Class 6 Maths Notes for Ratio And Proportion
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Page 1
NOTES
CLASS 6
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Page 2
RATIO AND PROPORTION
Key Points
There are two ways of comparison:
(i) By taking difference
(ii) By division
The comparison by division is called the ratio. In this way, we see how many times one quantity is to the other
quantity
Ratio
If we compare two quantities in terms of „how many times‟, then this comparison is known as the ratio. Ratio
is denoted by using the symbol „:‟
For comparison by ratio, the two quantities must be in the same units. If they are not, they must be expressed in
the same units before the ratio is taken
.
Equivalent Ratio
A ratio equivalent to a given ratio can be obtained by multiplying or dividing the numerator and denominator
by the same number. Thus, few ratios equivalent to 2 : 3 are 4 : 6, 6 : 9, 8 : 12, etc.
The orders in which the quantities are taken to express their ratio is important. Note that the ratio 2 : 3 is
different from 3 : 2.
A ratio can be expressed in its lowest form. For example, ratio 60 : 24 is in the form of a fraction. In its lowest
60 5
form = = 5 : 2. Thus in its lowest form ratio 60:24 is treated as 5 : 2.
24 2
Proportion
If two ratios are equal we say that they are in proportion and use the symbol to equate the two ratios.
For example, 2 : 4 = 60 : 120
we write 2 : 4 :: 60 : 120
and say that 2, 4, 60 and 120 are in proportion.
Again,
2 : 5 ≠ 60 : 15
We say that 2, 5, 60 and 15 are not in proportion.
So, if two ratios are not equal, then we say that they are not in proportion.
SOLVED EAMPLES
Find the ratio of the first quantity to the second.
(1) 25 beads, 40 beads (2) Rs 40 , Rs 120 (3) 25 beads : 40 beads
1) 25÷5=5 40÷5=8
=5:8 (HCF of 25 and 40 = 5)
(2) 40 rupees : 120 rupees = 40÷120
40÷40=1 120÷40=13
=1:3 (HCF of 40 and 120 = 40)
Ques2 .Reema has 24 notebooks and 18 books. Find the ratio of notebooks to books.
Sol. Number of notebooks = 24 Number of books = 18
Ratio of notebooks to books = Number of notebooks : Number of books
= 24 : 18
= 24÷6 18÷6
(HCF of 24 and 18 = 6)
Thus, the ratio of notebooks to books is 4:3
95
Key Points
There are two ways of comparison:
(i) By taking difference
(ii) By division
The comparison by division is called the ratio. In this way, we see how many times one quantity is to the other
quantity
Ratio
If we compare two quantities in terms of „how many times‟, then this comparison is known as the ratio. Ratio
is denoted by using the symbol „:‟
For comparison by ratio, the two quantities must be in the same units. If they are not, they must be expressed in
the same units before the ratio is taken
.
Equivalent Ratio
A ratio equivalent to a given ratio can be obtained by multiplying or dividing the numerator and denominator
by the same number. Thus, few ratios equivalent to 2 : 3 are 4 : 6, 6 : 9, 8 : 12, etc.
The orders in which the quantities are taken to express their ratio is important. Note that the ratio 2 : 3 is
different from 3 : 2.
A ratio can be expressed in its lowest form. For example, ratio 60 : 24 is in the form of a fraction. In its lowest
60 5
form = = 5 : 2. Thus in its lowest form ratio 60:24 is treated as 5 : 2.
24 2
Proportion
If two ratios are equal we say that they are in proportion and use the symbol to equate the two ratios.
For example, 2 : 4 = 60 : 120
we write 2 : 4 :: 60 : 120
and say that 2, 4, 60 and 120 are in proportion.
Again,
2 : 5 ≠ 60 : 15
We say that 2, 5, 60 and 15 are not in proportion.
So, if two ratios are not equal, then we say that they are not in proportion.
SOLVED EAMPLES
Find the ratio of the first quantity to the second.
(1) 25 beads, 40 beads (2) Rs 40 , Rs 120 (3) 25 beads : 40 beads
1) 25÷5=5 40÷5=8
=5:8 (HCF of 25 and 40 = 5)
(2) 40 rupees : 120 rupees = 40÷120
40÷40=1 120÷40=13
=1:3 (HCF of 40 and 120 = 40)
Ques2 .Reema has 24 notebooks and 18 books. Find the ratio of notebooks to books.
