Class 10 Maths Chapter 3 Exercise 3.3 Solution provides detailed, step-by-step explanations to help students understand key concepts and solve problems effectively.
Sample Questions and Answers:
A shopkeeper sells an article at a profit of 20%. If the cost price of the article is ₹500, what is the selling price?
To calculate the selling price, add 20% of ₹500 to ₹500. The selling price is ₹600.
A student scored 75% marks in the exam. If the total marks are 800, how many marks did the student get?
Multiply 75% of 800. The student scored 600 marks.
If the perimeter of a rectangle is 50 cm and the length is 15 cm, what is the width?
Using the perimeter formula, the width of the rectangle is 10 cm.
A car travels 60 km in 1 hour. How far will it travel in 5 hours at the same speed?
Multiply 60 km by 5 to get 300 km.
A box contains 5 red balls, 3 blue balls, and 2 green balls. What is the probability of drawing a red ball?
The probability is 5/10 or 1/2.
The price of a book increases by 10%. If the original price is ₹200, what is the new price?
The new price is ₹220 after a 10% increase.
A triangle has a base of 8 cm and a height of 6 cm. What is its area?
The area of the triangle is 24 square cm.
A fruit basket contains 5 apples, 3 bananas, and 2 oranges. What is the probability of picking a banana?
The probability of picking a banana is 3/10.
The ratio of the number of boys to girls in a class is 2:3. If there are 30 students in the class, how many are boys?
There are 12 boys in the class.
The speed of a train is 72 km/h. How much time will it take to cover 180 km?
The time taken will be 2.5 hours.
A person invests ₹10,000 at an interest rate of 5% per annum. How much interest will he earn in 2 years?
The interest earned will be ₹1,000.
A rectangle has a length of 12 cm and a breadth of 5 cm. What is the area of the rectangle?
The area is 60 square cm.
A box contains 4 red, 5 blue, and 6 green balls. What is the probability of drawing a green ball?
The probability of drawing a green ball is 6/15 or 2/5.
A car travels 100 km in 2 hours. What is its average speed?
The average speed of the car is 50 km/h.
The area of a square is 64 cm². What is the length of its side?
The side of the square is 8 cm.
The sum of two numbers is 50, and their difference is 10. What are the two numbers?
The two numbers are 30 and 20.
A gardener plants 20 trees in 4 rows. If each row has the same number of trees, how many trees are in each row?
Each row has 5 trees.
A person bought a bike for ₹25,000 and sold it for ₹28,000. What is his profit?
The profit is ₹3,000.
A recipe requires 200 grams of sugar for 4 servings. How much sugar is needed for 6 servings?
For 6 servings, 300 grams of sugar is needed.
The perimeter of a square is 36 cm. What is the length of one side of the square?
The side length is 9 cm.
A train travels at a speed of 90 km/h. How far will it travel in 3 hours?
The train will travel 270 km in 3 hours.
A boat covers a distance of 20 km in 2 hours. What is its speed?
The speed of the boat is 10 km/h.
A student scored 50 marks in a test out of 100. What is his percentage score?
The percentage score is 50%.
A shop sells an item for ₹200 after a 25% profit. What is the cost price of the item?
The cost price of the item is ₹160.
A farmer has a field of 200 m by 300 m. What is the area of the field?
The area of the field is 60,000 square meters.
A book originally costs ₹500. If there is a 20% discount, what is the new price?
The new price is ₹400 after the discount.
The sum of three consecutive numbers is 54. What are the numbers?
The numbers are 17, 18, and 19.
A store sells a laptop for ₹40,000 after a 10% discount. What was the original price?
The original price of the laptop was ₹44,444.44.
The area of a circle is 154 cm². What is the radius of the circle?
The radius of the circle is 7 cm.
The length of a rectangle is twice its breadth. If the area is 100 cm², what is the length and breadth?
The length is 20 cm, and the breadth is 10 cm.
A student scored 70 marks in an exam. If the total marks were 100, what is his percentage?
The percentage is 70%.
A water tank is filled in 3 hours. How much time will it take to fill the same tank at twice the rate?
It will take 1.5 hours to fill the tank at twice the rate.
A number is increased by 15% to give 115. What is the original number?
