Skip to main content

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion

Selina Concise Mathematics Class 6 ICSE Solutions – Proportion

Selina Concise Mathematics Class 6 ICSE Solutions – Proportion (Including Word Problems)


EXERCISE 12(A)

Question 1.

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)
(vi)and 14 : 16
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion

Question 2.
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
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion

Question 3.
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.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion

Question 4.
The first, second and the fourth terms of a proportion are 6, 18 and 75, respectively. Find its third term.
Solution:
Let the third term = x
6 : 18 : : x : 75
= 18 x x = 6 x 75
x =Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion= 25
The third term of proportion is 25

Question 5.
Find the second term of the proportion whose first, third and fourth terms are 9, 8 and 24 respectively.
Solution:
Let the second term = x
9 : x : : 8 : 24
=> x x 8 = 24 x 9
x =Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion= 3 x 9 = 27
The second term of proportion = 27

Question 6.
Find the fourth term of the proportion whose first, second and third terms are 18, 27, and 32 respectively.
Solution:
Let the fourth term = x
18 : 27 : : 32 : x
=> 18 x x = 27 x 32
=> x =Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion = 3 x 16 = 48
Fourth term = 48

Question 7.
The ratio of the length and the width of a school ground is 5 : 2. Find the length, if the width is 40 metres.
Solution:
Let the length = x m,
width = 40 m
The ratio of length to width = x : 40
as per given statement 5 : 2 = x : 40
=> 2 x x = 40 x 5
x =Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion= 20 x 5 = 100 m

Question 8.
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.
Solution:
Let, the sale of eggs on Sunday = x
Sale in week = Rs 360
According to question, 2 : 9 = x : 360
=> 9 x x = 360 x 2
x =Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion= Rs 80
Sale on Sunday = Rs 80

Question 9.
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.
Solution:
Let the weight of copper = x kg
Weight of zinc = 9.6 kg.
According to question,
9 : 8 = x : 9.6
=> 8 x x = 9 x 9.6
=> x =Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion= 9 x 1.2 = 10.8 kg.
Weight of cooper in alloy = 10.8

Question 10.
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.
Solution:
Let, the number of girls in school = x
Number of boys in school = 225
According to question 2 : 5 = x : 225
=> 5 x x = 2 x 225
x =Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion= 2 x 45 = 90
Number of girls in school = 90
Total number of student in the school = (number of boys + number of girls) = (225 + 90) = 315

Question 11.
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 ?
Solution:
Total number of students in all sections = 225
Given, One of every five students pass
Total students pass = 225 xSelina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion= 45 studetns

Question 12.
Make set of all possible proportions from the numbers 15, 18, 35 and 42.
Solution:
The possible proportions that can be made from the numbers 15, 18, 35 and 42 are
(i) 15 : 35 :: 18 : 42
(ii) 42 : 18 :: 35 : 15
(iii) 42 : 35 :: 18 : 15
(iv) 15 : 18 :: 35 : 42

EXERCISE 12(B)

Question 1.
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
Solution:
(iii) x : y = y : z

Question 2.
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
Solution:
(iii) and (iv)

Question 3.
Find the mean proportion between
(i) 3 and 27
(ii) 0.06 and 0.96
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion

Question 4.
Find the third proportional to :
(i) 36, 18
(ii) 5.25, 7
(iii) ₹ 1.60, ₹ 0.40
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion
=> x = 0.1

Question 5.
The ratio between 7 and 5 is same as the ratio between ₹ x and ₹ 20.50 ; find the value of x.
Solution:
Since, It is given that the ratio between 7 and 5 is same as the ratio between ₹ x and ₹ 20.50
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion

Question 6.
If (4x + 3y) : (3x + 5y) = 6 : 7, find :
(i) x : y
(ii) x, if y = 10
(iii) y, if x = 27
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion

Question 7.
IfSelina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion, find:
(i) x : y
(ii) x, if y = 70
(iii) y, if x = 33
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion

EXERCISE 12(C)

Question 1.
Are the following numbers in proportion:
(i) 32, 40, 48 and 60 ?
(ii) 12,15,18 and 20 ?
Solution:
(i) 32, 40, 48 and 60 are in proportion
if 32 : 40 = 48 : 60
if 32 x 60 = 40 x 48Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion
if 1920 = 1920
Which is true.
32, 40, 48 and 60 are in proportion
(ii) 12, 15, 18 and 20 are in proportion
if 12 : 15 = 18 : 20
if 12 x 20 = 15 x 18 {ad = bc}
if 240 = 270
which is not true.
12, 15, 18 and 20 are not in proportion.

