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Proportional Reasoning-2 Exercise 3.3 Class 8 Maths - Chapter 3 NCERT Solutions

Detailed NCERT Class 8 Maths Chapter 3 Proportional Reasoning-2 Exercise 3.3 solutions are provided on this page to help students understand the questions and grasp the concepts more easily. The solutions are prepared by the ALLEN expert team in accordance with the currently updated syllabus.The exercise is mostly about inverse proportion as it is about comparing how two quantities change with each other. It deals with how to find the inverse proportion from given values, how to determine if the product of two quantities remains constant and how to find the missing values when quantities are in inverse proportion.

1.0Download Class 8 Maths Chapter 3 Ex 3.3 NCERT Solutions PDF

Download the NCERT Class 8 Maths Chapter 3 Exercise 3.3 detailed solutions PDF for free and refer to it anytime for revision and practice.

Chapter 3 : Proportional Reasoning - 2 Exercise 3.3

2.0Detailed NCERT Solutions on Proportional Reasoning-2 Exercise 3.3 Class 8 Maths (Ganita Prakash Term 2)

1. Which of these are inverse proportion? (i)

x	40	80	25	16
y	20	10	32	50

(ii)

x	40	80	25	16
y	20	10	12.5	8

(iii)

x	30	90	150	10
y	15	5	3	45

Sol. (i) $x_{1} = 40, x_{2} = 80, x_{3} = 25, x_{4} = 16$

$y_{1} = 20, y_{2} = 10, y_{3} = 32, y_{4} = 50 x_{1} y_{1} = 40 \times 20 = 800 x_{2} y_{2} = 80 \times 10 = 800 x_{3} y_{3} = 25 \times 32 = 800 x_{4} y_{4} = 16 \times 50 = 800$

So, $x_{1} y_{1} = x_{2} y_{2} = x_{3} y_{3} = x_{4} y_{4} = 800$ $∴ x$ and y are in inverse proportion. (ii) $x_{1} = 40, x_{2} = 80, x_{3} = 25, x_{4} = 16$

$y_{1} = 20, y_{2} = 10, y_{3} = 12.5, y_{4} = 8 x_{1} y_{1} = 40 \times 20 = 800 x_{2} y_{2} = 80 \times 10 = 800 x_{3} y_{3} = 25 \times 12.5 = 312.5 x_{4} y_{4} = 16 \times 8 = 128$

So, $x_{1} y_{1} = x_{2} y_{2} \neq = x_{3} y_{3} \neq = x_{4} y_{4}$ $∴ x$ and $y$ are not in inverse proportion. (iii) $x_{1} = 30, x_{2} = 90, x_{3} = 150, x_{4} = 10$

$y_{1} = 15, y_{2} = 5, y_{3} = 3, y_{4} = 45 x_{1} y_{1} = 30 \times 15 = 450 x_{2} y_{2} = 90 \times 5 = 450 x_{3} y_{3} = 150 \times 3 = 450 x_{4} y_{4} = 10 \times 45 = 450$

So, $x_{1} y_{1} = x_{2} y_{2} = x_{3} y_{3} = x_{4} y_{4} = 450$ $∴ x$ and $y$ are in inverse proportion.

2. Fill in the empty cells if x and y are in inverse proportion.

x	16	12		36
y	9		48

Sol.

x	16	12	$X_{3}$	36
y	9	$y_{2}$	48	$y_{4}$

$∵ x$ and y are in inverse proportion. $∴ 16 \times 9 = 12 \times y_{2}$ $\Rightarrow y_{2} = \frac{16 \times 9}{12} = 12$ $∴ 16 \times 9 = x 3 \times 48$ $\Rightarrow x_{3} = \frac{16 \times 9}{48} = 3$ and $16 \times 9 = 36 \times y_{4}$ $\Rightarrow y_{4} = \frac{16 \times 9}{36} = 4$ $\Rightarrow y_{4} = 4$

3.0Key Concepts of Chapter 3 Proportional Reasoning-2 Exercise 3.3

Identifying whether two quantities are in inverse proportion using the given values.
Checking whether the product of corresponding values remains constant.
Understanding how two quantities change in opposite directions in inverse proportion.
Using the constant product to find missing values in an inverse proportion table.
Applying the constant product relationship to determine unknown values from given pairs of quantities.

