NCERT Solutions for Class 6 Maths Chapter 12 Ratio and Proportion
NCERT solutions for class 6 maths chapter 12 Ratio and Proportion: In our daily life, we compare things like he is taller than me by 10 cm, Ramesh got double of my marks in maths. The first statement is a comparison which means that the difference in height of both is 10 cm. The second statement is showing the ratio of marks. You can say that the ratio of marks obtained by Ramesh and it is 2: 1. In this article, you will get CBSE NCERT solutions for class 6 maths chapter 12 ratio and proportion. The second important topic of this chapter is proportion. If the ratio of the first two quantities is equal to the next two quantities then the 4 quantities are said to be in proportion. There are 15 questions explained in exercise 12.2 and exercise 12.3 with solutions for NCERT for class 6 maths chapter 12 Ratio and Proportion which will give you more clarity of the concept. For the comparison using ratios, the comparing quantities must have the same unit otherwise it will not give the right ratio. If comparing quantities do not have the same unit, first convert them into the same unit and then find the ratio. For example, if you want to find a ratio of 500 grams and 1 kilogram. So 1kg=1000g and the now the ratio is 500: 10000 or 1:2. Here order is very important if you have asked about the ratio of 1Kg and 500g, it would be 2:1. Since 1:2 not equal to 2:1 be careful about the order of the ratio. You should try to solve all the NCERT questions by yourself so you won't these silly mistakes. You can take help from the CBSE NCERT solutions for class 6 maths chapter 12 ratio and proportion. You can get NCERT solutions from class 6 to 12 for science and maths by clicking on the above link.
The main topics of NCERT Solutions for Class 6 Maths Chapter 12 are given below
12.1 Introduction
12.2 Ratio
12.3 Proportion
12.4 Unitary Method
Here are the NCERT Solutions for Class 6 Maths Chapter 12 Ratio and Proportion:
Solutions of NCERT for class 6 maths chapter 12 ratio and proportion topic 12.2 ratio
Answer:
number of boys = 20
number of girls = 40
So the required ratio is 1:2
Answer:
The distance covered in one hour by Ravi = 6 Km
The distance covered in one hour by Roshan = 4 Km
So the required ratio is 3:2
Answer:
Time taken by Saurabh = 15 minutes
Time taken by Sachin= 1 hour = 60 minutes. To find ratios we have to convert the given quantities to the same units. Here we are expressing both the quantities in minutes
the ratio of the time taken by Saurabh to the time taken by Sachin= 15:60=1:4
Answer:
Cost of toffee = 50 paise
cost of chocolate = 10 rupees
1rupee = 100 paise
Therefore, 10rupee = 1000 paise
So, the cost of chocolate = 1000 paise
the ratio of the cost of toffee to the cost of chocolate=50:1000=1:20
Answer:
Number of holidays in a year = 73
Number of days in a year = 365
the ratio of the number of holidays to the number of days in one year= 1:5
Question:1 Find the ratio of number of notebooks to the number of books in your bag.
Answer:
If there are 3 notebooks and 4 books in the bag then the ratio of the number of notebooks to the number of books =3:4
Question:2 Find the ratio of number of desks and chairs in your classroom.
Answer:
If there are 8 desk and 32 chairs then the ratio of number of desks and chairs is 8:32=1:4
Answer:
suppose there are 40 students in the class and 5 students are above 12 years, then there are 405=35 students below or equal to 12 years.
Then he ratio of the number of students with age above twelve years and the remaining students = 5:35=1:7
Question:4 Find the ratio of number of doors and the number of windows in your classroom.
Answer:
If there are four windows and one door then the ratio of the number of doors and the number of windows =1:4
Question:5 Draw any rectangle and find the ratio of its length to its breadth.
Answer:
Suppose a rectangle has length 10 cm and breadth of 7 cm then ratio of its length to its breadth=10:7
NCERT solutions for class 6 maths chapter 12 ratio and proportionExercise: 12.1
Question: 1(a) There are girls and boys in a class. What is the ratio of number of girls to the number of boys?
Answer:
Given,
Number of boys = 15
Number of girls = 20
So,
The ratio of the number of girls to the number of boys:
Question: 1(b) There are girls and boys in a class. What is the ratio of number of girls to the total number of students in the class?
Answer:
Given,
Number of boys = 15
Number of girls = 20
Total number of students = 15 + 20 = 35.
the ratio of the number of girls to the total number of students in the class:
Question: 2(a) Out of students in a class, like football, like cricket and remaining like tennis. Find the ratio of Number of students liking football to number of students liking tennis.