Sol. Number of notebooks = 24 Number of books = 18
Ratio of notebooks to books = Number of notebooks : Number of books
= 24 : 18
= 24÷6 18÷6
(HCF of 24 and 18 = 6)
Thus, the ratio of notebooks to books is 4:3
95
Page 3
Ques3 30 cricket players and 20 kho-kho players are training on a field. What is the ratio of cricket players to
the total number of players?
Number of cricket players = 30
Number of kho-kho players = 20
∴ Total no of player = Number of cricket players + Number of kho-kho players = 30 + 20 = 50
Ratio of cricket players to the total no of players = No of cricket players : Total no of player 50
= 30÷10, 50÷10
(HCF of 30 and 50 = 10)
Answer = 3:5
ASSIGNMENT
MCQ
Q1.Distances travelled by Hamid and Akhtar in an hour is 9 km and 12 km. Find the
the ratio of the speed of Hamid to the speed of Akhtar.
a)3:4 b)4:5 c) 2:3 d) 3:4
Q2. Find the ratio of the following 30 minutes to 1.5 hours
a) 3:4 b) 1:3 c) 1: 2 d) 2:3
Q3. Find the ratio of the following 40 cm to 1.5 m
a) 3:4 b)4:15 c) 4: 7 d) 3:5
Q4 Out of 30 students in a class, 6 like football,12 like cricket and remaining like tennis. Find
the ratio of number of students liking football to the number of students liking tennis.
a) 1:2 b) 3:4 c) 2:3 d) 1:3
Q5. There are 20 girls and 15 boys in a class. What is the ratio of the number of girls to the total number
of students in the class?
a) 4:5 b) 4:9 c) 5:7 d) 3: 5
Short Answer Type Question
Q1. Find the missing number in the box in the following proportion:
__ : 5 :: 12 : 60
Q2. A picture is 60cm wide and 1.8m long. Find the ratio of its width to its perimeter in lowest form
Q3. The greatest ratio among the ratios 2 : 3, 4 : 5, 5 : 6 and 6 : 7 is
Q4 Ratio of 5 paise to 25 paise is the same as the ratio of 20 paise to
Q5. If 3 : 2 is equivalent, to x : 4, then find x
Q6. The comparison of two numbers quantities by division is known as the ……………….
Q7 The lowest form of 25 : 75 is ……………….
Q8 A ………………… is a statement that two ratios are equal. [proportion/equation]
Q9. The ratio 30 : 45, in its lowest term is …………………
Q10. In a class, there are 30 girls and 20 boys. [Number of girls] : [Number of boys] = …………………
Long Answer Type
Q1. Express each of the following in the language of ratios:
(i) In a class, the number of girls in the merit list of the board examination is two times that of boys.
(ii) The number of students passing mathematics test is 2/3 of the number that appeared.
Q2. Express the following ratios in language of daily life:
(i) The ratio of the number of bad pencils to that of good pencils produced in a factory is 1: 9.
(ii) In India, the ratio of the number of villages to that of cities is about 2000: 1.
96
the total number of players?
Number of cricket players = 30
Number of kho-kho players = 20
∴ Total no of player = Number of cricket players + Number of kho-kho players = 30 + 20 = 50
Ratio of cricket players to the total no of players = No of cricket players : Total no of player 50
= 30÷10, 50÷10
(HCF of 30 and 50 = 10)
Answer = 3:5
ASSIGNMENT
MCQ
Q1.Distances travelled by Hamid and Akhtar in an hour is 9 km and 12 km. Find the
the ratio of the speed of Hamid to the speed of Akhtar.
a)3:4 b)4:5 c) 2:3 d) 3:4
Q2. Find the ratio of the following 30 minutes to 1.5 hours
a) 3:4 b) 1:3 c) 1: 2 d) 2:3
Q3. Find the ratio of the following 40 cm to 1.5 m
a) 3:4 b)4:15 c) 4: 7 d) 3:5
Q4 Out of 30 students in a class, 6 like football,12 like cricket and remaining like tennis. Find
the ratio of number of students liking football to the number of students liking tennis.
a) 1:2 b) 3:4 c) 2:3 d) 1:3
Q5. There are 20 girls and 15 boys in a class. What is the ratio of the number of girls to the total number
of students in the class?
a) 4:5 b) 4:9 c) 5:7 d) 3: 5
Short Answer Type Question
Q1. Find the missing number in the box in the following proportion:
__ : 5 :: 12 : 60
Q2. A picture is 60cm wide and 1.8m long. Find the ratio of its width to its perimeter in lowest form
Q3. The greatest ratio among the ratios 2 : 3, 4 : 5, 5 : 6 and 6 : 7 is
Q4 Ratio of 5 paise to 25 paise is the same as the ratio of 20 paise to
Q5. If 3 : 2 is equivalent, to x : 4, then find x
Q6. The comparison of two numbers quantities by division is known as the ……………….
