Arithmetic Aptitude for Competitive Exam Success

Arithmetic Aptitude

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Q. If 0.4 is expressed as a fraction, what is it?

A. 2/5
B. 1/4
C. 3/5
D. 1/2

Solution

0.4 = 4/10 = 2/5 after simplification.

Correct Answer: A — 2/5

Q. If 15% of a number is 45, what is the number?

A. 250
B. 300
C. 350
D. 400

Solution

Let the number be x. Then, 0.15x = 45. Therefore, x = 45/0.15 = 300.

Correct Answer: B — 300

Q. If 20 liters of a mixture contains 60% alcohol, how much alcohol is in the mixture?

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

Solution

Alcohol = 60% of 20 liters = 0.6 * 20 = 12 liters.

Correct Answer: B — 10 liters

Q. If 20% of a number is 50, what is the number?

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

Solution

Let the number be x. Then, 0.2x = 50. Therefore, x = 50 / 0.2 = 250.

Correct Answer: A — 200

Q. If 30% of a number is 150, what is the number?

A. 400
B. 450
C. 500
D. 600

Solution

Let the number be x. Then, 0.3x = 150. Therefore, x = 150 / 0.3 = 500.

Correct Answer: B — 450

Q. If 3x + 5 = 20, what is the value of x?

A. 3
B. 5
C. 7
D. 10

Solution

To solve for x, subtract 5 from both sides: 3x = 15. Then divide by 3: x = 5.

Correct Answer: A — 3

Q. If 40% of a number is 80, what is the number?

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

Solution

Let the number be x. Then, 0.4x = 80. So, x = 80 / 0.4 = 200.

Correct Answer: B — 200

Q. If 45% of a number is 90, what is the number?

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

Solution

Let the number be x. 0.45x = 90, x = 90/0.45 = 200

Correct Answer: B — 200

Q. If 5x + 3 = 23, what is the value of x?

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

Solution

To solve for x, subtract 3 from both sides: 5x = 20. Then divide by 5: x = 4.

Correct Answer: B — 3

Q. If 60% of a number is 120, what is the number?

A. 150
B. 180
C. 200
D. 250

Solution

Let the number be x. 0.6x = 120, x = 120/0.6 = 200

Correct Answer: C — 200

Q. If 60% of a number is 240, what is the number?

A. 360
B. 400
C. 420
D. 480

Solution

Let the number be x. Then, 0.6x = 240. Therefore, x = 240/0.6 = 400.

Correct Answer: B — 400

Q. If a 12-meter tall pole casts a shadow of 8 meters, what is the angle of elevation of the sun?

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

Solution

tan(θ) = height / shadow = 12 / 8 = 1.5; θ = tan^(-1)(1.5) ≈ 56.31 degrees

Correct Answer: C — 53.13 degrees

Q. If a bag contains 2 white, 3 black, and 5 blue balls, what is the probability of drawing a blue ball?

A. 1/5
B. 1/3
C. 1/2
D. 1/4

Solution

The total number of balls is 2 + 3 + 5 = 10. The probability of drawing a blue ball is 5/10 = 1/2.

Correct Answer: C — 1/2

Q. If a bag contains 2 white, 3 black, and 5 red balls, what is the probability of drawing a white ball?

A. 1/5
B. 1/4
C. 1/2
D. 1/10

Solution

The total number of balls is 2 + 3 + 5 = 10. The probability of drawing a white ball is 2/10 = 1/5.

Correct Answer: B — 1/4

Q. If a bag contains 4 apples and 6 oranges, what is the probability of randomly selecting an apple?

A. 2/5
B. 4/10
C. 1/3
D. 1/2

Solution

The total number of fruits is 4 + 6 = 10. The probability of selecting an apple is 4/10 = 2/5.

Correct Answer: A — 2/5

Q. If a bag contains 4 apples and 6 oranges, what is the probability of randomly selecting an orange?

A. 2/5
B. 3/5
C. 4/5
D. 1/5

Solution

The total number of fruits is 4 + 6 = 10. The probability of selecting an orange is 6/10 = 3/5.

Correct Answer: B — 3/5

Q. If a bag contains 4 red, 3 blue, and 5 green balls, what is the probability of drawing a green ball?

A. 1/3
B. 1/4
C. 5/12
D. 5/10

Solution

Total balls = 4 + 3 + 5 = 12. Probability of green ball = 5/12.

Correct Answer: C — 5/12

Q. If a bag contains 4 red, 3 green, and 5 blue marbles, what is the probability of drawing a blue marble?

A. 1/3
B. 1/4
C. 5/12
D. 5/10

Solution

Total marbles = 4 + 3 + 5 = 12. Probability of blue marble = 5/12.

