Arithmetic Study Resources for Competitive Exams

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Arithmetic MCQ & Objective Questions

Arithmetic is a fundamental branch of mathematics that plays a crucial role in academic success. Mastering arithmetic concepts is essential for students preparing for school exams and competitive tests. Practicing MCQs and objective questions not only enhances understanding but also boosts confidence, leading to better scores in exams. Engaging with practice questions helps identify important questions and reinforces key concepts necessary for effective exam preparation.

What You Will Practise Here

Basic operations: Addition, subtraction, multiplication, and division
Fractions and decimals: Conversions and calculations
Percentage calculations: Understanding and applying percentage concepts
Ratio and proportion: Solving problems involving ratios and proportions
Average: Calculating mean, median, and mode
Word problems: Translating real-life situations into mathematical expressions
Time and work: Understanding concepts related to time, speed, and efficiency

Exam Relevance

Arithmetic is a key topic in various examinations, including CBSE, State Boards, NEET, and JEE. Students can expect to encounter arithmetic questions in multiple-choice formats, often focusing on real-world applications and problem-solving. Common question patterns include direct calculations, word problems, and application of formulas, making it essential for students to be well-versed in this area to excel in their exams.

Common Mistakes Students Make

Misunderstanding the order of operations, leading to incorrect answers
Confusing fractions and decimals during conversions
Overlooking key details in word problems, resulting in wrong interpretations
Neglecting to simplify expressions before solving
Failing to apply percentage formulas correctly in practical scenarios

FAQs

Question: What are some effective strategies for solving arithmetic MCQs?
Answer: Focus on understanding the concepts, practice regularly, and learn to identify keywords in questions that guide you to the correct approach.

Question: How can I improve my speed in solving arithmetic problems?
Answer: Regular practice with timed quizzes and mock tests can significantly enhance your speed and accuracy in solving arithmetic problems.

Start your journey towards mastering arithmetic today! Solve practice MCQs and test your understanding to ensure you are well-prepared for your exams. Remember, consistent practice is the key to success!

Averages Mixtures & Alligation Partnerships Percentages Pipes & Cisterns Profit, Loss & Discount Ratio & Proportion Simple & Compound Interest Time & Work Time, Speed & Distance

Q. A and B are mixed in the ratio 1:4. If the total volume of the mixture is 100 liters, how many liters of liquid A are there?

A. 20 liters
B. 25 liters
C. 30 liters
D. 40 liters

Solution

Total parts = 1 + 4 = 5. Volume of A = (1/5) * 100 = 20 liters.

Correct Answer: A — 20 liters

Q. A and B are mixed in the ratio 2:3. If the total volume of the mixture is 50 liters, how much of liquid B is there?

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

Solution

Total parts = 2 + 3 = 5. Volume of B = (3/5) * 50 = 30 liters.

Correct Answer: B — 30 liters

Q. A and B are mixed in the ratio 2:3. If the total volume of the mixture is 50 liters, how much of liquid A is present?

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

Solution

The total parts in the mixture is 2 + 3 = 5. Liquid A is (2/5) * 50 = 20 liters.

Correct Answer: A — 20 liters

Q. A and B are mixed in the ratio 4:5. If the total volume of the mixture is 90 liters, how much of liquid B is present?

A. 40 liters
B. 50 liters
C. 45 liters
D. 30 liters

Solution

Total parts = 4 + 5 = 9. Volume of B = (5/9) * 90 = 50 liters.

Correct Answer: B — 50 liters

Q. A and B are mixed in the ratio 4:5. If the total volume of the mixture is 90 liters, how many liters of liquid B are there?

A. 40 liters
B. 50 liters
C. 45 liters
D. 30 liters

Solution

Total parts = 4 + 5 = 9. Volume of B = (5/9) * 90 = 50 liters.

Correct Answer: B — 50 liters

Q. A bag contains red and blue balls in the ratio of 3:5. If there are 40 blue balls, how many red balls are there?

A. 24
B. 30
C. 20
D. 32

Solution

The ratio of red to blue balls is 3:5. If there are 40 blue balls, we can set up the proportion: 3/5 = x/40. Solving for x gives us x = 24. Therefore, there are 24 red balls.

Correct Answer: A — 24

Q. A bag contains red and blue balls in the ratio of 5:3. If there are 40 red balls, how many blue balls are there?

A. 24
B. 30
C. 20
D. 16

Solution

The ratio of red to blue balls is 5:3. If there are 40 red balls, the number of blue balls can be calculated as (3/5) * 40 = 24 blue balls.

Correct Answer: A — 24

Q. A bank offers an interest rate of 5% per annum. If a customer deposits $1,000, how much interest will the customer earn in 3 years? (2023)

A. $150
B. $100
C. $50
D. $200

Solution

Interest = Principal * Rate * Time = $1,000 * 0.05 * 3 = $150.

Correct Answer: B — $100

Q. A bicycle is sold for $300 after a discount of 25%. What was the marked price?

A. $350
B. $375
C. $400
D. $450

Solution

Let the marked price be x. Selling Price = x - 25% of x = 0.75x. Thus, 0.75x = 300, so x = 400.

Correct Answer: B — $375

Q. A book is marked at $40. If a customer buys it at a 15% discount, what is the amount saved?

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

Solution

Discount = 15% of 40 = 6. Amount saved = $6.

Correct Answer: B — $6

Q. A book is sold for $150 after a discount of 25%. What was the marked price of the book? (2023)

A. $175
B. $180
C. $200
D. $210

Solution

Let the marked price be x. Selling Price = Marked Price - Discount = x - 0.25x = 0.75x. Thus, 0.75x = 150, so x = 200.