Q7 The lowest form of 25 : 75 is ……………….
Q8 A ………………… is a statement that two ratios are equal. [proportion/equation]
Q9. The ratio 30 : 45, in its lowest term is …………………
Q10. In a class, there are 30 girls and 20 boys. [Number of girls] : [Number of boys] = …………………
Long Answer Type
Q1. Express each of the following in the language of ratios:
(i) In a class, the number of girls in the merit list of the board examination is two times that of boys.
(ii) The number of students passing mathematics test is 2/3 of the number that appeared.
Q2. Express the following ratios in language of daily life:
(i) The ratio of the number of bad pencils to that of good pencils produced in a factory is 1: 9.
(ii) In India, the ratio of the number of villages to that of cities is about 2000: 1.
96
Page 4
Q3 The number of boys and girls in a school are 240and 180 respectively. Express the ratio of the number of
boys to that of the girls in the simplest form.
Q4 Avinash works as a lecturer and earns Rs 12000 per month. His wife who is a doctor earns Rs 15000 per
month. Find the following ratios:
(i) Avinash‟s income to the income of his wife.(ii) Avinash‟s income to their total income
Q5 . Of the 72 persons working in an office, 28 are men and the remaining are women. Find the ratio of the
number of:
(i) men to that of women,(ii) men to the total number of persons(iii) persons to that of women.
Q6. The length of a steel tape for measurements of buildings is 10 m and its width is 2.4 cm. What is the ratio
of its length to width?
Case Study Question
Q1. See the figure and find the ratio of
(i) The number of triangles to the number of circles inside the rectangle.
(ii) Number of squares to all the figures inside the rectangle.
(iii) The number of circles to all the figures inside the rectangle.
Q2. In a college, out of 4320 students, 2300 are girls. Find the ratio of
(a) Number of girls to the total number of students.
(b) The number of boys to the number of girls.
(c) The number of boys to the total number of students.
---------------------------------------------------------------------------------------------------------------------
97
boys to that of the girls in the simplest form.
Q4 Avinash works as a lecturer and earns Rs 12000 per month. His wife who is a doctor earns Rs 15000 per
month. Find the following ratios:
(i) Avinash‟s income to the income of his wife.(ii) Avinash‟s income to their total income
Q5 . Of the 72 persons working in an office, 28 are men and the remaining are women. Find the ratio of the
number of:
(i) men to that of women,(ii) men to the total number of persons(iii) persons to that of women.
Q6. The length of a steel tape for measurements of buildings is 10 m and its width is 2.4 cm. What is the ratio
of its length to width?
Case Study Question
Q1. See the figure and find the ratio of
(i) The number of triangles to the number of circles inside the rectangle.
(ii) Number of squares to all the figures inside the rectangle.
(iii) The number of circles to all the figures inside the rectangle.
Q2. In a college, out of 4320 students, 2300 are girls. Find the ratio of
(a) Number of girls to the total number of students.
(b) The number of boys to the number of girls.
(c) The number of boys to the total number of students.
---------------------------------------------------------------------------------------------------------------------
97
Page 5
PRACTICE TEST-1
General Instructions: Section-A contains 4 questions of 1 mark each.Section –B contains 3 questions of 2
marks each. Section-C contains 2 questions of 3 marks each. Section-D contains 1question of 4 mark
M.Marks:20 Time: 45 min
SECTION-A
Q1 The ratio of 150 g to 2 kg is 1
a)75 : 1(b) 40 : 3(c) 3 : 40(d) 3 : 200
Q2 The ratio of number of girls to the number of boys in a class is 5 : 4. If there are 1
25 girls in the class, then the number of boys in the class is
(a) 15(b) 20(c) 30(d) 40
Q3 If a, b, c and d are in proportion, then 1
a) ab = cd(b) ad = bc(c) ac = bd(d) none of these
Q4 The ratio 384 : 480 in the simplest form is 1
(a) 2 : 5(b) 3 : 5(c) 5 : 4(d) 4 : 5
SECTION-B
Q5 If 7 pencils cost ₹35, then find the cost of one dozen pencils . 2
Q6 Out of 45 students in a class, 20 students are boys and the remaining are girls. 2
Find the ratio of boys to girls and girls to boys.
Q7 The ratio of Julie's money to Pradeep's money is 4 : 6. If Julie has Rs. 500, how 2
much money does Pradeep have?
