NCERT Solutions for Class 6 Maths Chapter 12 Ratio and Proportion

Edited By Ramraj Saini | Updated on Apr 05, 2024 11:05 AM IST

NCERT Solutions for Class 6 Maths Chapter 12 Ratio and Proportion are discussed in this article. These NCERT solutions are created by the expert team at careers360 considering the latest CBSE syllabus 2024-25. 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 NCERT solutions for Class 6 Maths chapter 12 Ratio and Proportion.

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NCERT Solutions for Class 6 Maths Chapter 12 Ratio and Proportion - Important Formulae
NCERT Solutions for Class 6 Maths Chapter 12 Ratio and Proportion - Important Points
NCERT Solutions for Class 6 Maths Chapter 12 Ratio and Proportion
NCERT Class 6 Maths Chapter 12 Ratio and Proportion Topic 12.2 Ratio
NCERT Class 6 Maths Chapter 12 Ratio and Proportion Exercise 12.1
NCERT Class 6 Maths Chapter 12 Ratio and Proportion Topic 12.3 Proportion
NCERT Class 6 Maths Chapter 12 Ratio and Proportion Exercise 12.2
NCERT Class 6 Maths Chapter 12 Ratio and Proportion Topic 12.4 Unitary Method
NCERT Class 6 Maths Chapter 12 Ratio and Proportion Exercise 12.3
Ratio and Proportion Class 6 Maths Chapter 12-Topics
NCERT Solutions for Class 6 Mathematics Chapter Wise
Key Features of NCERT Solutions for Class 6 Maths Chapter 12:
NCERT Solutions for Class 6 - Subject Wise

$NCERT Solutions for Class 6 Maths Chapter 12 Ratio and Proportion$

NCERT Solutions for Class 6 Maths Chapter 12 Ratio and Proportion

It is advisable to also cover all the topics of NCERT Class 6 Maths Books to score well. If comparing quantities do not have the same unit, first convert them into the same unit and then find the ratio. Students must try to complete the NCERT Class 6 Maths Syllabus in at the earliest. You should try to solve all the NCERT questions by yourself so you won't these silly mistakes. You can take help from the NCERT Solutions for Class 6 .

NCERT Solutions for Class 6 Maths Chapter 12 Ratio and Proportion - Important Formulae

The ratio of a number ‘a’ to another number ‘b’ where b ≠ 0 is written as a fraction a/b also represented as a : b. Here the first term is a and the second term is b.
A ratio is said to be in the simplest form if its two terms have no common factor other than 1
The ratio of two numbers is usually expressed in its simplest form.
The ratio of two quantities is an abstract quantity, i.e., it has no units in itself.
An equality of two ratios is called a proportion. If a : b = c : d , then we write a : b :: c : d.
The numbers a, b, c, d are in proportion if the ratio of the first two is equal to the ratio of the last two, i.e., a : b = c : d.
If four numbers a, b, c, d are in proportion, then a and d are known as extreme terms and b and c are called middle terms.
Four numbers are in proportion if the product of extreme terms is equal to the product of middle terms, i.e., a : b :: c : d if and only if ad = bc.
From the terms of a given proportion, we can make three more proportions.
If a : b = b : c, then a, b, c are said to be in continued proportion.
if a, b, and c are in continued proportion, i.e., a : b :: b : c, then b is called the mean proportional between a and c.
Mean Proportion = b = √(ac)
Value of a given number of articles = (Value of one article) x (Number of articles)
Value of one article = (Value of given number of articles) / (Number of article).......... (Unitary Method)

For more, Download Ebook - NCERT Class 6 Maths: Chapterwise Important Formulas And Points

NCERT Solutions for Class 6 Maths Chapter 12 Ratio and Proportion - Important Points

Difference: The method of comparing quantities by taking the difference between them. It involves subtracting one quantity from another to determine the gap or distance between them.

Comparison by Ratio: A method of meaningful comparison between quantities by using division. It involves determining how many times one quantity is in relation to another quantity. The comparison is expressed in the form of a ratio, which represents the relative sizes or magnitudes of the quantities being compared.

