Arithmetic Aptitude for Competitive Exam Success

Arithmetic Aptitude

Area Average Bankers Discount Boats and Streams Calendar Chain Rule Clock Compound Interest Decimal Fraction Height and Distance Logarithm Mixture Numbers Odd Man Out and Series Partnership Percentage Permutation and Combination Pipes and Cistern Probability Problems on Ages Problems on H.C.F and L.C.M Problems on Numbers Problems on Trains Profit and Loss Races and Games Ratio and Proportion Simple Interest Simplification Square Root and Cube Root Stocks and Shares Surds and Indices Time and Distance Time and Work True Discount Volume and Surface Area

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Solution

The ratio of their investments is 30000:45000 = 2:3. A's share of the profit = 2/5 * 15000 = $6,000.

Correct Answer: B — $6,000

Q. A and B invest in a business with investments of $15,000 and $25,000 respectively. If the total profit is $20,000, how much does A receive?

A. $6,000
B. $8,000
C. $10,000
D. $12,000

Solution

Investment ratio = 15000:25000 = 3:5. A's share of profit = (3/8) * 20000 = $7,500.

Correct Answer: B — $8,000

Q. A and B start a business with investments of $12,000 and $18,000 respectively. If they make a profit of $9,000, how much will A receive?

A. $3,000
B. $4,000
C. $5,000
D. $6,000

Solution

The ratio of their investments is 12000:18000 = 2:3. A's share of the profit = 2/5 * 9000 = $3,600.

Correct Answer: B — $4,000

Q. A and B start a business with investments of $12,000 and $18,000 respectively. If they make a profit of $9,000, how much profit does A get?

A. $3,600
B. $4,000
C. $4,500
D. $5,400

Solution

Investment ratio = 12000:18000 = 2:3. A's share of profit = (2/5) * 9000 = $3,600.

Correct Answer: D — $5,400

Q. A and B started a business with investments of $10,000 and $15,000 respectively. What is the ratio of their profits after one year?

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

Solution

The ratio of their investments is 10000:15000 = 2:3. Therefore, the profit ratio is also 2:3.

Correct Answer: A — 2:3

Q. A bag contains 3 red balls and 2 blue balls. What is the probability of drawing a red ball?

A. 0.3
B. 0.4
C. 0.6
D. 0.5

Solution

The total number of balls is 3 + 2 = 5. The probability of drawing a red ball is 3/5 = 0.6.

Correct Answer: C — 0.6

Q. A bag contains 5 red balls and 3 blue balls. If the average weight of the red balls is 200 grams and the blue balls is 150 grams, what is the average weight of all the balls?

A. 175
B. 180
C. 185
D. 190

Solution

Total weight of red balls = 5 * 200 = 1000 grams. Total weight of blue balls = 3 * 150 = 450 grams. Total weight = 1000 + 450 = 1450 grams. Average weight = 1450 / 8 = 181.25.

Correct Answer: B — 180

Q. A bill of $1500 has a Banker's Discount of $45. What is the rate of interest for 6 months?

A. 5%
B. 6%
C. 7%
D. 8%

Solution

Rate = (BD x 100) / (Principal x Time) = (45 x 100) / (1500 x 6/12) = 6%

Correct Answer: A — 5%

Q. A bill of Rs. 10000 is discounted at 5% per annum for 1 year. What is the bankers' discount?

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

Solution

Bankers' Discount = (10000 × 5 × 1) / 100 = Rs. 500.

Correct Answer: A — Rs. 500

Q. A bill of Rs. 10000 is due in 1 year. If the Banker's Discount is Rs. 800, what is the rate of interest?

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

Solution

Banker's Discount = (Face Value * Rate * Time) / 100. 800 = (10000 * Rate * 1) / 100. Rate = 8%.

Correct Answer: B — 10%

Q. A bill of Rs. 12000 is discounted at 12% per annum for 9 months. What is the bankers' discount?

A. Rs. 900
B. Rs. 1200
C. Rs. 1000
D. Rs. 800

Solution

Bankers' Discount = (12000 × 12 × 0.75) / 100 = Rs. 900.

Correct Answer: B — Rs. 1200

Q. A bill of Rs. 12000 is due in 9 months. Calculate the Banker's Discount at the rate of 15% per annum.

A. Rs. 450
B. Rs. 300
C. Rs. 600
D. Rs. 900

Solution

Banker's Discount = (12000 × 15 × 0.75) / 100 = Rs. 1350.

Correct Answer: C — Rs. 600

Q. A bill of Rs. 12000 is due in 9 months. If the bankers' discount is Rs. 900, what is the rate of interest?

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

Solution

Rate = (BD × 100) / (Principal × Time) = (900 × 100) / (12000 × 0.75) = 12%.

Correct Answer: B — 12%

Q. A bill of Rs. 15000 is due in 3 months. If the bankers' discount is Rs. 450, what is the rate of interest?

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

Solution

Rate = (BD × 100) / (Principal × Time) = (450 × 100) / (15000 × 0.25) = 12%.

Correct Answer: B — 10%

Q. A bill of Rs. 15000 is due in 3 months. What is the Banker's Discount at the rate of 8% per annum?

A. Rs. 300
B. Rs. 400
C. Rs. 200
D. Rs. 600

Solution

Banker's Discount = (15000 × 8 × 0.25) / 100 = Rs. 300.

Correct Answer: B — Rs. 400

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