SECTION-C
Q8 A rectangular field is 80 m long and 60 m wide. Find the ratio of it's length to 3
perimeter.
Q9 The ratio of the number of apples to the oranges in a shop is 8 : 7. If there are 3
63 oranges, how many apples are there in the shop?
SECTION-D
Q10 A machine manufactures 75 cycle parts in 5 hours.
i)How many parts will it manufacture in 45 hours?
ii)In how many hours will it produce 150 parts?
98
General Instructions: Section-A contains 4 questions of 1 mark each.Section –B contains 3 questions of 2
marks each. Section-C contains 2 questions of 3 marks each. Section-D contains 1question of 4 mark
M.Marks:20 Time: 45 min
SECTION-A
Q1 The ratio of 150 g to 2 kg is 1
a)75 : 1(b) 40 : 3(c) 3 : 40(d) 3 : 200
Q2 The ratio of number of girls to the number of boys in a class is 5 : 4. If there are 1
25 girls in the class, then the number of boys in the class is
(a) 15(b) 20(c) 30(d) 40
Q3 If a, b, c and d are in proportion, then 1
a) ab = cd(b) ad = bc(c) ac = bd(d) none of these
Q4 The ratio 384 : 480 in the simplest form is 1
(a) 2 : 5(b) 3 : 5(c) 5 : 4(d) 4 : 5
SECTION-B
Q5 If 7 pencils cost ₹35, then find the cost of one dozen pencils . 2
Q6 Out of 45 students in a class, 20 students are boys and the remaining are girls. 2
Find the ratio of boys to girls and girls to boys.
Q7 The ratio of Julie's money to Pradeep's money is 4 : 6. If Julie has Rs. 500, how 2
much money does Pradeep have?
SECTION-C
Q8 A rectangular field is 80 m long and 60 m wide. Find the ratio of it's length to 3
perimeter.
Q9 The ratio of the number of apples to the oranges in a shop is 8 : 7. If there are 3
63 oranges, how many apples are there in the shop?
SECTION-D
Q10 A machine manufactures 75 cycle parts in 5 hours.
i)How many parts will it manufacture in 45 hours?
ii)In how many hours will it produce 150 parts?
98
Page 6
PRACTICE TEST-2
Mathematics
Class-VI
General Instructions: Section-A contains 5 questions of 1 mark each.Section –B contains 6 questions of 2
marks each. Section-C contains 3 questions of 3 marks each. Section-D contains 1question of 4 marks
M.Marks:30 Time: 90 min
SECTION-A
Q1 Find the missing term of the proportion whose three terms are mentioned 1
below.
8, ___, 32 , 12
a) b) c) d)
Q2 Find the simplest form of the given ratio 70 : 105. 1
a) B) c) d)
Q3 The ratio of 120 g to 2 kg is 1
a)3: 5 (b) 40 : 3(c) 3 : 40(d) 3 : 200
Q4 The ratio 384 : 450 in the simplest form is 1
(a) 2 : 5(b) 3 : 5(c) 5 : 4(d) 4 : 5
Q5 Find the ratio of the following 30 minutes to 1.5 hours 1
a) 3:4 b) 1:3 c) 1: 2 d) 2:3
SECTION-B
Q6 The weight of 9 similar books is 12 kg. What is the weight of 45 such books? 2
Q7 Find the fourth term of the proportion whose first three terms are mentioned 2
below.
3, 2, 9
Q8 Find the ratio of 2 years to 6 months. 2
Q9 The greatest ratio among the ratios 2 : 3, 4 : 5, 5 : 6 and 6 : 7 is 2
Q10 If 7 pencils cost ₹35, then find the cost of 20 pencils 2
Q11 The ratio of Smith's money to Paul's money is 4 : 6. If Smith has Rs. 200, how 2
much money does Paul have?
SECTION-C
Q12 The cost of 19 tables is Rs. 27854. How many tables can be bought for Rs. 3
51310.
Q13 A motorbike travels 260 km in 5 hours. How far it will travel in 15 hours 30 3
minutes?
99
Mathematics
Class-VI
General Instructions: Section-A contains 5 questions of 1 mark each.Section –B contains 6 questions of 2
marks each. Section-C contains 3 questions of 3 marks each. Section-D contains 1question of 4 marks
M.Marks:30 Time: 90 min
SECTION-A
Q1 Find the missing term of the proportion whose three terms are mentioned 1
below.