Correct Answer: C — 5/12

Q. If a bill of Rs. 15000 is discounted at 8% per annum for 6 months, what is the bankers' discount?

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

Solution

Bankers' Discount = (15000 × 8 × 0.5) / 100 = Rs. 600.

Correct Answer: B — Rs. 800

Q. If a bill of Rs. 20000 is discounted at 15% per annum for 4 months, what is the bankers' discount?

A. Rs. 1000
B. Rs. 1200
C. Rs. 1500
D. Rs. 2000

Solution

Bankers' Discount = (20000 × 15 × 1/3) / 100 = Rs. 1000.

Correct Answer: C — Rs. 1500

Q. If a boat can go 25 km/h in still water and the current is 5 km/h, how long will it take to travel 60 km downstream?

A. 1.5 hours
B. 2 hours
C. 2.5 hours
D. 3 hours

Solution

Speed downstream = 25 + 5 = 30 km/h. Time = Distance/Speed = 60/30 = 2 hours.

Correct Answer: B — 2 hours

Q. If a boat can travel 30 km upstream in 5 hours, what is the speed of the current if the speed of the boat in still water is 8 km/h?

A. 2 km/h
B. 3 km/h
C. 4 km/h
D. 5 km/h

Solution

Speed upstream = Distance/Time = 30 km / 5 h = 6 km/h. Speed of current = Speed of boat in still water - Speed upstream = 8 km/h - 6 km/h = 2 km/h.

Correct Answer: A — 2 km/h

Q. If a boat can travel 60 km downstream in 3 hours, and the speed of the stream is 6 km/h, what is the speed of the boat in still water?

A. 18 km/h
B. 20 km/h
C. 22 km/h
D. 24 km/h

Solution

Let the speed of the boat in still water be y km/h. Downstream speed = y + 6 km/h. Therefore, (y + 6) * 3 = 60. Solving gives y = 18 km/h.

Correct Answer: B — 20 km/h

Q. If a boat can travel 60 km downstream in 4 hours, what is the speed of the current if the speed of the boat in still water is 15 km/h?

A. 3 km/h
B. 4 km/h
C. 5 km/h
D. 6 km/h

Solution

Speed downstream = Distance/Time = 60 km / 4 h = 15 km/h. Speed of current = Speed downstream - Speed of boat in still water = 15 km/h - 15 km/h = 0 km/h.

Correct Answer: C — 5 km/h

Q. If a boat goes 20 km upstream in 4 hours, what is the speed of the current if the speed of the boat in still water is 10 km/h?

A. 2 km/h
B. 3 km/h
C. 4 km/h
D. 5 km/h

Solution

Speed upstream = Speed of boat - Speed of current. Distance = 20 km, Time = 4 hours. Speed upstream = 20/4 = 5 km/h. Thus, 10 - x = 5, so x = 5 km/h.

Correct Answer: A — 2 km/h

Q. If a box contains 10 balls, 4 of which are blue, what is the probability of selecting a blue ball?

A. 2/5
B. 1/2
C. 4/10
D. 3/10

Solution

The probability of selecting a blue ball is 4/10 = 2/5.

Correct Answer: A — 2/5

Q. If a car's value depreciates by 15% each year and its current value is $20,000, what will be its value after one year?

A. $15,000
B. $16,500
C. $17,000
D. $18,000

Solution

Value after one year = 20,000 - (15/100)*20,000 = 20,000 - 3,000 = $17,000.

Correct Answer: B — $16,500

Q. If a certain date is 45 days after February 15, how many days will it be in April?

A. 15
B. 16
C. 17
D. 18

Solution

February has 28 days in a non-leap year. From February 15 to February 28 is 13 days. 45 - 13 = 32 days left. March has 31 days, so 32 - 31 = 1 day into April. Thus, it will be April 1.

Correct Answer: B — 16

Q. If a certain month has 30 days, how many Sundays are there in that month?

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

Solution

A month with 30 days can have either 4 or 5 Sundays, depending on which day of the week it starts. If it starts on a Sunday, there will be 5 Sundays.

Correct Answer: B — 5

Q. If a certain month has 30 days, what is the probability that a randomly chosen day from that month is a weekend?

A. 1/3
B. 1/4
C. 2/7
D. 3/10

Solution

In a 30-day month, there are typically 8 weekend days (4 Saturdays and 4 Sundays). Probability = 8/30 = 4/15, which simplifies to approximately 1/3.

Correct Answer: A — 1/3

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