# NCERT solutions for Mathematics Exemplar Class 6 chapter 7 - Algebra [Latest edition]

## Chapter 7: Algebra

Exercise
Exercise [Pages 107 - 115]

### NCERT solutions for Mathematics Exemplar Class 6 Chapter 7 Algebra Exercise [Pages 107 - 115]

#### Choose the correct alternative:

Exercise | Q 1 | Page 107

If each match box contains 50 matchsticks, the number of matchsticks required to fill n such boxes is ______.

• 50 + n

• 50 n

• 50 ÷ n

• 50 – n

Exercise | Q 2 | Page 107

Amulya is x years of age now. 5 years ago her age was ______.

• (5 – x) years

• (5 + x) years

• (x – 5) years

• (5 ÷ x) years

Exercise | Q 3 | Page 107

Which of the following represent 6 × x?

• 6x

• x/6

• 6 + x

• 6 - x

Exercise | Q 4 | Page 107

Which of the following is an equation?

• x + 1

• x – 1

• x – 1 = 0

• x + 1 > 0

Exercise | Q 5 | Page 107

If x takes the value 2, then the value of x + 10 is ______.

• 20

• 12

• 5

• 8

Exercise | Q 6 | Page 108

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

• (x + 6) metres

• (x ÷ 6) metres

• (x – 6) metres

• (6 ÷ x) metres

Exercise | Q 7 | Page 108

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

• x + 2 = 5

• x – 2 = 0

• 2x + 1 = 0

• x + 3 = 6

Exercise | Q 8 | Page 108

For any two integers x and y, which of the following suggests that operation of addition is commutative ?

• x + y = y + x

• x + y > x

• x – y = y – x

• x × y = y × x

Exercise | Q 9 | Page 108

Which of the following equations does not have a solution in integers?

• x + 1 = 1

• x – 1 = 3

• 2x + 1 = 6

• 1 – x = 5

Exercise | Q 10 | Page 108

In algebra, a × b means ab, but in arithmetic 3 × 5 is ______.

• 35

• 53

• 15

• 8

Exercise | Q 11 | Page 108

In algebra, letters may stand for ______.

• Known quantities

• Unknown quantities

• Fixed numbers

• None of these

Exercise | Q 12 | Page 108

Variable means that it ______.

• Can take only a few values

• Has a fixed value

• Can take different values

• Can take only 2 values

Exercise | Q 13 | Page 108

10 – x means ______.

• 10 is subtracted x times

• x is subtracted 10 times

• x is subtracted from 10

• 10 is subtracted from x

Exercise | Q 14 | Page 108

Savitri has a sum of Rs x. She spent Rs 1000 on grocery, Rs 500 on clothes and Rs 400 on education, and received Rs 200 as a gift. How much money (in Rs) is left with her?

• x – 1700

• x – 1900

• x + 200

• x – 2100

Exercise | Q 15 | Page 109

The perimeter of the triangle shown in the figure is ______.

• 2x + y

• x + 2y

• x + y

• 2x – y

Exercise | Q 16 | Page 109

The area of a square having each side x is ______.

• x × x

• 4x

• x + x

• 4 + x

Exercise | Q 17 | Page 109

The expression obtained when x is multipled by 2 and then subtracted from 3 is ______.

• 2x – 3

• 2x + 3

• 3 – 2x

• 3x – 2

Exercise | Q 18 | Page 109

q/2 = 3 has a solution ______.

• 6

• 8

• 3

• 2

Exercise | Q 19 | Page 109

x – 4 = – 2 has a solution ______.

• 6

• 2

• – 6

• – 2

Exercise | Q 20 | Page 109

4/2 = 2 denotes a ______.

• Numerical equation

• Algebraic expression

• Equation with a variable

• False statement

Exercise | Q 21 | Page 109

Kanta has p pencils in her box. She puts q more pencils in the box. The total number of pencils with her are ______.

• p + q

• pq

• p – q

• p/q

Exercise | Q 22 | Page 109

The equation 4x = 16 is satisfied by the following value of x ______.

• 4

• 2

• 12

• –12

Exercise | Q 23 | Page 109

I think of a number and on adding 13 to it, I get 27. The equation for this is ______.

• x – 27 = 13

• x – 13 = 2

• x + 27 = 13

• x + 13 = 27

#### Fill in the blank:

Exercise | Q 24 | Page 110

The distance (in km) travelled in h hours at a constant speed of 40 km per hour is ______.

Exercise | Q 25 | Page 110

p kg of potatoes are bought for Rs 70. Cost of 1 kg of potatoes (in Rs) is ______.

Exercise | Q 26 | Page 110

An auto rickshaw charges Rs 10 for the first kilometre then Rs 8 for each such subsequent kilometre. The total charge (in Rs) for d kilometres is ______.

Exercise | Q 27 | Page 110

If 7x + 4 = 25, then the value of x is ______.

Exercise | Q 28 | Page 110

The solution of the equation 3x + 7 = –20 is ______.

