000
C. $9,000
D. $12,000

Solution

Profit ratio = 4:5. If A's profit is $8,000, then B's profit = (5/4) * 8000 = $10,000.

Correct Answer: B — $10,000

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Q. A and B invest in a business in the ratio 4:5. If the total profit is $45,000, how much does A receive?

A. $20,000
B. $18,000
C. $15,000
D. $25,000

Solution

Total parts = 4 + 5 = 9. A's share = 4/9 * 45000 = $20,000.

Correct Answer: B — $18,000

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Q. A and B invest in a business in the ratio 4:6. If A's profit is $2,400, what is the total profit?

A. $4,800
B. $6,000
C. $8,000
D. $9,600

Solution

Profit ratio = 4:6 = 2:3. If A's share is $2400, total profit = (2400 * 5) / 2 = $6,000.

Correct Answer: A — $4,800

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Q. A and B invest in a business in the ratio 5:3. If the total profit is $1600, how much does B receive?

A. $600
B. $800
C. $700
D. $500

Solution

Total parts = 5 + 3 = 8. B's share = (3/8) * 1600 = $600.

Correct Answer: A — $600

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Q. A and B invest in a business in the ratio 5:7. If B's investment is $14,000, what is A's investment?

A. $10,000
B. $12,000
C. $15,000
D. $16,000

Solution

If B's investment is 7 parts = $14,000, then 1 part = $14,000/7 = $2,000. A's investment = 5 parts = 5 * $2,000 = $10,000.

Correct Answer: B — $12,000

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Q. A and B invest in a business in the ratio 5:7. If the total profit is $24,000, how much does A receive?

A. $10,000
B. $12,000
C. $14,000
D. $16,000

Solution

Total parts = 5 + 7 = 12. A's share = 5/12 * 24000 = $10,000.

Correct Answer: B — $12,000

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Q. A and B invest in a business in the ratio 5:7. If the total profit is $24,000, how much profit does B receive?

A. $10,000
B. $12,000
C. $14,000
D. $16,000

Solution

Total parts = 5 + 7 = 12. B's share = (7/12) * 24000 = $14,000.

Correct Answer: B — $12,000

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Q. A and B invest in a business in the ratio of 1:4. If the total profit is $5000, how much does A receive?

A. $1000
B. $500
C. $2000
D. $1500

Solution

Total parts = 1 + 4 = 5. A's share = (1/5) * 5000 = $1000.

Correct Answer: A — $1000

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Q. A and B invest in a business in the ratio of 3:2. If A's investment is $9000, what is B's investment?

A. $6000
B. $4500
C. $3000
D. $7500

Solution

If A's investment is $9000 and the ratio is 3:2, then B's investment = (2/3) * 9000 = $6000.

Correct Answer: A — $6000

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Q. A and B invest in a business with A investing $12,000 and B investing $18,000. If the total profit is $30,000, how much does A receive?

A. $12,000
B. $10,000
C. $8,000
D. $15,000

Solution

Total investment = 12000 + 18000 = 30000. A's share = (12000/30000) * 30000 = $12,000.

Correct Answer: B — $10,000

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Q. A and B invest in a business with A investing $2000 and B investing $3000. If they make a profit of $1000, how much profit does A get?

A. $400
B. $600
C. $500
D. $300

Solution

Total investment = 2000 + 3000 = $5000. A's share = (2000/5000) * 1000 = $400.

Correct Answer: B — $600

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Q. A and B invest in a business with A investing $2000 and B investing $3000. If they make a profit of $1000, how much does A get?

A. $400
B. $600
C. $500
D. $300

Solution

Total investment = 2000 + 3000 = 5000. A's share = (2000/5000) * 1000 = $400.

Correct Answer: B — $600

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Q. A and B invest in a business with A investing $2000 and B investing $8000. If they incur a loss of $1000, how much loss does A bear?

A. $200
B. $250
C. $300
D. $400

Solution

Total investment = 2000 + 8000 = $10000. A's share of loss = (2000/10000) * 1000 = $200.

Correct Answer: B — $250

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Q. A and B invest in a business with A investing $25,000 and B investing $35,000. If the total profit is $50,000, how much does A receive?

A. $20,000
B. $15,000
C. $18,000
D. $25,000

Solution

Total investment = 25000 + 35000 = 60000. A's share = (25000/60000) * 50000 = $20,000.

Correct Answer: A — $20,000

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Q. A and B invest in a business with A investing $30,000 and B investing $45,000. If they make a profit of $15,000, how much does A get?

A. $5,000
B. $6,000
C. $7,000
D. $8,000

Solution

The ratio of their investments is 30,000:45,000 = 2:3. A's share of profit = 2/5 * 15000 = $6,000.

Correct Answer: B — $6,000

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Q. A and B invest in a business with A investing $3000 and B investing $5000. If they incur a loss of $400, how much loss does B bear?

A. $200
B. $250
C. $300
D. $150

Solution

Total investment = 3000 + 5000 = $8000. B's share of loss = (5000/8000) * 400 = $250.

Correct Answer: B — $250

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Q. A and B invest in a business with A investing $3000 and B investing $7000. If the profit is divided in the ratio of their investments, what is A's share if the total profit is $5000?

A. $1500
B. $2000
C. $1000
D. $2500

Solution

Total investment = 3000 + 7000 = $10000. A's share = (3000/10000) * 5000 = $1500.

Correct Answer: A — $1500

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Q. A and B invest in a business with A investing $40,000 and B investing $60,000. If they make a profit of $30,000, how much profit does B get?

A. $12,000
B. $15,000
C. $18,000
D. $20,000

Solution

Total investment = $40,000 + $60,000 = $100,000. B's share = 60000/100000 * 30000 = $18,000.

Correct Answer: C — $18,000

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Q. A and B invest in a business with A investing $7000 and B investing $3000. If they make a profit of $2000, how much does A get?

A. $1400
B. $1200
C. $1600
D. $1800

Solution

Total investment = 7000 + 3000 = $10000. A's share = (7000/10000) * 2000 = $1400.

Correct Answer: A — $1400

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Q. A and B invest in a business with A investing $8000 and B investing $12000. If they incur a loss of $2000, how much loss does B bear?

A. $800
B. $1200
C. $1000
D. $600

Solution

Total investment = 8000 + 12000 = $20000. B's share of loss = (12000/20000) * 2000 = $1200.

Correct Answer: B — $1200

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Arithmetic Aptitude

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