8, ___, 32 , 12
a) b) c) d)
Q2 Find the simplest form of the given ratio 70 : 105. 1
a) B) c) d)
Q3 The ratio of 120 g to 2 kg is 1
a)3: 5 (b) 40 : 3(c) 3 : 40(d) 3 : 200
Q4 The ratio 384 : 450 in the simplest form is 1
(a) 2 : 5(b) 3 : 5(c) 5 : 4(d) 4 : 5
Q5 Find the ratio of the following 30 minutes to 1.5 hours 1
a) 3:4 b) 1:3 c) 1: 2 d) 2:3
SECTION-B
Q6 The weight of 9 similar books is 12 kg. What is the weight of 45 such books? 2
Q7 Find the fourth term of the proportion whose first three terms are mentioned 2
below.
3, 2, 9
Q8 Find the ratio of 2 years to 6 months. 2
Q9 The greatest ratio among the ratios 2 : 3, 4 : 5, 5 : 6 and 6 : 7 is 2
Q10 If 7 pencils cost ₹35, then find the cost of 20 pencils 2
Q11 The ratio of Smith's money to Paul's money is 4 : 6. If Smith has Rs. 200, how 2
much money does Paul have?
SECTION-C
Q12 The cost of 19 tables is Rs. 27854. How many tables can be bought for Rs. 3
51310.
Q13 A motorbike travels 260 km in 5 hours. How far it will travel in 15 hours 30 3
minutes?
99
Page 7
Q14 Q4 Avinash works as a lecturer and earns Rs 12000 per month. His wife who is 3
a doctor earns Rs 15000 per month. Find the following ratios:
(i) Avinash‟s income to the income of his wife.
(ii) Avinash‟s income to their total income
SECTION-D
Q15 Q5 . Of the 72 persons working in an office, 28 are men and the remaining are 4
women. Find the ratio of the number of:
(i) men to that of women,
(ii) men to the total number of persons
(iii) persons to that of women.
----------------------------------------------------------------------------------------------------------------
ANSWERS OF ASSIGNMENT QUESTIONS
MCQ ANS SAQ ANSWERS LAQ ANSWER
Q1 d Q1 X= 1 Q1 2:1
Q2 b Q2 1:8 Q2 Do it
Q3 b Q3 6:7 Q3 4:3
Q4 a Q4 100 Q4 (i) 4:5
(ii) 4:9
Q5 a Q5 6 Q5 (i) 7:11
(ii) 7:18
(iii) 18:11
Q6 Ratio Q6 1250:3
Q7 1:3
Q8 Proportion
Q9 2:3
Q10 3:2
100
a doctor earns Rs 15000 per month. Find the following ratios:
(i) Avinash‟s income to the income of his wife.
(ii) Avinash‟s income to their total income
SECTION-D
Q15 Q5 . Of the 72 persons working in an office, 28 are men and the remaining are 4
women. Find the ratio of the number of:
(i) men to that of women,
(ii) men to the total number of persons
(iii) persons to that of women.
----------------------------------------------------------------------------------------------------------------
ANSWERS OF ASSIGNMENT QUESTIONS
MCQ ANS SAQ ANSWERS LAQ ANSWER
Q1 d Q1 X= 1 Q1 2:1
Q2 b Q2 1:8 Q2 Do it
Q3 b Q3 6:7 Q3 4:3
Q4 a Q4 100 Q4 (i) 4:5
(ii) 4:9
Q5 a Q5 6 Q5 (i) 7:11
(ii) 7:18
(iii) 18:11
Q6 Ratio Q6 1250:3
Q7 1:3
Q8 Proportion
Q9 2:3
Q10 3:2
100
Page 8
Study Materials
Notes
Model Papers Class 6 Notes
Sample Papers Class 7 Notes
Half Yearly Sample Papers Class 8 Notes
Class 9 Notes
Important Resources
Class 10 Notes
Periodic Table
Class 11 Notes
Writing Skills / Formats
Maps of India / World Class 12 Notes
Books and Solutions
NCERT Books
NCERT Book Solutions
HC Verma Chapter Wise Solutions
RD Sharma Solutions
CGBSE Solutions
Notes
Model Papers Class 6 Notes
Sample Papers Class 7 Notes
Half Yearly Sample Papers Class 8 Notes
Class 9 Notes
Important Resources
Class 10 Notes
Periodic Table
Class 11 Notes
Writing Skills / Formats
Maps of India / World Class 12 Notes
Books and Solutions
NCERT Books
NCERT Book Solutions
HC Verma Chapter Wise Solutions
RD Sharma Solutions
CGBSE Solutions
Document Details
| Board / Org | Aglasem |
| Exam | Class 6 |
| Type | Notes |
| Pages | 8 |
| Language | english |
| Updated | 24 Sep 2026 |