Selina solutions concise mathematics class 6 icse Solutions for Chapter 12 proportion including word problems

Exercises in Chapter 12 proportion including word problems Grade 6

Exercise 12(A)

Exercise 12(B)

Exercise 12(C)

Questions in Exercise 12(A)

Q1)

In each of the following, check whether or not the given ratios form a proportion :

(i) 8 : 16 and 12 : 15

(ii) 16 : 28 and 24 : 42

(iii) 12 ÷ 3 and 8 ÷ 2

(iv) 25 : 40 and 20 : 32

$(v)\frac{15}{18}and\frac{10}{12}$

$(vi)\frac{7}{8}and\ 14:16$

Q2) Find the value of x in each of the following proportions :

(i) x : 4 = 6 : 8

(ii) 14 : x = 7 : 9

(iii) 4 : 6 = x : 18

(iv) 8 : 10 = x : 25

(v) 5 : 15 = 4 : x

(vi) 16 : 24 = 6 : x

Q3) Find the value of x so that the given four numbers are in proportion :

(i) x, 6, 10 and 15

(ii) x, 4, 15 and 30

(iii) 2, x, 10 and 25

(iv) 4, x, 6 and 18

(v) 9, 12, x and 8

(vi) 4, 10, 36 and x

(vii) 7, 21, x and 45

(viii) 6, 8, 12 and x.

Q4) The first, second and the fourth terms of a proportion are 6, 18 and 75, respectively. Find its third term.

Q5) Find the second term of the proportion whose first, third and fourth terms are 9, 8 and 24 respectively.

Q6) Find the fourth term of the proportion whose first, second and third terms are 18, 27, and 32 respectively.

Q7) The ratio of the length and the width of a school ground is 5 : 2. Find the length, if the width is 40 metres.

Q8) The ratio of the sale of eggs on a Sunday and that of the whole week at a grocery shop was 2 : 9. If the total value of the sale of eggs in the same week was Rs 360, find the value of the sale of eggs that Sunday.

Q9) The ratio of copper and zinc in an alloy is 9 : 8. If the weight of zinc, in the alloy, is 9.6 kg ; find the weight of copper in the alloy.

Q10) The ratio of the number of girls to the number of boys in a school is 2 : 5. If the number of boys is 225 ; find:

(i) the number of girls in the school.

(ii) the number of students in the school.

Q11) In a class, one out of every 5 students pass. If there are 225 students in all the sections of a class, find how many pass?

Q12) Make set of all possible proportions from the numbers 15, 18, 35 and 42.

Questions in Exercise 12(B)

Q1) If x, y and z are in continued proportion, then which of the following is true :

(i) x : y = x : z

(ii) x : x = z : y

(iii) x : y = y : z

(iv) y : x = y : z

Q2) Which of the following numbers are in continued proportion :

(i) 3, 6 and 15

(ii) 15, 45 and 48

(iii) 6, 12 and 24

(iv) 12, 18 and 27

Q3) Find the mean proportion between

(i) 3 and 27

(ii) 0.06 and 0.96

Q4) Find the third proportional to :

(i) 36, 18

(ii) 5.25, 7

(iii) ₹ 1.60, ₹ 0.40

Q5) The ratio between 7 and 5 is same as the ratio between ₹ x and ₹ 20.50 ; find the value of x.

Q6) If (4x + 3y) : (3x + 5y) = 6 : 7, find :

(i) x : y

(ii) x, if y = 10

(iii) y, if x = 27

Q7) If $\frac{2y\ +\ 5x}{3y\ -\ 5x}=2\frac{1}{2}$ , find:

(i) x : y

(ii) x, if y = 70

(iii) y, if x = 33

Questions in Exercise 12(C)

Q1) Are the following numbers in proportion:

(i) 32, 40, 48 and 60 ?

(ii) 12,15,18 and 20 ?

Q2) Find the value of x in each of the following such that the given numbers are in proportion.

(i) 14, 42, x and 75

(ii) 45, 135, 90 and x

Q3) The costs of two articles are in the ratio 7 : 4. If the cost of the first article is Rs. 2,800 ; find the cost of the second article.

Q4) The ratio of the length and the width of a rectangular sheet of paper is 8 : 5. If the width of the sheet is 17.5 cm; find the length.

Q5) The ages of A and B are in the ratio 6 : 5. If A’s age is 18 years, find the age of B.

Q6) A sum of Rs. 10, 500 is divided among A, B and C in the ratio 5 : 6 : 4. Find the share of each.

Q7) Do the ratios 15 cm to 2 m and 10 sec to 3 minutes form a proportion?

Q8)Do the ratios 2 kg : 80 kg and 25 g : 625g form a proportion ?

Q9) 10 kg of sugar cost ₹ 350. If x kg sugar of the same kind costs ₹ 175, find the value of x

Q10) The length of two ropes are in the ratio 7 : 5. Find the length of:

(i) shorter rope, if the longer one is 22.5 m

(ii) longer rope, if the shorter is 9.8 m.

Q11) If 4, x and 9 are in continued proportion, find the value of x.

Q12) If 25, 35 and x are in continued proportion, find the value of x.

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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