Exercise | Q 29 | Page 110

‘x exceeds y by 7’ can be expressed as ______.

Exercise | Q 30 | Page 110

‘8 more than three times the number x’ can be written as ______.

Exercise | Q 31 | Page 110

Number of pencils bought for Rs x at the rate of Rs 2 per pencil is ______.

Exercise | Q 32 | Page 110

The number of days in w weeks is ______.

Exercise | Q 33 | Page 110

Annual salary at r rupees per month alongwith a festival bonus of Rs 2000 is ______.

Exercise | Q 34 | Page 110

The two digit number whose ten’s digit is ‘t’ and units’s digit is ‘u’ is ______.

Exercise | Q 35 | Page 110

The variable used in the equation 2p + 8 = 18 is ______.

Exercise | Q 36 | Page 110

x metres = ______ centimetres.

Exercise | Q 37 | Page 110

p litres = ______ millilitres.

Exercise | Q 38 | Page 110

r rupees = ______ paise.

Exercise | Q 39 | Page 110

If the present age of Ramandeep is n years, then her age after 7 years will be ______.

Exercise | Q 40 | Page 110

If I spend f rupees from 100 rupees, the money left with me is ______ rupees.

#### State whether the following statement is True or False:

Exercise | Q 41 | Page 111

0 is a solution of the equation x + 1 = 0.

• True

• False

Exercise | Q 42 | Page 111

The equations x + 1 = 0 and 2x + 2 = 0 have the same solution.

• True

• False

Exercise | Q 43 | Page 111

If m is a whole number, then 2 m denotes a multiple of 2.

• True

• False

Exercise | Q 44 | Page 111

The additive inverse of an integer x is 2x.

• True

• False

Exercise | Q 45 | Page 111

If x is a negative integer, – x is a positive integer.

• True

• False

Exercise | Q 46 | Page 111

2x – 5 > 11 is an equation.

• True

• False

Exercise | Q 47 | Page 111

In an equation, the LHS is equal to the RHS.

• True

• False

Exercise | Q 48 | Page 111

In the equation 7k – 7 = 7, the variable is 7.

• True

• False

Exercise | Q 49 | Page 111

a = 3 is a solution of the equation 2a – 1 = 5.

• True

• False

Exercise | Q 50 | Page 111

The distance between New Delhi and Bhopal is not a variable.

• True

• False

Exercise | Q 51 | Page 111

t minutes are equal to 60t seconds.

• True

• False

Exercise | Q 52 | Page 111

x = 5 is the solution of the equation 3x + 2 = 20.

• True

• False

Exercise | Q 53 | Page 111

‘One third of a number added to itself gives 8’, can be expressed as x/3 + 8 = x.

• True

• False

Exercise | Q 54 | Page 111

The difference between the ages of two sisters Leela and Yamini is a variable.

• True

• False

Exercise | Q 55 | Page 111

The number of lines that can be drawn through a point is a variable.

• True

• False

#### choose a letter x, y, z, p etc...., wherever necessary, for the unknown (variable) and write the corresponding expressions:

Exercise | Q 56 | Page 111

One more than twice the number.

Exercise | Q 57 | Page 111

20°C less than the present temperature.

Exercise | Q 58 | Page 111

The successor of an integer.

Exercise | Q 59 | Page 111

The perimeter of an equilateral triangle, if side of the triangle is m.

Exercise | Q 60 | Page 111

Area of the rectangle with length k units and breadth n units.

Exercise | Q 61 | Page 111

Omar helps his mother 1 hour more than his sister does.

Exercise | Q 62 | Page 112

Two consecutive odd integers.

Exercise | Q 63 | Page 112

Two consecutive even integers.

Exercise | Q 64 | Page 112

Multiple of 5.

Exercise | Q 65 | Page 112

The denominator of a fraction is 1 more than its numerator.

Exercise | Q 66 | Page 112

The height of Mount Everest is 20 times the height of Empire State building.

Exercise | Q 67 | Page 112

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.

Exercise | Q 68 | Page 112

z is multiplied by –3 and the result is subtracted from 13.

Exercise | Q 69 | Page 112

p is divided by 11 and the result is added to 10.

Exercise | Q 70 | Page 112

x times of 3 is added to the smallest natural number.

Exercise | Q 71 | Page 112

6 times q is subtracted from the smallest two digit number.

Exercise | Q 72 | Page 112

Write two equations for which 2 is the solution.

Exercise | Q 73 | Page 112

Write an equation for which 0 is a solution.

Exercise | Q 74 | Page 112

Write an equation whose solution is not a whole number.

#### Change the statements, converting expressions into statements in ordinary language:

Exercise | Q 75 | Page 112

A pencil costs Rs p and a pen costs Rs 5p.

Exercise | Q 76 | Page 112

Leela contributed Rs. y towards the Prime Minister’s Relief Fund. Leela is now left with Rs. (y + 10000).

Exercise | Q 77 | Page 112

Kartik is n years old. His father is 7n years old.

