Selina solutions concise mathematics class 6 icse Solutions for Chapter 22 simple linear equations including word problems

Exercises in Chapter 22 simple linear equations including word problems Grade 6

Exercise 22(A)

Exercise 22(B)

Exercise 22(C)

Exercise 22(D)

Revision Exercise

Questions in Exercise 22(A)

Q1) Solve:

(i) x + 2 = 6

(ii) x + 6 = 2

(iii) y + 8 = 5

(iv) x + 4 = - 3

(v) y + 2 = - 8

(vi) b + 2.5 = 4.2

(vii) p + 4.6 = 8.5

(viii) y + 3.2 = - 6.5

(ix) a + 8.9 = - 12.6

(x) x + $2\frac{1}{3}$ = 5

(xi) z + 2 = $4\frac{1}{5}$

(xii) m + $3\frac{1}{2}=4\frac{1}{4}$

(xiii) x + 2 = $1\frac{1}{4}$

(xiv) y + $5\frac{1}{3}$ = 4

(xv) a + $3\frac{1}{5}=1\frac{1}{2}$

Q2) Solve:

(i) x - 3 = 2

(ii) m - 2 = - 5

(iii) b - 5 = 7

(iv) a - 2.5 = - 4

(v) y - $3\frac{1}{2}$ = 6

(vi) z - $2\frac{1}{3}$ = - 6

(vii) p - 5.4 = 2.7

(viii) x - 1.5 = - 4.9

(ix) n - 4 = $4\frac{1}{5}$

Q3) Solve:

(i) 3x = 12

(ii) 2y = 9

(iii) 5z = 8.5

(iv) 2.5m = 7.5

(v) 3.2p = 16

(vi) 2a = 4.6

Q4) Solve:

(i) $\frac{x}{2}=5$

(ii) $\frac{y}{3}=-2$

(iii) $\frac{a}{5}=-15$

(iv) $\frac{z}{4}=3\frac{1}{4}$

(v) $\frac{m}{6}=2\frac{1}{2}$

(vi) $\frac{n}{7}=-2.8$

Q5) Solve:

(i) $-2x=8$

(ii) $-3.5y=14$

(iii) $-5z=4$

(iv) $-5=a+3$

(v) $2=p+5$

(vi) $4.5=m-2.7$

(vii) $3\frac{2}{5}=x-2\frac{1}{3}$

(viii) $5=m+3\frac{4}{7}$

(ix) $-2\frac{1}{5}=y-4$

Questions in Exercise 22(B)

Q1) Solve:

(i) 2x + 5 = 17

(ii) 3y - 2 = 1

(iii) 5p + 4 = 29

(iv) 4a - 3 = -27

(v) 2z + 3 = -19

(vi) 7m - 1 = 20

(vii) 2.4x - 3 = 4.2

(viii) 4m + 9.4 = 5

(ix) 6y + 4 = -4.4

Q2) Solve:

(i) $\frac{x}{3}-5=2$

(ii) $\frac{y}{2}-3=8$

(iii) $\frac{z}{7}+1=2\frac{1}{2}$

(iv) $\frac{a}{2.4}-5=2.4$

(v) $\frac{b}{1.6}+3=-2.5$

(vi) $\frac{m}{4}-4.6=-3.1$

Q3) Solve:

(i) -8m - 2 = -10

(ii) 4x + 2x = 3 + 5

(iii) 4x - x + 5 = 8

(iv) 6x + 2 = 2x + 10

(v) 18 - (2a - 12) = 8a

(vi) 3x + 5 + 2x + 6 + x = 4x + 21

(vii) 3.5x - 9 - 3 = x + 1

(viii) 8x + 6 + 2x - 4 = 4x + 8

(ix) - m + (3m - 6m) = - 8 - 14

(x) 5x - 14 = x - (24 + 4x)

Questions in Exercise 22(C)

Q1) 5 – x = 3

Q2) 2 – y = 8

Q3) 8.4 – x = -2

Q4) $x+2\frac{1}{5}=3$

Q5) $y-3\frac{1}{2}=2\frac{1}{3}$

Q6) $5\frac{2}{3}-z=2\frac{1}{2}$

Q7) 1.6z = 8

Q8) 3a = - 2.1

Q9) $\frac{z}{4}=-1.5$

Q10) $\frac{z}{6}=-1\frac{2}{3}$

Q12) 2.4z = -4.8

Q13) 2y - 5 = -11

Q14) 2x + 4.6 = 8

Q15) 5y - 3.5 = 10

Q16) 3x + 2 = -2.2

Q17) $\frac{y}{2}-5=1$

Q18) $\frac{z}{3}-1=-5$

Q19) $\frac{x}{4}+3.6=-1.1$

Q20) -3y – 2 = 10

Q21) 4z – 5 = 3 – z

Q22) 7x – 3x + 2 =22

Q23) 6y + 3 = 2y + 11

Q24) 3 (x + 5) = 18

Q25) 5 (x – 2) – 2 (x + 2) = 3

Q26) (5x – 3) 4 = 3

Q27) 3(2x + 1) – 2(x – 5) -5 (5 – 2x) = 16

Questions in Exercise 22(D)

Q1) A number increased by 17 becomes 54. Find the number.

Q2) A number decreased by 8 equals 26, find the number.

Q3) One-fourth of a number added to two- seventh of it gives 135; find the number.

Q4) Two-fifths of a number subtracted from three-fourths of it gives 56, find the number.

Q5) A number is increased by 12 and the new number obtained is multiplied by 5. If the resulting number is 95, find the original number.

Q6) A number is increased by 26 and the new number obtained is divided by 3. If the resulting number is 18; find the original number.