Same Unit: In order to compare quantities by ratio, they must be expressed in the same unit. If the quantities are initially in different units, they need to be converted to a common unit before the ratio can be calculated.

Same Ratio in Different Situations: It is possible for the same ratio to occur in different contexts or situations. The ratio between two quantities remains constant regardless of the specific scenario in which it is being used.

Order of Ratios: The order in which quantities are taken to express their ratio is significant. The ratio 3:2 is distinct from the ratio 2:3, indicating that the position or arrangement of quantities in a ratio affects its meaning.

Ratio as a Fraction: A ratio can be treated as a fraction, with the numerator representing one quantity and the denominator representing another quantity. This allows for mathematical operations involving ratios, such as addition, subtraction, multiplication, and division.

Equivalent Ratios: Two ratios are considered equivalent if the fractions corresponding to them are equivalent. Ratios can be scaled up or down while maintaining their equivalence. For example, the ratio 3:2 is equivalent to 6:4 or 12:8.

Lowest Form of a Ratio: A ratio can be expressed in its simplest or lowest form by reducing it to its smallest possible integer values. For instance, the ratio 50:15 can be simplified to 10:3 by dividing both terms by their greatest common divisor.

Proportion: Four quantities are said to be in proportion if the ratio of the first and second quantities is equal to the ratio of the third and fourth quantities. Proportions establish relationships and comparisons between multiple sets of quantities.

Order in Proportions: The order of terms in a proportion is crucial. The arrangement of quantities must remain consistent across the ratios to ensure a valid proportion. Altering the order of terms can result in a different comparison or relationship.

Unitary Method: The unitary method is a technique used to solve problems involving proportions and ratios. It involves finding the value of one unit and then calculating the value of the desired number of units based on that reference. It is often used in solving problems related to cost, price, or measurement.

Free Download NCERT Solutions for Class 6 Maths Chapter 12 Ratio and Proportion For CBSE Exam

NCERT Solutions for Class 6 Maths Chapter 12 Ratio and Proportion

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NCERT Class 6 Maths Chapter 12 Ratio and Proportion Topic 12.2 Ratio

Question:1 In a class, there are 20 boys and 40 girls. What is the ratio of the number of boys to the number of girls?

Answer: number of boys = 20

number of girls = 40

$\frac{number \ of\ boys}{number\ of\ girls}=\frac{20}{40}=\frac{2}{4}=\frac{1}{2}$

So the required ratio is 1:2

Question:2 Ravi walks 6 km in an hour while Roshan walks 4 km in an hour What is the ratio of the distance covered by Ravi to the distance covered by Roshan?

Answer: The distance covered in one hour by Ravi = 6 Km

The distance covered in one hour by Roshan = 4 Km

$\frac{ The \ distance \ covered \ by \ Ravi }{ The \ distance \ covered \ by\ Roshan}=\frac{6}{4}=\frac{3}{2}$

So the required ratio is 3:2

Question:1 Saurabh takes 15 minutes to reach school from his house and Sachin takes one hour to reach school
from his house. Find the ratio of the time taken by Saurabh to the time taken by Sachin.

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

Question:2 Cost of a toffee is 50 paise and cost of a chocolate is rupees 10. Find the ratio of the cost of a toffee to the cost of a chocolate.

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

Question:3 In a school, there were 73 holidays in one year. What is the ratio of the number of holidays to the number of days in one year?

Answer: Number of holidays in a year = 73

Number of days in a year = 365

$\frac{number \ of \ holidays }{number \ of \ days \ in \ one \ year}=\frac{73}{365}=\frac{73}{73\times5}=\frac{1}{5}$

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 desks and 32 chairs then the ratio of number of desks and chairs is 8:32=1:4

Question:3 Find the number of students above twelve years of age in your class. Then, find the ratio of the number of students with age above twelve years and the remaining students.

Answer: suppose there are 40 students in the class and 5 students are above 12 years, then there are 40-5=35 students below or equal to 12 years.