Answer:
Given,
Total Number of a student = 30
Number of students who like football = 6
Number of students who like cricket = 12
Number of remaining student wh play tennis = 30  6  12
= 12
Now,
The ratio of Number of students liking football to the number of students liking tennis:
Question: 2 (b) Out of students in a class, like football, like cricket and remaining like tennis. Find the ratio of Number of students liking cricket to total number of students.
Answer:
Given,
Total Number of a student = 30
Number of students who like football = 6
Number of students who like cricket = 12
Number of remaining student wh play tennis = 30  6  12
= 12
Now, The ratio of Number of students liking cricket to the total number of students:
Question: 3 See the figure and find the ratio of
(a) Number of triangles to the number of circles inside the rectangle.
(b) Number of squares to all the figures inside the rectangle.
(c) Number of circles to all the figures inside the rectangle.
Answer:
From the figure, we can see that inside the rectangle,
Number of triangles = 3
Number of squares = 2
Number of circles = 2
So,
(a) The number of triangles to the number of circles inside the rectangle:
(b) Number of squares to all the figures inside the rectangle:
(c) The number of circles to all the figures inside the rectangle:
Answer:
As we know,
So,
Speed of Hamid :
Speed of Akhtar :
Hence, the ratio of the speed of Hamid to the speed of Akhtar:
.
Question: 5 Fill in the following blanks:
[Are these equivalent ratios?]
Answer:
Equating all the fraction, we get
Yes, They are equivalent ratios.
Question: 6 Find the ratio of the following :
Answer:
(a)Ratio of
(b) Ratio of
(c) Ratio of to
(d) The ratio of minutes to minutes
Question: 7 Find the ratio of the following:
Answer:
(a) minutes to hours
As we know,
So,
Hence the ratio of minutes to hours:
(b) to
As we know,
So,
Hence the ratio of to
(c) paise to
As we know,
Hence the ratio of paise to
(d) to
As we know,
So
Hence the ratio of to :
Question: 8(a) In a year, Seema earns and saves . Find the ratio of Money that Seema earns to the money she saves.
Answer:
Money that Seema earns =
the money that Seema saves.=
So, The ratio of Money that Seema earns to the money she saves:
.
Hence the required ratio is 3:1.
Question: 8(b) In a year, Seema earns and saves . Find the ratio of Money that she saves to the money she spends.
Answer:
Money that Seema earns =
the money that Seema saves.=
The amount of money Seema spends =
So, The ratio of Money that she saves to the money she spends.
.
Hence the required ratio is 1:2.
Answer:
Given
Number of Teacher = 102
Number of students = 3300
So, the ratio of the number of teachers to the number of students:
Hence the required ratio is 17 : 550
Question: 10 In a college, out of students, are girls. Find the ratio of
(a) Number of girls to the total number of students.
(b) Number of boys to the number of girls.
(c) Number of boys to the total number of students.
Answer:
Given
Total number of students = 4320
Number of girls = 2300
The number of boys = 4320  2300
= 2020
So,
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:
(a) Number of students who opted basketball to the number of students who opted table tennis.
(b) Number of students who opted cricket to the number of students opting basketball.
(c) Number of students who opted basketball to the total number of students.
Answer:
Total number of students = 1800
Number of students who opted for basketball = 750
Number of students who opted for cricket= 800
Number of students who opted for Table Tennis = 1800  750  800
= 250
Now,
The ratio of
(a) The number of students who opted basketball to the number of students who opted table tennis:
(b) The number of students who opted cricket to the number of students opting basketball:
(c) The number of students who opted basketball to the total number of students:
Question: 12 Cost of a dozen pens is and cost of ball pens is . Find the ratio of the cost of a pen to the cost of a ball pen.
Answer:
Cost of 12 ( a dozen ) pens = Rs 180
Cost of 1 pen = 180 / 12 = Rs 15
Cost of 8 ball pens = Rs 56
Cost of 1 ball pen = 56 / 8 = Rs 7
So,
the ratio of the cost of a pen to the cost of a ball pen:
.
Answer:
Given Breadth and Length is in proportion
Maintaining that proportion, we get.
Breadth of the hall (in m) 
10 
20 
40 
Length of the hall (in m) 
25 
50 
100 
Question: 14 Divide pens between Sheela and Sangeeta in the ratio of
Answer:
Given
Total number of pens = 20
The required ratio between Sheela and Sangeeta = 3 : 2
On adding the numbers in ratio we get 3 + 2 = 5.
So
Sheela will have 3/5 of the total pen :
and Sangeeta will have 2/5 of the total pen:
Hence Sheela will get 12 pens and Sangeeta will get 8 pens.
Answer:
Given,
Total money = Rs 36
Bhoomikas age = 12 years
Shreya's age = 15 years.