Q7) The age of a man is 27 years more than the age of his son. If the sum of their ages is 47 years, find the age of the son and his father.

Q8) The difference between the ages of Gopal and his father is 26 years. If the sum of their ages is 56 years, find the ages of Gopal and his father.

Q9) When two consecutive natural numbers are added, the sum is 31; find the numbers.

Q10) When three consecutive natural numbers are added, the sum is 66, find the numbers.

Q11) A natural number decreased by 7 is 12. Find the number.

Q12) One fourth of a number added to one- sixth of itself is 15. Find the number.

Q13) A whole number is increased by 7 and the new number so obtained is multiplied by 5; the result is 45. Find the number.

Q14) The age of a man and the age of his daughter differ by 23 years and the sum of their ages is 41 years. Find the age of the man.

Q15) The difference between the ages of a woman and her son is 19 years and the sum of their ages is 37 years; find the age of the son.

Q16) Two natural numbers differ by 6 and the sum of them is 36. Find the larger number.

Q17) The difference between the two numbers is 15. Taking the smaller number as x; find:

(i) the expression for a larger number.

(ii) the larger number, if the sum of these numbers is 71.

Q18) The difference between the two numbers is 23. Taking the larger number as x, find:

(i) the expression for a smaller number.

(ii) the smaller number, if the sum of these two numbers is 91.

Q19) Find three consecutive integers such that their sum is 78.

Q20) The sum of three consecutive numbers is 54. Taking the middle number as x, find:

(i) expression for the smallest number and the largest number.

(ii) the three numbers.

Questions in Revision Exercise

Q1) Solve each of the following equations:

(i) 2x + 3 = 7

(ii) 2x - 3 = 7

(iii) 2x ÷ 3 = 7

(iv) 3x - 8 - 13

(v) 3y + 8 = 13

(vi) 3y ÷ 8 = 13

(vii) $x-3=5\frac{1}{2}$

(viii) $\frac{3}{5}x+4=13$

(ix) $u+3\frac{1}{4}=4\frac{1}{3}$

(x) 5x – 2.4 = 4.9

(xi) 5y + 4.9 = 2.4

(xii) 48 z + 3.6 = 1.2

(xiii) $\frac{x}{2}-3=5$

(xiv) $\frac{y}{3}+7=2$

(xv) $\frac{2m}{3}=8\frac{2}{3}$

(xvi) -3x + 4 = 10

(xvii) 5 = x - 3

(xviii) 8y = 3 - 3y

(xix) 4x + 4.9 = 6.5

(xx) 3z + 2 = -4

(xxi) 7y - 18 = 17

(xxii) $\frac{x}{1.2}-6=1$

(xxiii) $\frac{z}{2.4}+3.6=5.1$

(xxiv) $\frac{y}{1.8}-2.1=-2.8$

(xxv) 7x – 2 = 4x + 7

(xvi) 3y -(y + 2) = 4

(xxvii) 3z – 18 = z – (12 – 4z)

(xxviii) $x-2\frac{1}{2}=5\frac{1}{2}$

(xxix) $3\frac{2}{3}-y=2\frac{1}{2}$

(xxx) $2z-2\frac{1}{2}=3\frac{1}{2}$

(xxxi) 5x – 2x + 15 = 27

(xxxii) 5y – 15 = 27 -2y

(xxxiii) 7z + 15 = 3z – 13

(xxxiv) 2 (x -3) – 3 (x-4) =12

(xxxv) (7y + 8) + 7 = 8

(xxxvi) 2(z – 5) +3 (z + 2) -(3 – 5z) = 10

Q2) A natural number decreased by 7 is 12. Find the number.

Q3) One-fourth of a number added to one-sixth of It is 15. Find the number.

Q4) A whole number is increased by 7 and the number so obtained is multiplied by 5; the result is 45. Find the whole number.

Q5) The age of a man and the age of his daughter differ by 23 years and the sum of their ages is 41 years. Find the age of the man.

Q6) The difference between the ages of a woman and her son is 19 years and the sum of their ages is 37 years; find the age of the son.

Q7) Two natural numbers differ by 6 and their sum is 36. Find the larger number.

Q8) The difference between the two numbers is 15. Taking the smaller number as x; find :

(i) the expression for the larger number.

(ii) the larger number, if the sum of these numbers is 71.

Q9) The difference between the two numbers is 23. Taking the larger number as x, find :

(i) the expression for a smaller number.

(ii) the smaller number, if the sum of these two numbers is 91.

Q10) Find the three consecutive integers whose sum is 78.

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Chapters in this book

Number System (Consolidating the Sense of Numberness)

Estimation

Numbers in India and International System (With Comparison)

Place Value

Natural Numbers and Whole Numbers (Including Patterns)

Negative Numbers and Integers

Number Line

HCF and LCM

Playing with Numbers

Sets

Ratio

Proportion (Including Word Problems)

Unitary Method

Fractions

Decimal Fractions

Percent (Percentage)

Idea of Speed, Distance and Time

Fundamental Concepts (Algebra)

Fundamental Operations (Related to Algebraic Expressions)

Substitution (Including Use of Brackets as Grouping Symbols)

Framing Algebraic Expressions (Including Evaluation)

Simple (Linear) Equations (Including Word Problems)

Fundamental Concepts (Geometry)

Angles (With their Types)

Properties of Angles and Lines (Including Parallel Lines)

Triangles (Including Types, Properties and Construction)

Quadrilateral

Polygons

The Circle

Revision Exercise on Symmetry (Including Constructions on Symmetry)

Recognition of Solids

Perimeter and Area of Plane Figures

Data Handling (Including Pictograph and Bar Graph)

Mean and Median