4.0Benefits of NCERT Solutions Class 8 Maths Chapter 3 Exercise 3.3

Explains how to identify inverse proportion by checking the given pairs of values.
Shows how to verify inverse proportion by checking whether the product of corresponding values remains constant.
Helps understand how one quantity changes when the other increases or decreases in inverse proportion.
Provides step-by-step methods to find missing values in a table when two quantities are in inverse proportion.
Makes it easier to apply the constant product relationship while solving the questions.

NCERT Class 8 Maths Ch. 3 Proportional Reasoning - 2 Other Exercises:-

Exercise 3.1

Exercise 3.2

Exercise 3.3

Exercise 3.4

NCERT Solutions Class 8 Maths All Chapters:-

Chapter 1 : Fractions in Disguise

Chapter 2 : The Baudhayana - The Pythagoras Theorem

Chapter 3 : Proportional Reasoning - 2

Chapter 4 : Exploring Some Geometric Themes

Chapter 5 : Tales by Dots and Lines

Chapter 6 : Algebra Play

Chapter 7 : Area

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Proportional Reasoning-2 Exercise 3.3 Class 8 Maths - Chapter 3 NCERT Solutions

Detailed NCERT Class 8 Maths Chapter 3 Proportional Reasoning-2 Exercise 3.3 solutions are provided on this page to help students understand the questions and grasp the concepts more easily. The solutions are prepared by the ALLEN expert team in accordance with the currently updated syllabus.The exercise is mostly about inverse proportion as it is about comparing how two quantities change with each other. It deals with how to find the inverse proportion from given values, how to determine if the product of two quantities remains constant and how to find the missing values when quantities are in inverse proportion.

1.0Download Class 8 Maths Chapter 3 Ex 3.3 NCERT Solutions PDF

Download the NCERT Class 8 Maths Chapter 3 Exercise 3.3 detailed solutions PDF for free and refer to it anytime for revision and practice.

Chapter 3 : Proportional Reasoning - 2 Exercise 3.3

2.0Detailed NCERT Solutions on Proportional Reasoning-2 Exercise 3.3 Class 8 Maths (Ganita Prakash Term 2)

1. Which of these are inverse proportion? (i)

x	40	80	25	16
y	20	10	32	50

(ii)

x	40	80	25	16
y	20	10	12.5	8

(iii)

x	30	90	150	10
y	15	5	3	45

Sol. (i) $x_{1} = 40, x_{2} = 80, x_{3} = 25, x_{4} = 16$

$y_{1} = 20, y_{2} = 10, y_{3} = 32, y_{4} = 50 x_{1} y_{1} = 40 \times 20 = 800 x_{2} y_{2} = 80 \times 10 = 800 x_{3} y_{3} = 25 \times 32 = 800 x_{4} y_{4} = 16 \times 50 = 800$

So, $x_{1} y_{1} = x_{2} y_{2} = x_{3} y_{3} = x_{4} y_{4} = 800$ $∴ x$ and y are in inverse proportion. (ii) $x_{1} = 40, x_{2} = 80, x_{3} = 25, x_{4} = 16$

$y_{1} = 20, y_{2} = 10, y_{3} = 12.5, y_{4} = 8 x_{1} y_{1} = 40 \times 20 = 800 x_{2} y_{2} = 80 \times 10 = 800 x_{3} y_{3} = 25 \times 12.5 = 312.5 x_{4} y_{4} = 16 \times 8 = 128$

So, $x_{1} y_{1} = x_{2} y_{2} \neq = x_{3} y_{3} \neq = x_{4} y_{4}$ $∴ x$ and $y$ are not in inverse proportion. (iii) $x_{1} = 30, x_{2} = 90, x_{3} = 150, x_{4} = 10$

$y_{1} = 15, y_{2} = 5, y_{3} = 3, y_{4} = 45 x_{1} y_{1} = 30 \times 15 = 450 x_{2} y_{2} = 90 \times 5 = 450 x_{3} y_{3} = 150 \times 3 = 450 x_{4} y_{4} = 10 \times 45 = 450$

So, $x_{1} y_{1} = x_{2} y_{2} = x_{3} y_{3} = x_{4} y_{4} = 450$ $∴ x$ and $y$ are in inverse proportion.