Now According to the question,
we are dividing 36 in ratio 15 : 12.
So, the sum of number in ratio = 15 + 12 = 27
Hence
amount of money Shreya gets:
Rs .
Amount of money Sangeeta gets :
Hence Shreya and Sangeeta get 20 Rs and 16 Rs respectively.
Question:1 6 Present age of father is years and that of his son is years. Find the ratio of
(a) Present age of father to the present age of son.
(b) Age of the father to the age of son, when son was years old.
(c) Age of father after years to the age of son after years.
(d) Age of father to the age of son when father was years old.
Answer:
Given, Present age of father = years and that of his son = years.
The ratio of
(a) Present age of father to the present age of the son:
(b) Age of the father to the age of the son, when the son was 12 years old:
(c) Age of father after 10 years to the age of son after 10 years:
(d) Age of father to the age of son when father was 30 years old.
NCERT solutions for class 6 maths chapter 12 ratio and proportion topic 12.3 proportion
Answer:
1. 1 : 5 and 3 : 15
So the ratios are in proportion
2. 2 : 9 and 18 : 81
So So the ratios are in proportion
3. 15 : 45 and 5 : 25
The given ratios are not equal, so they are not in proportion
4. 4 : 12 and 9 : 27
The given ratios are equal, so they are in proportion
5. ` 10 to ` 15 and 4 to 6
The given ratios are equal, so they are in proportion
Solutions of NCERT for class 6 maths chapter 12 ratio and proportionExercise: 12.2
Question: 1 Determine if the following are in proportion.
Answer:
(a)
Since (1) and (2) are equal, Yes they are in proportion.
(b)
Since (1) and (2) are not equal, No they are not in proportion.
(c)
Since (1) and (2) are not equal, No they are not in proportion.
(d)
Since (1) and (2) are not equal, No they are not in proportion.
(e)
Since (1) and (2) are equal, Yes they are in proportion.
(f)
Since (1) and (2) are equal, Yes they are in proportion.
Question: 2 Write True ( T ) or False ( F ) against each of the following statements :
Answer:
(a)
As we can see (1) and (2) are equal So, They are in proportion.
Hence the statement is True.
(b)
As we can see (1) and (2) are equal So, They are in proportion.i.e
. .
Hence the statement is True.
(c)
As we can see (1) and (2) are not equal So, They are not in proportion.
Hence the statement is False.
(d)
As we can see (1) and (2) are equal So, They are in proportion.i.e.
Hence the statement is True.
(e)
As we can see (1) and (2) are not equal So, They are not in proportion.
Hence the statement is False.
(f)
As we can see (1) and (2) are equal So, They are in proportion.i.e.
Hence the statement is True.
Question: 3 Are the following statements true?
Answer:
(a) persons : persons =
As we can see (1) is equal to (2), They are in proportion.
Hence The statement is True.
(b) litres : litres =
As we can see (1) is equal to (2), They are in proportion.
Hence The statement is True.
(c) =
As we can see (1) is equal to (2), They are in proportion.
Hence The statement is True.
(d)
As we can see (1) is equal to (2), They are in proportion.
Hence The statement is True.
(e) hours : hours
As we can see (1) is not equal to (2), They are not in proportion.
Hence the statement is False.
(b) litres : litres and bottles : bottles
Answer:
(a)
As we can see (1) and (2) are equal, they are in proportion.
Middle Terms: 1 m and Rs 40
Extreme Terms: 25 cm and Rs 160.
(b) litres: litres and bottles : bottles
As we can see (1) and (2) are equal, they are in proportion.
Middle Terms: 65 litres and 6 bottles
Extreme Terms: 39 litres and 10 bottles.
(c)
As we can see (1) and (2) are not equal, they are not in proportion.
(d)
As we can see (1) and (2) are equal, they are in proportion.
Middle Terms: 2.5 litres and Rs 4
Extreme Terms:200 mL and Rs 50.
Solutions for class 6 maths chapter 12 ratio and proportions topic 12.4 unitary method
Question:2 Read the table and fill in the boxes.
Answer:
Time 
Distance travelled by Karan 
Distance travelled by Kriti 
2 hours 
8 
6 
1 hour 
4 
3 
4 hours 
16 
12 
Distance travelled in 1 hour will be half of the distance travelled in 2 hours. Distance travelled in 4 hours will be double of the distance travelled in 2 hours
CBSE NCERT solutions for class 6 maths chapter 12 ratio and proportionExercise: 12.3
Question: 1 If the cost of of cloth is find the cost of of cloth.
Answer:
Given,
Cost of 7 m cloth = Rs 1470
So
Cost of 1 m cloth :
So,
Cost of 5 m cloth :
Hence the cost of 5 m cloth is Rs 1050.
