Class 6 Maths NCERT Exemplar Solutions Chapter 7 Algebra
Free PDF download of NCERT Exemplar for Class 6 Maths Chapter 7 Algebra solved by expert Maths teachers on Vedantu.com as per NCERT (CBSE) Book guidelines. Chapter 7 Algebra exercise questions with solutions to help you to revise the complete syllabus and score more marks in your examinations.
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Access NCERT Exemplar Solutions for Class 6 Mathematics Chapter 7 - Algebra
In examples 1 to 3, write the correct answer from the given four options:
Example 1:
(A)
(B)
(C)
(D)
Ans: (b)
Example 2:
(A)
(B)
(C)
(D)
Ans: (c).
Example 3: Which of the following is an equation?
(A)
(B)
(C)
(D)
Ans: (b)
Example 4: Fill in the blanks to make it a true statement:
Ans:
Example 5: State true or false:
Ans: False
Give an expression for each of the examples 6 to 8:
Example 6:
Ans: If the number is
If
Example 7: Megha’s age (in years) is
Ans: If the daughter’s age is
And
Hence, the age of Megha (in years)
Example 8: Anagha, Sushant and Faizal are climbing the steps to a hilltop. Anagha is at the step p. Sushant is
Ans: If Anagha is at step
So, he is at the step
Also, Faizal is
total number of steps to the hill top is
Therefore, the total number of steps =
In examples 9 and 10, change the statements, converting expressions
into statements in ordinary language.
Example 9: Cost of a pencil is Rs
Ans: Cost of a pen is
Example 10: Manisha is
Ans: Manisha’s uncle is five times Manisha's age. Her aunt is
In questions 1 to 23, out of the four given options, only one is correct. Write the correct answer.
1.If each match box contains
(A)
(B)
(C)
(D)
Ans: (B)
Given, number of matchsticks in a box are
Then, for n box
2. Amulya is
(A)
(B)
(C)
(D)
Ans: (C)
Given, that the present age of Amulya is
Then,
3. Which of the following represents
(A)
(B)
(C)
(D)
Ans: (A)
As
4. Which of the following is an equation?
(A)
(B)
(C)
(D)
Ans: (C)
As we know, expression with variable, constant and equal sign is a form of simple equation.
5. If
(A)
(B)
(C)
(D)
Ans: (B)
Given, that
Putting the value of
then
6. If the perimeter of a regular hexagon is
(A)
(B)
(C)
(D)
Ans: (B)
Perimeter of a hexagon is given by
Then,
7. Which of the following equations has
(A)
(B)
(C)
(D)
Ans: (B)
Hence, the solution of the given equation
8. For any two integers
(A)
(B)
(C)
(D)
Ans: (A)
9. Which of the following equations does not have a solution in integers?
(A)
(B)
(C)
(D)
Ans: (C)
Which is not an integer.
10. In algebra,
(A) 35
(B) 53
(C) 15
(D) 8
Ans: (C)
Because,
11. In algebra, letters may stand for
(A) Known quantities
(B) unknown quantities
(C) Fixed numbers
(D) none of these
Ans: (B)
In algebra, letters may stand for unknown quantities which we call variable.
12. “Variable” means that it
(A) Can take different values
(B) Has a fixed value
(C) Can take only 2 values
(D) Can take only three values
Ans: (A)
“Variable” means that it has unknown values and can take different values.
13.
(A)
(B)
(C)
(D)
Ans: (C)
14. Savitri has a sum of Rs
(A)
(B)
(C)
(D)
Ans: (A)
Given, Total amount spent by Savitri
If total amount Savitri has
Therefore, Left amount
15. The perimeter of the triangle shown in Fig. 7.1 is

(A) 2x + y
(B) x + 2y
(C) x + y
(D) 2x – y
Ans: (A)
Addition of all Sides is called the perimeter of a given figure.
Perimeter of triangle
16. The area of a square having each side x is
(A) x × x
(B) 4x
(C) x + x
(D) 4 + x
Ans: (A)
Given, side of a square
We know, area of square
17. The expression obtained when x is multiplied by 2 and then subtracted from 3 is
(A) 2x – 3
(B) 2x + 3
(C) 3 – 2x
(D) 3x – 2
Ans: (C)
When
And subtracted from
18.