Exercise | Q 78 | Page 112

The maximum temperature on a day in Delhi was p°C. The minimum temperature was (p – 10)°C.

Exercise | Q 79 | Page 112

John planted t plants last year. His friend Jay planted 2t + 10 plants that year.

Exercise | Q 80 | Page 112

Sharad used to take p cups tea a day. After having some health problem, he takes p – 5 cups of tea a day.

Exercise | Q 81 | Page 112

The number of students dropping out of school last year was m. Number of students dropping out of school this year is m – 30.

Exercise | Q 82 | Page 113

Price of petrol was Rs. p per litre last month. Price of petrol now is Rs. (p – 5) per litre.

Exercise | Q 83 | Page 113

Khader’s monthly salary was Rs. P in the year 2005. His salary in 2006 was Rs. (P + 1000).

Exercise | Q 84 | Page 113

The number of girls enrolled in a school last year was g. The number of girls enrolled this year in the school is 3g – 10.

Exercise | Q 85.(a) | Page 113

Translate the following statements into an equation, using x as the variable:

13 subtracted from twice a number gives 3.

Exercise | Q 85.(b) | Page 113

Translate the following statements into an equation, using x as the variable:

One-fifth of a number is 5 less than that number.

Exercise | Q 85.(c) | Page 113

Translate the following statements into an equation, using x as the variable:

Two-third of number is 12.

Exercise | Q 85.(d) | Page 113

Translate the following statements into an equation, using x as the variable:

9 added to twice a number gives 13.

Exercise | Q 85.(e) | Page 113

Translate the following statements into an equation, using x as the variable:

1 subtracted from one-third of a number gives 1.

Exercise | Q 86.(a) | Page 113

Translate the following statements into an equation:

The perimeter (p) of an equilateral triangle is three times of its side (a).

Exercise | Q 86.(b) | Page 113

Translate the following statements into an equation:

The diameter (d) of a circle is twice its radius (r).

Exercise | Q 86.(c) | Page 113

Translate the following statements into an equation:

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.

Exercise | Q 86.(d) | Page 113

Translate the following statements into an equation:

Amount (a) is equal to the sum of principal (p) and interest (i).

Exercise | Q 87 | Page 113

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 grand father’s age is 8 times of her age. ______
Exercise | Q 88 | Page 114

If m is a whole number less than 5, complete the table and by inspection of the table, find the solution of the equation 2m – 5 = – 1:

 m 2m – 5
Exercise | Q 89 | Page 114

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?

Exercise | Q 90 | Page 114

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?

Exercise | Q 91 | Page 114

What is the area of a square whose side is m cm?

Exercise | Q 92 | Page 114

Perimeter of a triangle is found by using the formula P = a + b + c, where a, b and c are the sides of the triangle. Write the rule that is expressed by this formula in words.

Exercise | Q 93 | Page 114

Perimeter of a rectangle is found by using the formula P = 2(l + w), where l and w are respectively the length and breadth of the rectangle. Write the rule that is expressed by this formula in words.

Exercise | Q 94 | Page 114

On my last birthday, I weighed 40 kg. If I put on m kg of weight after a year, what is my present weight?

Exercise | Q 95.(i) | Page 114

Length and breadth of a bulletin board are r cm and t cm, respectively.

What will be the length (in cm) of the aluminium strip required to frame the board, if 10 cm extra strip is required to fix it properly.

Exercise | Q 95.(ii) | Page 114

Length and breadth of a bulletin board are r cm and t cm, respectively.

If x nails are used to repair one board, how many nails will be required to repair 15 such boards?

Exercise | Q 95.(iii) | Page 114

Length and breadth of a bulletin board are r cm and t cm, respectively.

If 500 sq cm 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?

Exercise | Q 95.(iv) | Page 114

Length and breadth of a bulletin board are r cm and t cm, respectively.

What will be the expenditure for making 23 boards, if the carpenter charges Rs x per board.

Exercise | Q 96.(i) | Page 115

Sunita is half the age of her mother Geeta. Find their ages after 4 years?

Exercise | Q 96.(ii) | Page 115

Sunita is half the age of her mother Geeta. Find their ages before 3 years?

#### Match the items of Column I with that of Column II:

Exercise | Q 97 | Page 115
 Column I Column II (i) The number of corners of a quadrilateral (A) = (ii) The variable in the equation 2p + 3 = 5 (B) constant (iii) The solution of the equation x + 2 = 3 (C) +1 (iv) solution of the equation 2p + 3 = 5 (D) –1 (v) A sign used in an equation (E) p (F) x

Exercise

## NCERT solutions for Mathematics Exemplar Class 6 chapter 7 - Algebra

NCERT solutions for Mathematics Exemplar Class 6 chapter 7 (Algebra) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Mathematics Exemplar Class 6 solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Mathematics Exemplar Class 6 chapter 7 Algebra are Introduction to Algebra, The Idea of a Variable, Use of Variables in Common Rules, Expressions with Variables, Concept of Equation, The Solution of an Equation.

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