Then the 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 a length of 10 cm and a breadth of 7 cm then the ratio of its length to its breadth=10:7

NCERT Class 6 Maths Chapter 12 Ratio and Proportion Exercise 12.1

Question: 1(a) There are $20$ girls and $15$ 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:

$=\frac{20}{15}=\frac{4}{3}=4:3$

Question: 1(b) There are $20$ girls and $15$ 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:

$=\frac{20}{20+15}=\frac{20}{35}=\frac{4}{7}=4:7$

Question: 2(a) 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 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:

$=\frac{6}{12}=\frac{1}{2}=1:2$

Question: 2 (b) 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 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:

$=\frac{12}{30}=\frac{6}{15}=\frac{2}{5}=2:5$

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.

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:

$\frac{3}{2}=3:2$

(b) Number of squares to all the figures inside the rectangle:

$\frac{2}{7}=2:7$

Question: 4 Distances travelled by Hamid and Akhtar in an hour are $9\; km$ and $12\; km.$ Find the ratio of speed of Hamid to the speed of Akhtar.

Answer: As we know,

$speed=\frac{distance}{time}$

So,

Speed of Hamid :

$speed=\frac{distance}{time}=\frac{9km}{1hour}=9km/h$

Speed of Akhtar :

$speed=\frac{distance}{time}=\frac{12km}{1hour}=12km/h$

Hence, the ratio of the speed of Hamid to the speed of Akhtar:

$\frac{9}{12}=\frac{3}{4}=3:4$ .

Question: 5 Fill in the following blanks:

$\frac{15}{18}=\frac{\square }{6}=\frac{10}{\square}=\frac{\square }{30}$ [Are these equivalent ratios?]

Answer: Equating all the fraction, we get

$\frac{15}{18}=\frac{5 }{6}=\frac{10}{12}=\frac{25 }{30}$

Yes, They are equivalent ratios.

Question: 6 Find the ratio of the following :

(a) $81 \; to \; 108$

(b) $98 \; to \; 63$

(d) $30$ minutes to $45$ minutes

Answer: (a)Ratio of $81 \; to \; 108$

$= \frac{81}{108}=\frac{27}{36}=\frac{3}{4}=3:4$

(b) Ratio of $98 \; to \; 63$

$= \frac{98}{63}=\frac{14}{9}=14:9$

$= \frac{33}{121}=\frac{3}{11}=3:11$

(d) The ratio of $30$ minutes to $45$ minutes

$= \frac{30}{45}=\frac{6}{9}=\frac{2}{3}=2:3$

Question: 7 Find the ratio of the following:

(a) $30$ minutes to $1.5$ hours

(b) $40\; cm$ to $1.5 \; cm$

(d) $500\; mL$ to $2\; litres$

Answer: (a) $30$ minutes to $1.5$ hours

As we know,

$1 \:hour = 60\:minutes$

So,

$1.5 \:hour =1.5\times 60=90\:minutes$

Hence the ratio of $30$ minutes to $1.5$ hours:

$\frac{30}{90}=\frac{3}{9}=\frac{1}{3}=1:3$

(b) $40\; cm$ to $1.5m$

As we know,

$1 \:m= 100\:cm$

So,

$1.5 \:m=1.5\times 100=150\:cm$

Hence the ratio of $40\; cm$ to $1.5 \:m=1.5\times 100=150\:m$

$\frac{40}{150}=\frac{4}{15}=4:15.$

As we know,

$1 \:rupee= 100\:paise$

Hence the ratio of $55$ paise to $Rs.1$

$\frac{55}{100}=\frac{11}{20}=11:20$

(d) $500\; mL$ to $2\; litres$

As we know,

$1 \:litre= 1000\:mL$

$2 \:litre= 2\times1000=2000\:mL$

Hence the ratio of $500\; mL$ to $2\; litres$ :

$\frac{500}{2000}=\frac{1}{4}=1:4$

Question: 8(a) In a year, Seema earns $Rs.1,50,000$ and saves $Rs.50,000$ . Find the ratio of Money that Seema earns to the money she saves.