(A) 6
(B) 8
(C) 3
(D) 2
Ans: (A)
19. x – 4 = – 2 has a solution
(A) 6
(B) 2
(C) – 6
(D) – 2
Ans: (B)
As
20.
(A) Numerical equation
(B) algebraic expression
(C) Equation with a variable
(D) false statement
Ans: (A)
It denotes a numerical equation.
21. Kanta has p pencils in her box. She puts more pencils in the box. The total numbers of pencils with her are
(A) p + q
(B) pq
(C) p – q
(D)
Ans: (A)
Kanta has
Hence, total pencils
22. The equation 4x = 16 is satisfied by the following value of x
(A) 4
(B) 2
(C) 12
(D) –12
Ans: (A)
Solving:
23. I think of a number and on adding 13 to it, I get 27. The equation for this is
(A) x – 27 = 13
(B) x – 13 = 27
(C) x + 27 = 13
(D) x + 13 = 27
Ans: (D)
If the number is
Then according to the question:
In question 24 to 40 fill in the blanks to make the statements true:
24. The distance (in km) travelled in
Ans:
We know, Distance = speed
25. P kg of potatoes is bought for Rs 70. Cost of 1kg of potatoes (in Rs) is __________.
Ans:
Given,
Cost of
26. An auto rickshaw charges Rs 10 for the first kilometer then Rs 8 for each such subsequent kilometer. The total charge (in Rs) for d kilometers is __________.
Ans:
Charges for first kilometer
Charges for subsequent kilometers
Charge for
27. If
Ans:
Solving the given equation:
28. The solution of the equation
Ans:
On solving the given equation:
29. „X exceeds y by 7‟ can be expressed as __________.
Ans:
If
30. „8 more than three times the number x‟ can be written as __________.
Ans:
31. Number of pencils bought for Rs x at the rate of Rs 2 per pencil is __________.
Ans:
Given: Rate of each pencil
number of pencils bought for
32. The number of days in w weeks is __________.
Ans:
Number of days in a week
Number of days in
33. Annual salary at r rupees per month along with a festival bonus of Rs 2000 is __________.
Ans:
Salary per month
We know,
Therefore, annual salary
Annual salary in addition to festival bonus
34. The two digit number whose ten’s digit is “t‟ and unit’s digit is “u‟ is __________.
Ans:
If two-digit number which have ‟ten’s digit “t‟ and unit’s digit “u‟ is
35. The variable used in the equation
Ans:
Variable used in the equation
36. x meters = __________ centimeters.
Ans:
As we know that,
Therefore,
37. P liters = __________ milliliters.
Ans:
As we know that,
Therefore,
38. R rupees = __________ paisa.
Ans:
As we know that,
Therefore,
39. If the present age of Ramandeep is n years, then her age after 7 years will be __________.
Ans:
Given that:
Present age of Ramandeep
Ramandeep age after
40. If I spend f rupees from 100 rupees, the money left with me is __________ rupees.
Ans:
Total amount
Spent amount
So, If f rupees spent from 100 rupees, the money left
In question 41 to 45, state whether the statements are true or false.
41. 0 is a solution of the equation
Ans: False
42. The equations
Ans: True
As on multiplying
43. If m is a whole number, then 2m denotes a multiple of 2.
Ans: True
44. The additive inverse of an integer
Ans: False
Additive inverse of
45. If x is a negative integer, – x is a positive integer.
Ans: True
The Addition of a negative integer is always a positive integer.
46.
Ans: False
Because, a simple equation is formed with variable, constant and equal sign and in this equation equality is absent.
47. In an equation, the LHS is equal to the RHS.
Ans: True
48. In the equation
Ans: False
Variable is
49.
Ans: True
If
Putting the value of
Hence, verified.
50. The distance between New Delhi and Bhopal is not a variable.
Ans: True
Because it’s a defined distance between two cities.
51. t minutes are equal to 60t seconds.
Ans: True
As,
52.
Ans: False
Putting the value of
53. ‘One third of a number added to itself gives 8’, can be expressed as
Ans: False
If the number is
One third of a number is
And if it is added to itself then
54. The difference between the ages of two sisters Leela and Yamini is a variable.
Ans: False
No, it is a number.