Question: 2 Ekta earns in days. How much will she earn in days?
Answer:
Given
Amount of money earned in 10 days:
So,
Amount of money earned in 1 day :
So,
Amount of Money earned in 30 days :
Hence Ekta will earn 9000 Rs in 30 days.
Answer:
Given
The measure of rain in 3 days :
So,
The measure of rain in 1 day :
And Hence,
The measure of rain in 7 days :
Therefore, 644 mm rain will fall in a week.
Question: 4(a) Cost of 5 kg of wheat is
What will be the cost of of wheat?
Answer:
Given,
The cost of 5 kg of wheat:
So,
The cost of 1 kg of wheat :
And Hence,
The cost of 8 kg of wheat :
Therefore, the cost of 8 kg of wheat is Rs 146.40.
Question: 4(b) Cost of of wheat is
What quantity of wheat can be purchased in
Answer:
Given,
The cost of 5 kg of wheat:
So,
The cost of 1 kg of wheat :
So, The amount of wheat which can be bought in Rs 183:
Hence 10 kg of wheat can be bought in Rs 183.
Answer:
Temperature drop in 30 days :
So, Temperature drop in 1 day :
And Hence, The Temperature drop in 10 days :
Hence if the temperature rate remains the same, there will be a drop of 5 degrees in the next 10 days.
Answer:
Given
Rent of 3 months :
So,
Rent of 1 month :
And Hence Using unity principle
Rent of 1 year (12 months ) :
Therefore, The total rent for one year is Rs 60000.
Question: 7 Cost of 4 dozen bananas is How many bananas can be purchased for
Answer:
Given,
Number of bananas we can buy in Rs 180 = 4 dozen = 12 x 4 = 48
The number of bananas we can buy in Rs 1 :
So, the number of bananas we can buy in Rs 90:
Hence we can buy 24 bananas in Rs 90.
Question: 8 The weight of 72 books is What is the weight of 40 such books?
Answer:
Given,
The weight of 72 books = 9 kg
So, The weight of 1 book :
And hence,
The weight of 40 such books:
Hence, the weight of 40 books will be 5 kg.
Question: 9 A truck requires of diesel for covering a distance of .How much diesel will be required by the truck to cover a distance of
Answer:
Given
Diesel requires for covering 594 km = 108 litres
So,
Diesel requires for covering 1 km :
And hence,
Diesel requires for covering 1650 km :
Hence The truck will require 300 litres of diesel to cover the distance of 1650 km.
Question: 10 Raju purchases pens for and Manish buys pens for Can you say who got the pens cheaper?
Answer:
Cost of Raju's 10 pens = Rs 150
Cost of Raju's 1 pen :
And
Cost of Manish's 7 pens = Rs 84
Cost of Manish's 1 pen;
As we can see the cost of Raju's 1 pen is 15 and the cost of Manish's 1 pen is 12, Manish got the pen at a cheaper rate.
Question: 11 Anish made runs in overs and Anup made runs in overs. Who made more runs per over?
Answer:
Anish's Case:
runs in 6 overs = 42
So, runs in 1 over:
Anup's Case:
Run in 7 overs = 63
So, Runs in 1 over :
As we can see Anup made more runs per over.
NCERT Solutions for Class 6 Mathematics  Chapterwise
Chapters No. 
Chapters Name 
Chapter  1 
Solutions of NCERT for class 6 maths chapter 1 Knowing Our Numbers 
Chapter  2 
CBSE NCERT solutions for class 6 maths chapter 2 Whole Numbers 
Chapter  3 
NCERT solutions for class 6 maths chapter 3 Playing with Numbers 
Chapter  4 
Solutions of NCERT for class 6 maths chapter 4 Basic Geometrical Ideas 
Chapter  5 
CBSE NCERT solutions for class 6 maths chapter 5 Understanding Elementary Shapes 
Chapter  6 

Chapter  7 

Chapter  8  
Chapter  9 
CBSE NCERT solutions for class 6 maths chapter 9 Data Handling 
Chapter 10 

Chapter 11 

Chapter 12 
CBSE NCERT solutions for class 6 maths chapter 12 Ratio and Proportion 
Chapter 13 

Chapter 14 
Solutions of NCERT for class 6 maths chapter 14 Practical Geometry 
NCERT Solutions for Class 6  Subject wise
Benefits of NCERT solutions for class 6 maths chapter 12 ratio and proportion

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All the questions in CBSE NCERT solutions for class 6 maths chapter 12 ratio and proportion are explained in a stepbystep manner so it will be very easy for you to understand the concept.
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 It will help you understand the concept as well as solving some reallife problems.
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