The original number is 100.
A family spends ₹12,000 on groceries per month. How much will they spend in 6 months?
They will spend ₹72,000 in 6 months.
A book is sold for ₹150, which is 25% more than its cost price. What is the cost price?
The cost price of the book is ₹120.
The volume of a cube is 64 cm³. What is the length of one side?
The side length is 4 cm.
A box contains 6 red, 7 blue, and 8 yellow balls. What is the probability of drawing a yellow ball?
The probability of drawing a yellow ball is 8/21.
A cyclist travels 40 km in 2 hours. What is his average speed?
The average speed of the cyclist is 20 km/h.
The length of a rectangular garden is 10 m, and the width is 6 m. What is the perimeter of the garden?
The perimeter of the garden is 32 meters.
A person earns ₹50,000 per month. If he spends 60% of his salary, how much does he save?
He saves ₹20,000.
A person buys a shirt for ₹600 and sells it at a 15% profit. What is the selling price?
The selling price is ₹690.
A ball is thrown upward with a speed of 20 m/s. How high will it go before coming to a stop?
The maximum height reached will be 20 meters.
A car runs 150 km in 3 hours. What is its speed?
The speed of the car is 50 km/h.
A student obtained 80 marks out of 100 in the first exam and 90 marks out of 100 in the second exam. What is his average score?
The average score is 85%.
A company manufactures 300 units of a product every day. How many units will it produce in 10 days?
The company will produce 3,000 units in 10 days.
A student read 40 pages of a book in 1 hour. How many pages will he read in 5 hours?
He will read 200 pages in 5 hours.
A person invests ₹5,000 at an annual interest rate of 8%. How much interest will he earn in 3 years?
He will earn ₹1,200 in 3 years.
A rectangle has a length of 14 cm and a breadth of 6 cm. What is the perimeter of the rectangle?
The perimeter of the rectangle is 40 cm.
A shop sells a pair of shoes for ₹1,200 after applying a 20% discount. What was the original price of the shoes?
The original price of the shoes was ₹1,500.
The sum of two numbers is 50, and one number is 10 more than the other. What are the numbers?
The numbers are 20 and 30.
Recommended Indian Books for Class 10 Maths Chapter 3 Exercise 3.3 Solution
"Mathematics for Class 10" by R.D. Sharma
Publication: Dhanpat Rai Publications
Content: This book covers all chapters of the class 10 curriculum, including Chapter 3. Exercise 3.3 focuses on geometric progressions and problems related to them. The book provides detailed explanations and multiple solved examples to help students understand the core concepts.
"Concise Mathematics" by R.S. Aggarwal
Publication: S. Chand Publishing
Content: This book offers a thorough explanation of various topics with a focus on exercises like 3.3. It provides step-by-step solutions to problems related to quadratic equations and linear equations, making it ideal for mastering key concepts.
"Together with Mathematics" by Arya Publications
Publication: Arya Publications
Content: Known for its clear and concise approach, this book offers a range of practice questions and solutions for Chapter 3. Exercise 3.3 includes applications of algebra and solving real-life problems with quadratic equations.
"R.S. Aggarwal Mathematics Class 10" by R.S. Aggarwal
Publication: S. Chand Publishing
Content: This textbook is known for its vast range of practice questions, with an easy-to-understand explanation of concepts in Chapter 3. Exercise 3.3 explores more complex problem-solving approaches, with real-world applications.
"New Mathematics Today for Class 10" by M.L. Aggarwal
Publication: Bharati Bhawan Publishers
Content: With its simple language and clear step-by-step solutions, this book tackles Chapter 3, Exercise 3.3. It explains the concepts of algebraic expressions and linear equations in a manner that is both engaging and educational.
"All in One Mathematics" by Arihant Experts
Publication: Arihant Publications
Content: Offering both theoretical explanations and an array of solved exercises, this book provides a rich collection of practice questions. Chapter 3 Exercise 3.3 focuses on algebra, ratio, and proportion problems.
"Mathematics Class 10" by S.K. Gupta & Anubhuti Gangal
Publication: Dhanpat Rai Publications
Content: The book provides in-depth explanations of Chapter 3 concepts, focusing on quadratic equations and solving them using algebraic methods. Exercise 3.3 challenges students to apply their knowledge to more complex problems.