Question 2.
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
Solution:
14, 42, x and 75 are in proportion
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion
=> 14 x 75 =x x 42
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion

Question 3.
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.
Solution:
Ratio in the cost of two articles = 7 : 4
Cost of first article = Rs. 2800
Let cost of the second article = x
7 : 4 = 2800 : x
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion

Question 4.
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.
Solution:
Let length of sheet = x cm
Ratio in length and breadth = 8 : 5
and width = 17.5 cm
8 : 5 = x : 17.5
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion
Length of sheet = 28 cm

Question 5.
The ages of A and B are in the ratio 6 : 5. If A’s age is 18 years, find the age of B.
Solution:
Ratio in the ages of A and B = 6 : 5
A’s age = 18 years
Let B’s age = x years
6 : 5 = 18 : x
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion

Question 6.
A sum of Rs. 10, 500 is divided among A, B and C in the ratio 5 : 6 : 4. Find the share of each.
Solution:
Total amount = Rs. 10, 500
Ratio in A, B, and C = 5 : 6 : 4
Sum of ratio = 5 + 6 + 4 = 15
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion

Question 7.
Do the ratios 15 cm to 2 m and 10 sec to 3 minutes form a proportion ?
Solution:
15 cm : 2 m : : 10 sec : 3 min
15 cm : 2 x 100 cm :: 10 sec : 30 x 60 sec
15 : 200 :: 10 : 1800
3 : 40 :: 1 : 180
No, they donot form a proportion

Question 8.
Do the ratios 2 kg : 80 kg and 25 g : 625 g form a proportion ?
Solution:
2 kg : 80 kg : : 25 g : 625 g
2 : 80 :: 25 : 625
1 : 40 :: 1 : 25
No, they donot form a proportion.

Question 9.
10 kg sugar cost ₹ 350. If x kg sugar of the same kind costs ₹ 175, find the value of x
Solution:
10 kg of sugar costs = ₹ 350
and x kg of sugar cost = ₹ 175
A.T.Q.
10 kg : x kg :: 350 : 175
=> 10 x 175 = 350 x x
=> 350x= 1750
=> x =Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion= 5
Hence, 5 kg of sugar costs ₹ 175

Question 10.
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 ni
(ii) longer rope, if the shorter is 9.8 m.
Solution:
Length of the ropes are in the ratio = 7 : 5
(i) Let the length of shorter rope = x
Length of longer rope = 22.5 m
A.T.Q.
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion

Question 11.
If 4, x and 9 are in continued proportion, find the value of x.
Solution:
4, x and 9 are in continued proportion
=> 4 : x = x : 9
=> x2 = 9 x 4
=> x = √36
x = 6

Question 12.
If 25, 35 and x are in continued proportion, find the value of x.
Solution:
25, 35 and x are in continued proportion
=> 25 : 35 = 35 : x
=> 25 x x = 35 x 35
=> x =Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion
=> x = 49

Popular posts from this blog

ICSE Solutions for Class 9 History and Civics | Indian History World Developments and Civics ICSE Class IX Question Answers Total Solutions APC Avichal Publishing Company BB Tayal

📚  ICSE Solutions for Class 9 History and Civics ICSE Solutions for Class 9 History and Civics Indian History, World Developments and Civics for ICSE Class- IX by BB-Tayal of Avichal Publishing Company (APC) Buy ICSE Total History & Civics For Class 9 (Latest Syllabus 2022 ) Online Icse Total History & Civics For Class 9 (Latest Syllabus 2022) HISTORY The Harappan Civilization Early Vedic Civilization The Later Vedic Age India in the 6th Century BC: Rise of Jainism and Buddhism The Mauryan Empire The Sangam Age: Kingdoms and The Social and Economic Conditions The Age of the Guptas South India and the Cholas The Delhi Sultanate The Mughal Empire The Composite Culture: Bhakti Movement, Sufism and Influence of Christianity on Indian Society The Renaissance The Reformation Industrial Revolution and Capitalism and Socialism CIVICS Our Constitution and Its Preamble Fundamental Rights, Fundamental Duties and...

ICSE Solutions for Class 9 History and Civics - The Harappan Civilization

ICSE Solutions for Class 9 History and Civics – The Harappan Civilization ICSE Solutions for Class 9 History and Civics – The Harappan Civilization Exercises Question 1. Mention any two sources to reconstruct the Harappan Civilization. Answer: The remains of the two towns, Mohenjo-daro and Harappan reveal and remarkable sense of town planning—the drainage system, the Great Bath, the Assembly Hall and other public buildings. From Seals we come to know about the physical features, dress, ornaments and religious beliefs of the people. Question 2. Why did the Indus Valley Civilization come to be known as Harappan Civilization? Answer: Indus Valley Civilization came to be known as Harappan Civilization because this Civilization flourished in the pre-historic cities of Harappan in West Punjab and Mohenjo-daro in Sind. Question 3. Mention any two important centres of the Indus Valley Civilization. Answer: Northern and Western parts of India and the present day Pakistan. ...

ICSE Solutions for Class 9 History and Civics - Early Vedic Civilization

ICSE Solutions for Class 9 History and Civics – Early Vedic Civilization ICSE Solutions for Class 9 History and Civics – Early Vedic Civilization EXERCISES Question 1. Name any two early Aryan settlements. Answer: The early Aryans settled in the Sapta-Sindhu region which comprised the five rivers of Punjab namely—Jhelum, Chenab, Ravi, Beas and Sutlej and the river Indus (Sindhuj and the river Sarasvati. Question 2. Name the first of the Vedas. Or Which is the oldest Vedic literature. Answer: The Rig Veda is the oldest Vedic literature. Question 3. What does the Rijj Veda contain ? Answer: It contains hymns in praise of different Gods and Goddesses like – Indra, varuna and Agni. Question 4. Mention any of the Vedic hymns that enables us reconstruct the Early Vedic Civilization. Answer: Agni. Agni was the personification of the ‘sacrificial fire.’ Sacrifices or yajnas occupied a prominent place in the early Vedic religion. Agni was thought of a mess...