Answer: Money that Seema earns = $Rs.1,50,000$

the money that Seema saves.= $Rs.50,000$

So, The ratio of Money that Seema earns to the money she saves:

$=\frac{150000}{50000}=\frac{3}{1}=3:1$ .

Hence the required ratio is 3:1.

Question: 8(b) In a year, Seema earns $Rs. 1,50,000$ and saves $Rs. 50,000$ . Find the ratio of Money that she saves to the money she spends.

Answer: Money that Seema earns = $Rs.1,50,000$

the money that Seema saves.= $Rs.50,000$

The amount of money Seema spends = $Rs\: 150,000-Rs\:50,000=100,000.$

So, The ratio of Money that she saves to the money she spends.

$=\frac{50000}{100000}=\frac{1}{2}=1:2$ .

Hence the required ratio is 1:2.

Question: 9 There are $102$ teachers in a school of $3300$ students. Find the ratio of the number of teachers to the number of students.

Answer: Given

Number of Teacher = 102

Number of students = 3300

So, the ratio of the number of teachers to the number of students:

$\frac{102}{3300}=\frac{17}{550}=17:550.$

Hence the required ratio is 17 : 550

Question: 10 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) Number of boys to the number of girls.

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:

$=\frac{2300}{4320}=\frac{230}{432}=\frac{115}{216}=115:216$

(b) The number of boys to the number of girls:

$=\frac{2020}{2300}=\frac{101}{115}=101:115$

$=\frac{2020}{4320}=\frac{101}{216}=101:216$

Question: 11 Out of $1800$ students in a school, $750$ opted basketball, $800$ opted cricket and remaining opted table tennis. If a student can opt only one game, find the ratio of

(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.

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:

$\frac{750}{250}=\frac{3}{1}=3:1$

(b) The number of students who opted cricket to the number of students opting basketball:

$\frac{800}{750}=\frac{16}{15}=16:15$

$\frac{750}{1800}=\frac{5}{12}=5:12$

Question: 12 Cost of a dozen pens is $Rs.180$ and cost of $8$ ball pens is $Rs.56$ . 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:

$=\frac{15}{7}=15:7$ .

Question: 13 Consider the statement: Ratio of breadth and length of a hall is $2:5,$ Complete the following table that shows some possible breadths and lengths of the hall.

Answer: Given Breadth and Length is in proportion $2:5,$

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 $20$ pens between Sheela and Sangeeta in the ratio of $3:2,$

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.

Sheela will have 3/5 of the total pen :

$=\frac{3}{5}\times20=3\times4=12$

and Sangeeta will have 2/5 of the total pen:

$=\frac{2}{5}\times20=2\times4=8$

Hence Sheela will get 12 pens and Sangeeta will get 8 pens.

Question: 15 Mother wants to divide $Rs.36$ between her daughters Shreya and Bhoomika in the ratio of their ages. If age of Shreya is $15$ years and age of Bhoomika is $12$ years, find how much Shreya and Bhoomika will get.

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:

$=\frac{15}{27}\times36$

$=\frac{15}{3}\times4$

$=5\times4$

$=20$ Rs .

Amount of money Sangeeta gets :

$=\frac{12}{27}\times36=\frac{12}{3}\times4=4\times4=16.$

Hence Shreya and Sangeeta get 20 Rs and 16 Rs respectively.

Question:1 6 Present age of father is $42$ years and that of his son is $14$ 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 the son was 12 years old.

(d) Age of father to the age of son when father was $30$ years old.

Answer: Given, Present age of father = $42$ years and that of his son = $14$ years.

The ratio of

(a) Present age of father to the present age of the son:

$=\frac{42}{14}=\frac{3}{1}=3:1$

(b) Age of the father to the age of the son, when the son was 12 years old:

$=\frac{42-2}{14-2}=\frac{40}{12}=\frac{10}{3}=10:3$

$=\frac{42+10}{14+10}=\frac{52}{24}=\frac{13}{6}=13:6.$

(d) Age of father to the age of son when father was 30 years old.

