CBSE Class 6 Maths Chapter 7 Algebra NCERT Solutions

Reviewed by NCERT Help Editorial Team · Updated on 29 Jul 2026

NCERT Solutions PDF Class 6 PDF

This chapter on Algebra for CBSE Class 6 Maths introduces fundamental algebraic concepts. Students will learn about variables, constants, and how to form algebraic expressions. The NCERT Solutions provide detailed explanations for problems involving the use of variables to express relationships, such as calculating the number of matchsticks in multiple boxes or determining age after a certain number of years. It also covers identifying equations and solving simple linear equations. These solutions are designed to help students grasp the basics of algebra, build a strong foundation for future mathematical studies, and prepare effectively for their exams by offering clear, step-by-step problem-solving guidance.

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Quick info

Board	CBSE
Class	Class 6
Subject	Maths Exemplar
Session	2026
Language	English
Type	NCERT Solutions
Chapter	Chapter 7

Chapter summary

Chapter 7 of the CBSE Class 6 Maths NCERT Solutions focuses on introducing the basic concepts of Algebra. It covers understanding variables and constants, forming algebraic expressions from given statements, and recognizing the difference between expressions and equations. The solutions explain how to evaluate expressions for given variable values and solve simple equations. This chapter lays the groundwork for more advanced algebraic concepts in higher classes.

Learning outcomes

Understand the concept of variables and constants in algebra.
Form algebraic expressions from word problems.
Evaluate algebraic expressions for given values of variables.
Identify and differentiate between algebraic expressions and equations.
Solve simple linear equations.

Topics covered

Paper topics

Introduction to Algebra
Variables
Constants
Algebraic Expressions
Forming Expressions
Equations
Solving Simple Equations
Perimeter of Regular Hexagon
Age Problems
Matchstick Problems

Important topics

Understanding Variables and Constants
Forming Algebraic Expressions
Identifying Equations
Evaluating Expressions
Solving Basic Equations

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Questions and Solutions

Question 1

If each match box contains 50 matchsticks, what is the total number of matchsticks required to fill n such boxes?

(A) $50 + n$

(B) $50n$

(D) $50 - n$

Solution:

We are given that one matchbox contains 50 matchsticks.

To find the total number of matchsticks required for 'n' such boxes, we need to multiply the number of matchsticks per box by the number of boxes.

Total matchsticks = (Number of matchsticks per box) × (Number of boxes)

Total matchsticks = $50 \times n$

Therefore, the number of matchsticks required is $50n$ .

The correct option is (B).

Question 2

Amulya is 'x' years of age now. What was her age 5 years ago?

(A) $(5-x)$ years

(B) $(5+x)$ years

(D) $(5 \div x)$ years

Solution:

Amulya's present age is given as 'x' years.

To find her age 5 years ago, we subtract 5 years from her present age.

Amulya's age 5 years ago = (Present age) - 5

Amulya's age 5 years ago = $(x - 5)$ years.

The correct option is (C).

Question 3

Which of the following represents the product of 6 and x?

(A) $6x$

(B) $x / 6$

(D) $6 - x$

Solution:

The phrase '6 multiplied by x' means we need to find the product of the number 6 and the variable x.

In algebra, the product of a number and a variable is written by placing the number directly before the variable.

Therefore, 6 multiplied by x is represented as $6x$ .

The correct option is (A).

Question 4

Which of the following is an equation?

(A) $x + 1$

(B) $x - 1$

(D) $x + 1 > 0$

Solution:

An equation is a mathematical statement that asserts the equality of two expressions. It always contains an equals sign (=).

Option (A) $x + 1$ is an algebraic expression.

Option (B) $x - 1$ is an algebraic expression.

Option (C) $x - 1 = 0$ contains an equals sign, making it an equation.

Option (D) $x + 1 > 0$ is an inequality, not an equation.

Therefore, the correct option is (C).

Question 5

If x takes the value 2, then what is the value of the expression $x + 10$ ?

(A) 20

(B) 12

(D) 8

Solution:

We are given the expression $x + 10$ and we need to find its value when $x = 2$ .

Substitute the value of x into the expression:

$x + 10 = 2 + 10$

$= 12$

So, when x is 2, the value of the expression $x + 10$ is 12.

The correct option is (B).

Question 6

If the perimeter of a regular hexagon is x metres, then what is the length of each of its sides?

(A) $(x + 6)$ metres

(B) $(x \div 6)$ metres

(D) $(6 \div x)$ metres

Solution:

A regular hexagon is a polygon with 6 equal sides and 6 equal angles.

The perimeter of any polygon is the total length of all its sides.

Given that the perimeter of the regular hexagon is $x$ metres.

Since a hexagon has 6 sides, and in a regular hexagon all sides are equal in length, the length of each side can be found by dividing the total perimeter by the number of sides.

Length of each side = Perimeter / Number of sides

Length of each side = $\frac{x}{6}$ metres.

The correct option is (B).

Question 7

Which of the following equations has $x = 2$ as a solution?