Correct Answer: C — $200

Q. A book is sold for $45 after a discount of 10%. What is the marked price of the book?

A. $50
B. $55
C. $60
D. $65

Solution

Let the marked price be x. Selling Price = x - 10% of x = 45. Thus, 0.9x = 45, so x = $50.

Correct Answer: A — $50

Q. A box contains 5 red balls and 3 blue balls. If one ball is drawn at random, what is the probability that it is blue?

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

Solution

Total balls = 5 + 3 = 8. Probability of drawing a blue ball = Number of blue balls / Total balls = 3/8.

Correct Answer: B — 3/8

Q. A car travels 60 km in 1 hour and 30 minutes. What is its average speed in km/h?

A. 40
B. 50
C. 45
D. 60

Solution

Time taken is 1.5 hours. Average speed = distance/time = 60/1.5 = 40 km/h.

Correct Answer: C — 45

Q. A car travels a distance in the ratio of 3:2 at two different speeds. If the total distance is 150 km, how much distance does it cover at the first speed?

A. 90 km
B. 60 km
C. 75 km
D. 45 km

Solution

The total parts of the ratio 3:2 = 5. The distance covered at the first speed is (3/5) * 150 km = 90 km.

Correct Answer: A — 90 km

Q. A car travels at a speed of 60 km/h and a bike travels at 40 km/h. What is the ratio of the speeds of the car to the bike?

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

Solution

The speed of the car is 60 km/h and the speed of the bike is 40 km/h. The ratio of their speeds is 60:40, which simplifies to 3:2.

Correct Answer: A — 3:2

Q. A car's value depreciates by 20% each year. If the car's initial value is $25,000, what will be its value after 2 years?

A. $10,000
B. $12,000
C. $16,000
D. $20,000

Solution

After 1 year: $25,000 - (0.20 * 25,000) = $20,000. After 2 years: $20,000 - (0.20 * 20,000) = $16,000.

Correct Answer: C — $16,000

Q. A car's value depreciates by 20% each year. If the car's initial value is $25,000, what will be its value after two years?

A. $15,000
B. $16,000
C. $18,000
D. $20,000

Solution

After the first year, the value is $25,000 - (20% of $25,000) = $20,000. After the second year, the value is $20,000 - (20% of $20,000) = $16,000.

Correct Answer: B — $16,000

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

A. $16,000
B. $15,000
C. $14,000
D. $18,000

Solution

The depreciation amount is 20% of $20,000, which is $4,000. Therefore, the value after one year is $20,000 - $4,000 = $16,000.

Correct Answer: A — $16,000

Q. A certain amount of money is invested at a compound interest rate of 10% per annum. How long will it take for the investment to double?

A. 7.2 years
B. 10 years
C. 5 years
D. 8 years

Solution

Using the Rule of 72, time = 72/r = 72/10 = 7.2 years.

Correct Answer: A — 7.2 years

Q. A certain amount of money is invested at a compound interest rate of 12% per annum. If the amount becomes $5000 after 3 years, what was the principal?

A. $3500
B. $4000
C. $4500
D. $4800

Solution

Using A = P(1 + r)^t, we rearrange to find P = A / (1 + r)^t. Thus, P = 5000 / (1.12)^3 = $4000.

Correct Answer: B — $4000

Q. A certain amount of money triples itself in 15 years at compound interest. What is the annual interest rate?

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

Solution

Using the formula A = P(1 + r)^n, we can set up the equation 3P = P(1 + r)^15. Solving for r gives approximately 6%.

Correct Answer: B — 6%

Q. A chemist has a solution that is 25% acid. How much of this solution must be mixed with 10 liters of a solution that is 50% acid to obtain a solution that is 40% acid?

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

Solution

Let x be the liters of 25% solution. The equation is 0.25x + 0.5(10) = 0.4(x + 10). Solving gives x = 15 liters.

Correct Answer: C — 15 liters

Q. A class has 30 students, and 40% of them are girls. How many boys are there in the class? (2023)

A. 12
B. 18
C. 20
D. 24

Solution

Number of girls = 40% of 30 = 12. Therefore, number of boys = 30 - 12 = 18.

Correct Answer: B — 18

Q. A company has 120 employees, and 25% of them are in the sales department. How many employees are not in the sales department?

A. 90
B. 80
C. 70
D. 75

Solution

25% of 120 is 30, so the number of employees not in the sales department is 120 - 30 = 90.

Correct Answer: A — 90

Q. A company reported a profit of 20% on its sales. If the sales amount to $50,000, what is the profit earned by the company?

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

Solution

Profit = 20% of $50,000 = 0.20 * 50,000 = $10,000.

Correct Answer: B — $10,000

Q. A company reports a profit margin of 20%. If the total revenue is $500,000, what is the profit amount? (2023)

A. $80,000
B. $100,000
C. $120,000
D. $150,000

Solution

Profit = 20% of $500,000 = 0.2 * 500,000 = $100,000.

Correct Answer: B — $100,000

Q. A company reports a profit margin of 25%. If the total revenue is $200,000, what is the profit amount?

A. $40,000
B. $50,000
C. $60,000
D. $70,000

Solution

Profit amount = 25% of $200,000 = 0.25 * 200,000 = $50,000.

Correct Answer: B — $50,000

Q. A company reports a profit margin of 30%. If the cost price of a product is $200, what is the selling price?

A. $240
B. $260
C. $280
D. $300

Solution

Selling Price = Cost Price + Profit = 200 + (30% of 200) = 200 + 60 = $260.

Correct Answer: A — $240

Q. A company reports a profit margin of 30%. If the total revenue is $500,000, what is the profit amount? (2023)

A. $150,000
B. $200,000
C. $100,000
D. $250,000

Solution

Profit = 30% of $500,000 = 0.3 * 500,000 = $150,000.

Correct Answer: A — $150,000

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