55. The number of lines that can be drawn through a point is a variable
Ans: False
A line is the distance between two points which is not variable.
In questions 56 to 74, choose a letter x, y, z, p etc...., wherever necessary, for the unknown (variable) and write the corresponding expressions:
56. One more than twice the number.
Ans:
Let, the number be
and twice of the number is
According to the question,
57.
Ans:
If the present temperature is
58. The successor of an integer.
Ans: We know that the successor of an integer is an integer.
if the integer is
59. The perimeter of an equilateral triangle, if the side of the triangle is m.
Ans: The perimeter of an equilateral triangle
And given side
Therefore, perimeter of an equilateral triangle
60. Area of the rectangle with length k units and breadth n units.
Ans: Given: length
Breadth
Area of rectangle
Therefore,
61. Omar helps his mother 1 hour more than his sister does.
Ans: If Omar`s sister helps for
Then,
Omar helps his mother
62. Two consecutive odd integers.
Ans:
63. Two consecutive even integers.
Ans: If,
64. Multiple of 5.
Ans: If,
Then as a multiple of
65. The denominator of a fraction is 1 more than its numerator.
Ans: If numerator of a fraction is
Then denominator will be
So, the fraction is
66. The height of Mount Everest is 20 times the height of the Empire State building.
Ans: If the height of the Empire =
Then,
Height of the Mount Everest will be =
67. If a note book costs Rs p and a pencil costs Rs 3, then the total cost (in Rs) of two note books and one pencil.
Ans: Given: a note book costs
And a pencil costs
Then,
Cost of two pencils
Now, total cost
68. z is multiplied by –3 and the result is subtracted from 13.
Ans: As per question,
69. p is divided by 11 and the result is added to 10.
Ans: As per question:
70. x times of 3 is added to the smallest natural number.
Ans: As we know, smallest natural number is
Therefore, according to question:
Now,
71. 6 times q is subtracted from the smallest two-digit number.
Ans: As asked in question:
subtracted from the smallest two-digit number
72. Write two equations for which 2 is the solution.
Ans: Required equations for which
73. Write an equation for which 0 is a solution.
Ans: Required equations for which
74. Write an equation whose solution is not a whole number.
Ans: For equation
In questions 75 to 84, change the statements, converting expressions into statements in ordinary language:
75. A pencil costs Rs p and a pen costs Rs 5p.
Ans: Given: a pencil costs =
And a pen costs
Therefore, we can say, the cost of one pen is
76. Leela contributed Rs y towards the Prime Minister‟s Relief Fund. Leela is now left with Rs
Ans:
According to the given condition it can be said that the amount left with Leela is Rs. 10,000 more than the amount she contributed towards the Prime Minister‟s Relief Fund.
77. Kartik is n years old. His father is 7 years old.
Ans: According to the given condition it can be said that Kartik’s father is 7 times the age of kartik.
78. The maximum temperature on a day in Delhi was
Ans: According to the given condition it can be said that the minimum temperature on a day in Delhi was
79. John planted t plants last year. His friend Jay planted
Ans: According to the given condition it can be said that John`s friend Jay planted
80. Sharad used to take
Ans: According to the given condition it can be said that due to the health issue Sharad reduces the
81. The number of students dropping out of school last year was m. Number of students dropping out of school this year is
Ans: According to the given condition it can be said that the number of students dropping out this year is
82. Price of petrol was Rs p per liter last month. Price of petrol now is Rs
Ans: According to the given condition it can be said that the price of petrol decreases by
83. Khader’s monthly salary was Rs
Ans: According to the given condition it can be said that in 2006 Khader`s monthly salary is 1000 more than the last year's monthly salary.
84. The number of girls enrolled in a school last year was g. The number of girls enrolled this year in the school is
Ans: According to the given condition it can be said that the number of girls enrolled this year is
85. Translate each of the following statements into an equation, using
(a) 13 subtracted from twice a number gives 3.
(b) One fifth of a number is 5 less than that number.
(c) Two-third of the number is 12.
(d) 9 added to twice a number gives 13.
(e) 1 subtracted from one-third of a number gives 1.
