#### Chapters

## Chapter 7: Algebra

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

#### Choose the correct alternative:

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

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

Which of the following represent 6 × x?

`6x`

`x/6`

`6 + x`

`6 - x`

Which of the following is an equation?

x + 1

x – 1

x – 1 = 0

x + 1 > 0

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

20

12

5

8

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

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

x + 2 = 5

x – 2 = 0

2x + 1 = 0

x + 3 = 6

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

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

x + 1 = 1

x – 1 = 3

2x + 1 = 6

1 – x = 5

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

35

53

15

8

In algebra, letters may stand for ______.

Known quantities

Unknown quantities

Fixed numbers

None of these

Variable means that it ______.

Can take only a few values

Has a fixed value

Can take different values

Can take only 2 values

10 – x means ______.

10 is subtracted x times

x is subtracted 10 times

x is subtracted from 10

10 is subtracted from x

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

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

2x + y

x + 2y

x + y

2x – y

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

x × x

4x

x + x

4 + x

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

2x – 3

2x + 3

3 – 2x

3x – 2

`q/2` = 3 has a solution ______.

6

8

3

2

x – 4 = – 2 has a solution ______.

6

2

– 6

– 2

`4/2` = 2 denotes a ______.

Numerical equation

Algebraic expression

Equation with a variable

False statement

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`

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

4

2

12

–12

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:

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

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

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 ______.

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

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

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

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

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

The number of days in w weeks is ______.

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

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

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

x metres = ______ centimetres.

p litres = ______ millilitres.

r rupees = ______ paise.

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

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

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

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

True

False

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

True

False

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

True

False

The additive inverse of an integer x is 2x.

True

False

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

True

False

2x – 5 > 11 is an equation.

True

False

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

True

False

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

True

False

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

True

False

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

True

False

t minutes are equal to 60t seconds.

True

False

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

True

False

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

True

False

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

True

False

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:

One more than twice the number.

20°C less than the present temperature.

The successor of an integer.

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

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

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

Two consecutive odd integers.

Two consecutive even integers.

Multiple of 5.

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

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

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.

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

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

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

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

Write two equations for which 2 is the solution.

Write an equation for which 0 is a solution.

Write an equation whose solution is not a whole number.

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

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

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

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

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

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

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

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

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

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

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.

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

13 subtracted from twice a number gives 3.

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

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

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

Two-third of number is 12.

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

9 added to twice a number gives 13.

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

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

Translate the following statements into an equation:

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

Translate the following statements into an equation:

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

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.

Translate the following statements into an equation:

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

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. | ______ |

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 |

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?

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?

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

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.

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.

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

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.

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?

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?

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.

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

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:

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 |

## Chapter 7: Algebra

## 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.

Using NCERT Class 6 solutions Algebra exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in NCERT Solutions are important questions that can be asked in the final exam. Maximum students of CBSE Class 6 prefer NCERT Textbook Solutions to score more in exam.

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