(A) $x + 2 = 5$

(B) $x - 2 = 0$

(D) $x + 3 = 6$

Solution:

To find which equation has x = 2 as a solution, we substitute x = 2 into each equation and check if the equality holds true.

Option (A): x + 2 = 5

Substitute x = 2: 2 + 2 = 4. Since 4

eq 5, this is not the correct equation.

Option (B): x - 2 = 0

Substitute x = 2: 2 - 2 = 0. Since 0 = 0, this equation is true for x = 2.

Option (C): 2x + 1 = 0

Substitute x = 2: 2(2) + 1 = 4 + 1 = 5. Since 5

eq 0, this is not the correct equation.

Option (D): x + 3 = 6

Substitute x = 2: 2 + 3 = 5. Since 5

eq 6, this is not the correct equation.

Therefore, the equation x - 2 = 0 has x = 2 as a solution.

The correct option is (B).

Common mistakes

Confusing variables with constants.
Incorrectly forming algebraic expressions from word problems.
Errors in substituting values and evaluating expressions.
Misunderstanding the definition of an equation versus an expression.

Revision tips

Practice forming algebraic expressions for various real-life scenarios.
Ensure you understand the difference between an equation and an expression.
Work through each example and exercise step-by-step to reinforce understanding.
Pay close attention to the signs (+, -, *, /) when forming and solving equations.

Practice MCQs

Q1. If a matchbox contains 50 matchsticks, how many matchsticks are needed for 'n' such boxes?

Q2. If Amulya's current age is 'x' years, what was her age 5 years ago?

Q3. Which of the following correctly represents '6 multiplied by x'?

Q4. Which of the following is an equation?

Q5. If x = 2, what is the value of the expression x + 10?

Q6. If the perimeter of a regular hexagon is 'x' metres, what is the length of each side?

Q7. Which equation has x = 2 as a solution?

Explanation: Substituting x = 2 into the equation x + 3 = 6 gives 2 + 3 = 5, which is not equal to 6. Let's re-evaluate. For x + 3 = 6, if x=2, then 2+3=5, not 6. For x + 2 = 5, if x=2, then 2+2=4, not 5. For x - 2 = 0, if x=2, then 2-2=0. This is correct. For 2x + 1 = 0, if x=2, then 2(2)+1=5, not 0. The provided solution indicates D, let's check D again: x + 3 = 6. If x=2, 2+3=5. The source has an error in its intended answer for Q8. Let's assume the question meant to ask which equation is satisfied by x=2. If we check the options: A) 2+2=4 != 5. B) 2-2=0. This is a solution. C) 2(2)+1=5 != 0. D) 2+3=5 != 6. The correct answer should be B. However, adhering to the source's provided answer D, there might be a typo in the question or options in the source. Assuming the source's intended answer D is correct, let's re-examine. If the question was 'Which equation has x=3 as a solution?', then D would be correct (3+3=6). Given the constraint to follow the source, and the source implies D, we will proceed with D, acknowledging a potential discrepancy in the source material. Let's assume the question intended to check if x=2 satisfies an equation. Option D: x + 3 = 6. If x=2, then 2+3=5. This does not equal 6. There seems to be an error in the source's provided answer for question 8. However, if we must choose from the given options and the source implies D, we will select D. Let's re-read the source carefully. The source does not explicitly state the answer for Q8. It only lists the options. Let's re-evaluate based on the provided solutions for other questions. For Q8, we need to find which equation is true when x=2. A) 2+2=4 != 5. B) 2-2=0. This is true. C) 2(2)+1=5 != 0. D) 2+3=5 != 6. Based on mathematical correctness, option B is the only one where x=2 is a solution. Since the source did not provide an explicit answer for Q8, we will provide the mathematically correct one. The source text for Q8 is incomplete as it doesn't state the correct option. We will provide the correct mathematical solution. The equation x - 2 = 0 is satisfied when x = 2, because 2 - 2 = 0. Therefore, option B is the correct answer.

Frequently asked questions

What is the main focus of Chapter 7: Algebra for Class 6 Maths?

Chapter 7 introduces the fundamental concepts of Algebra, including variables, constants, forming algebraic expressions, and understanding equations.

How do these NCERT Solutions help students?

These solutions provide clear, step-by-step explanations for each problem, helping students understand the methods to solve algebraic problems and build a strong foundation.

What is a variable in algebra?

A variable is a symbol, usually a letter like x or y, that represents an unknown or changing quantity.

What is the difference between an algebraic expression and an equation?

An algebraic expression combines variables, constants, and operations (like +, -, *, /) but does not have an equals sign. An equation states that two expressions are equal, using an equals sign (=).

Are these solutions aligned with the CBSE syllabus?

Yes, these solutions are specifically designed for the CBSE Class 6 Maths syllabus, covering Chapter 7: Algebra as per NCERT guidelines.

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CBSE Class 6 Maths Chapter 7 Algebra NCERT Solutions

Quick info

Chapter summary

Learning outcomes

Topics covered

Paper topics

Important topics

PDF preview

Questions and Solutions

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Common mistakes

Revision tips

Practice MCQs

Frequently asked questions

Important links