Ans:
(a) Let, the number be
Now,
(b) Let, the number be
Now, one fifth of a number is
(c) Let, the number be
Now, Two-third of number is
(d) If the number is
Now, according to question:
(e) If the number is
Now, according to question:
86. Translate each of the following statements into an equation:
(a) The perimeter (p) of an equilateral triangle is three times of its side (a).
(b) The diameter (d) of a circle is twice its radius (r).
(c) The selling price (s) of an item is equal to the sum of the cost price (c) of an item and the profit (p) earned.
(d) Amount (a) is equal to the sum of principal (p) and interest (i).
Ans:
(a) Let the side be
Then perimeter of an equilateral triangle is
(b) Given: diameter
(c) Given that the selling price (s) of an item is equal to the sum of the cost price (c) of an item and the profit (p) earned then,
Selling price = cost price + profit
(d) Given that amount (a) is equal to the sum of principal (p) and interest (i)
Amount = principal + interest
87. Let Kanika’s present age be x years. Complete the following table, showing ages of her relatives:
Situation (described in ordinary language) | Expressions |
(i) Her brother is 2 years younger. | |
(ii) Her father’s age exceeds her age by 35 years. | |
(iii) Mother’s age is 3 years less than that of her father. | |
(iv) Her grandmother’s age is 8 times her age. |
Ans: If the age of Kanika is
Situation (described in ordinary language) | Expressions |
(i) Her brother is 2 years younger. | |
(ii) Her father’s age exceeds her age by 35 years. | |
(iii) Mother’s age is 3 years less than that of her father. | Age of her mother is |
(iv) Her grandmother’s age is 8 times her age. | Age of her grandmother is |
88. If m is a whole number less than 5, complete the table and by inspection of the table, find the solution of the equation
m | |||||
2m-5 |
Ans:
m | 0 | 1 | 2 | 3 | 4 |
2m-5 | -5 | -3 | -1 | 1 | 3 |
If
At
At
At
At
At
Therefore, the solution of
89. A class with p students has planned a picnic. Rs 50 per student is collected, out of which Rs 1800 is paid in advance for transport. How much money is left with them to spend on other items?
Ans: Given:
Number of students in class
Collected amount from p students
Paid in advance for transport
Now, Left amount to spend on other items
90. In a village, there are 8 water tanks to collect rain water. On a particular day, x litres of rain water is collected per tank. If 100 litres of water was already there in one of the tanks, what is the total amount of water in the tanks on that day?
Ans: Given: Rain water collected by each tank of water
Number of water tank in a village
Rain water collected by
But if
91. What is the area of a square whose side is m cm?
Ans: We know, area of square
Given side
Area of square is:
92. Perimeter of a triangle is found by using the formula
Ans: Perimeter of a triangle is the addition of all sides.
93. Perimeter of a rectangle is found by using the formula
Ans: Two times the sum of its length and breadth is called the perimeter of a rectangle.
94. On my last birthday, I weighed 40kg. If I put on m kg of weight after a year, what is my present weight?
Ans: Given that,
Present weight = Last year weight + weight put on after a year
Last year weight
Put on weight is
95. Length and breadth of a bulletin board are r cm and t cm, respectively.
(i) What will be the length (in cm) of the aluminum strip required to frame the board, if 10cm extra strip is required to fix it properly.
(ii) If x nails are used to repair one board, how many nails will be required to repair 15
such boards?
(iii) If 500sqcm extra cloth per board is required to cover the edges, what will be the total area of the cloth required to cover 8 such boards?
(iv) What will be the expenditure for making 23 boards, if the carpenter charges Rs x per board.
Ans: Given: length of a board
(i) Strip required to frame the board = perimeter of the board
But
Total length of aluminum strip
(ii) Nails required to repair 1 board
Then number of nails required to repair
(iii) Cloth required to cover the edges of one board
Area of the cloth required of one board = Area of the board = length x breadth
Area of the cloth required of
Therefore, total area of the cloth required of
(iv) Charges per board
Then, the charges for 23 boards
96. Sunita is half the age of her mother Geeta. Find their ages
(i) After 4 years?
(ii) 3 years?