2. Fill in the empty cells if x and y are in inverse proportion.

x	16	12		36
y	9		48

Sol.

x	16	12	$X_{3}$	36
y	9	$y_{2}$	48	$y_{4}$

$∵ x$ and y are in inverse proportion. $∴ 16 \times 9 = 12 \times y_{2}$ $\Rightarrow y_{2} = \frac{16 \times 9}{12} = 12$ $∴ 16 \times 9 = x 3 \times 48$ $\Rightarrow x_{3} = \frac{16 \times 9}{48} = 3$ and $16 \times 9 = 36 \times y_{4}$ $\Rightarrow y_{4} = \frac{16 \times 9}{36} = 4$ $\Rightarrow y_{4} = 4$

3.0Key Concepts of Chapter 3 Proportional Reasoning-2 Exercise 3.3

Identifying whether two quantities are in inverse proportion using the given values.
Checking whether the product of corresponding values remains constant.
Understanding how two quantities change in opposite directions in inverse proportion.
Using the constant product to find missing values in an inverse proportion table.
Applying the constant product relationship to determine unknown values from given pairs of quantities.

4.0Benefits of NCERT Solutions Class 8 Maths Chapter 3 Exercise 3.3

Explains how to identify inverse proportion by checking the given pairs of values.
Shows how to verify inverse proportion by checking whether the product of corresponding values remains constant.
Helps understand how one quantity changes when the other increases or decreases in inverse proportion.
Provides step-by-step methods to find missing values in a table when two quantities are in inverse proportion.
Makes it easier to apply the constant product relationship while solving the questions.

Frequently Asked Questions

What is covered in Class 8 Maths Chapter 3 Exercise 3.3?

How can you identify inverse proportion in Exercise 3.3?

How do you check whether the given values are in inverse proportion?

How are missing values found in Exercise 3.3?

What type of questions are included in Exercise 3.3?

How can ALLEN NCERT Solutions help with Exercise 3.3?

Join ALLEN!

Proportional Reasoning-2 Exercise 3.3 Class 8 Maths - Chapter 3 NCERT Solutions

1.0Download Class 8 Maths Chapter 3 Ex 3.3 NCERT Solutions PDF

2.0Detailed NCERT Solutions on Proportional Reasoning-2 Exercise 3.3 Class 8 Maths (Ganita Prakash Term 2)

3.0Key Concepts of Chapter 3 Proportional Reasoning-2 Exercise 3.3

4.0Benefits of NCERT Solutions Class 8 Maths Chapter 3 Exercise 3.3

Frequently Asked Questions

What is covered in Class 8 Maths Chapter 3 Exercise 3.3?

How can you identify inverse proportion in Exercise 3.3?

How do you check whether the given values are in inverse proportion?

How are missing values found in Exercise 3.3?

What type of questions are included in Exercise 3.3?

How can ALLEN NCERT Solutions help with Exercise 3.3?

Join ALLEN!

Proportional Reasoning-2 Exercise 3.3 Class 8 Maths - Chapter 3 NCERT Solutions

1.0Download Class 8 Maths Chapter 3 Ex 3.3 NCERT Solutions PDF

2.0Detailed NCERT Solutions on Proportional Reasoning-2 Exercise 3.3 Class 8 Maths (Ganita Prakash Term 2)

3.0Key Concepts of Chapter 3 Proportional Reasoning-2 Exercise 3.3

4.0Benefits of NCERT Solutions Class 8 Maths Chapter 3 Exercise 3.3