"Mathematics for Class 10" by Lakhmir Singh & Manjit Kaur
Publication: S. Chand Publishing
Content: This book is excellent for beginners, offering simple explanations of complex concepts. Exercise 3.3 offers a balanced mix of theory and application-based questions in topics like linear equations and algebra.
"Mathematics Class 10" by K.K. Gupta
Publication: Ramesh Publishing House
Content: A comprehensive resource that offers clear and concise solutions, this book focuses on solving quadratic equations and algebraic identities in Exercise 3.3.
"Problems in Calculus of One Variable" by I.A. Maron
Publication: Jai Prakash Nath & Co.
Content: While primarily focused on calculus, this book offers unique insights into Chapter 3’s algebraic content, especially for students aiming to go beyond basic concepts. Exercise 3.3 provides a higher level of problem-solving to challenge students.
"Mathematics Class 10" by R.K. Bansal
Publication: R.K. Bansal
Content: Offering extensive practice problems, this book explains key topics in Chapter 3, with an emphasis on algebraic expressions, solving equations, and real-life application problems.
"Target Mathematics" by S.K. Gupta
Publication: S.K. Gupta
Content: Focuses on providing strategic approaches to solve mathematical problems. Exercise 3.3 contains detailed practice questions on quadratic equations and their real-world applications.
"Mathematics for Class 10" by M.K. Pandey
Publication: Evergreen Publications
Content: With clear, systematic solutions, this book covers Chapter 3 in great detail, offering comprehensive coverage of algebraic topics and problem-solving in Exercise 3.3.
"Xam Idea Mathematics" by Rajiv Kapoor
Publication: Xam Idea Publications
Content: A popular reference for students, this book offers a variety of question types for practice, including algebraic and geometric problems found in Exercise 3.3.
"Class 10 Mathematics" by K.D. Sharma
Publication: Goyal Brothers Prakashan
Content: Known for its detailed explanation of concepts and well-structured practice problems, this book provides a range of practice questions aligned with Exercise 3.3 to build a strong foundation in algebra.
Class 10 Maths Chapter 3 Exercise 3.3 Solution
Chapter 3 of Class 10 Maths deals with quadratic equations, a topic that plays a significant role in higher mathematics. Exercise 3.3 within this chapter specifically addresses the practical applications of quadratic equations in real-world scenarios. Students encounter problems involving the formation of quadratic equations, solving them, and using algebraic identities to derive solutions.
To begin with, students are introduced to the concept of a quadratic equation in the general form ax2+bx+c=0ax^2 + bx + c = 0ax2+bx+c=0, where aaa, bbb, and ccc are constants. This forms the foundation of the problems found in Exercise 3.3. These questions challenge students to recognize the structure of quadratic equations, identify their coefficients, and solve them using methods like factorization and the quadratic formula.
In this exercise, you’ll find a variety of problem types designed to build proficiency in solving equations. For instance, some questions might involve solving for unknowns in real-world contexts, such as finding the dimensions of an object when certain conditions are provided. Other problems may require students to work with algebraic identities to simplify complex expressions before solving for the variable.
One important aspect that makes Exercise 3.3 essential for Class 10 students is its emphasis on word problems. These problems encourage students to apply mathematical theory to everyday situations, which enhances their critical thinking and problem-solving abilities. The ability to translate real-life scenarios into mathematical models is a skill that will serve students well, not just in exams but also in real-world decision-making.
Moreover, as the chapter progresses, students are introduced to more advanced methods of solving quadratic equations. This includes using the discriminant to determine the nature of the roots, as well as graphical methods where students plot the equation and find the roots by identifying the x-intercepts.
In addition to solving equations, Chapter 3 also emphasizes the importance of verifying solutions. After solving the quadratic equation, students are encouraged to substitute their solutions back into the original equation to check for accuracy. This step ensures that the solutions are correct and helps to reinforce their understanding of the methods used.
Overall, the problems in Exercise 3.3 are designed to strengthen students' algebraic manipulation skills, improve their understanding of quadratic equations, and enable them to apply these concepts effectively.
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