Ans:
Let, the present age of Geeta
Then the age of Sunita
(i) After
Sunita’s age
(ii) Before 3 years
Geeta’s age
Sunita’s age
97. Match the items of Column I with that of Column II:
Column I | ColumnII |
(i) The number of corners of a quadrilateral | (A)= |
(ii) The variable in the equation | (B) constant |
(iii) The solution of the equation | (C) +1 |
(iv) solution of the equation | (D) -1 |
(v) A sign used in an equation | (E) p (F) x |
Ans:
(i) Corners of a quadrilateral is
(ii) The variable in the equation
(iii) The solution of the equation
(iv) Solution of the equation
(v) A sign used in an equation is “=” hence, A
Column I | Column II |
(i) The number of corners of a quadrilateral | Constant |
(ii) The variable in the equation | |
(iii) The solution of the equation | |
(iv) solution of the equation |
|
(v) A sign used in an equation |
“=” |
NCERT Exemplar Class 6 Maths Algebra
NCERT exemplar consists of questions different from the textbook to give students more sums for practice. It helps you to test your learning and prepare well for the exams. Class 6 Algebra is an important topic considering from an exam point of view, and exemplar problems benefit you to secure a good rank.
Algebra Chapter 7 Class 6 NCERT
Algebra uses letters and other general symbols to represent formulas or any quantities. It has variables, operators, and constants. Letters represent variables, symbols represent operators, and the remaining constants are numbers. Letters stand for numbers, and operation performs on numbers, e.g. addition, subtraction, multiplication and division.
E.g. 2x+3=7
In the above example, ‘X’ is variable, and numbers are constants. An arithmetic operation of addition is performed. Consider algebra as a helper to show problems in the mathematical expression.
How To Download Class 6 Chapter 7 Algebra Exemplar Solutions
Download the solution of problems from NCERT Exemplar from the link. All you need to do is sign in. NCERT doesn’t provide answers to the exemplar sums students need to solve them under the guidance of their teachers to get an in-depth understanding of the concepts. You can find other helpful resources like textbook solutions on our website and Vedantu mobile app. Experts crafted the answer in a detailed fashion to explain all questions and the topic related to them.
FAQs on NCERT Exemplar for Class 6 Maths Solutions Chapter 7 Algebra
1. Is it essential to learn Algebra from NCERT Class 6 textbook?
Yes, it is essential to learn Algebra from the NCERT textbook. Class 6 textbook covers the updated CBSE syllabus. Moreover, it helps you build your foundation for higher Classes. Algebra performs a crucial role in solving and forming equations. Studying from the NCERT makes it easy to understand complex topics. Teachers available on Vedantu teaches you from this textbook and supports you in solving problems. After understanding the variables and numbers, it becomes easy to do a variety of algebraic maths.
2. Can students complete Class 6 Chapter Algebra in a few days?
Yes, students can finish it in seven to eight days if they give 1-2 hours of each day to it. But every student is unique. It depends only on their ability to consume content. Algebra is a compelling Chapter, and it makes maths look easy for those who are very skilled at calculations. To complete it in a week, students need to follow a routine. They need to solve textbook sums and NCERT examples to collect learned topics. Vedantu provides free solutions to exemplar sums.
3. What are the topics students learned in the Algebra Chapter of Class 6?
Students learn eleven topics in total from the Algebra Chapter. In the beginning, it is about matchstick patterns topics that help students to learn about variables. Later, they read the rules of geometry and arithmetic. In the end, students face the expression with variables and some solved examples provided in the Chapter. All these topics make you understand how to form equations using algebra. You cannot miss this Chapter as it completes the mathematics journey.
4. Where can I get solutions for other Chapters of Class 6 NCERT maths exemplar?
Vedantu provides NCERT exemplar solutions for free all you need to do is sign in from your device. These solutions help you correct your mistakes and reorganise your mistakes. The NCERT example comes without answers, and students need to solve it in Class and at home after finishing a Chapter. Subject Matter Experts of maths guides you thoroughly to get answers to all these questions. Join online maths Classes and learn from the best maths teachers.
5. What is the best way to learn Algebra?
The best way to learn algebra is by working hard. You need to win over your fear of numbers and focus on your goal. Vedantu gives you a platform to learn from the best faculties of India. They explain things with animated images which students feel easy to grasp. You can join online tuition from anywhere and clear your doubts from the teachers on one-on-one interaction. What makes algebra interesting is it opens a new window of maths, and learning it on a platform like Vedantu is fun.