$=\frac{42-12}{14-12}=\frac{30}{2}=\frac{15}{1}=15:1$

NCERT Class 6 Maths Chapter 12 Ratio and Proportion Topic 12.3 Proportion

Question: Check whether the given ratios are equal, i.e. they are in proportion. If yes, then write them in the proper form.
1. 1 : 5 and 3 : 15
2. 2 : 9 and 18 : 81
3. 15 : 45 and 5 : 25
4. 4 : 12 and 9 : 27
5. ` 10 to ` 15 and 4 to 6

Answer: 1. 1 : 5 and 3 : 15

$\frac{3}{15}=\frac{3}{3\times5}=\frac{1}{5}$

So the ratios are in proportion
2. 2 : 9 and 18 : 81

$\frac{2}{9}=\frac{2\times9}{9\times9}=\frac{18}{81}$

So So the ratios are in proportion
3. 15 : 45 and 5 : 25

$\\\frac{15}{45}=\frac{1}{3}\\\frac{5}{25}=\frac{1}{5}$

The given ratios are not equal, so they are not in proportion
4. 4 : 12 and 9 : 27

$\\\frac{4}{12}=\frac{1}{3}\\\frac{9}{27}=\frac{1}{3}$

The given ratios are equal, so they are in proportion
5. ` 10 to ` 15 and 4 to 6

$\\\frac{10}{15}=\frac{2}{3}\\\frac{4}{6}=\frac{2}{3}$

The given ratios are equal, so they are in proportion

NCERT Class 6 Maths Chapter 12 Ratio and Proportion Exercise 12.2

Question: 1 Determine if the following are in proportion.

(a) $15,45,40,120$

(b) $33,121,9,96$

(d) $32,48,70,210$

(e) $4,6,8,12$

(f) $33,44,75,100$

Answer: (a) $15,45,40,120$

$\frac{15}{45}=\frac{1}{3}........(1)$

$\frac{40}{120}=\frac{1}{3}........(2)$

Since (1) and (2) are equal, Yes they are in proportion.

(b) $33,121,9,96$

$\frac{33}{121}=\frac{3}{11}........(1)$

$\frac{9}{96}=\frac{3}{32}........(2)$

Since (1) and (2) are not equal, No they are not in proportion.

$\frac{24}{28}=\frac{6}{7}........(1)$

$\frac{36}{48}=\frac{3}{4}........(2)$

Since (1) and (2) are not equal, No they are not in proportion.

(d) $32,48,70,210$

$\frac{32}{48}=\frac{2}{3}........(1)$

$\frac{70}{210}=\frac{1}{3}........(2)$

Since (1) and (2) are not equal, No they are not in proportion.

(e) $4,6,8,12$

$\frac{4}{6}=\frac{2}{3}........(1)$

$\frac{8}{12}=\frac{2}{3}........(2)$

Since (1) and (2) are equal, Yes they are in proportion.

(f) $33,44,75,100$

$\frac{33}{44}=\frac{3}{4}........(1)$

$\frac{75}{100}=\frac{3}{4}........(2)$

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 :

(a) $16:24::20:30$

(b) $21:6::35:10$

(d) $8:9::24:27$

(e) $5.2:3.9::3:4$

(f) $0.9:0.36::10:4$

Answer: (a) $16:24::20:30$

$\frac{16}{24}=\frac{2}{3}.......(1)$

$\frac{20}{30}=\frac{2}{3}.......(2)$

As we can see (1) and (2) are equal So, They are in proportion.

$16:24::20:30$

Hence the statement is True.

(b) $21:6::35:10$

$\frac{21}{6}=\frac{7}{2}.......(1)$

$\frac{35}{10}=\frac{7}{2}.......(2)$

As we can see (1) and (2) are equal So, They are in proportion.i.e

. $21:6::35:10$ .

Hence the statement is True.

$\frac{12}{18}=\frac{2}{3}.......(1)$

$\frac{28}{12}=\frac{7}{3}.......(2)$

As we can see (1) and (2) are not equal So, They are not in proportion.

Hence the statement is False.

(d) $8:9::24:27$

$\frac{8}{9}=\frac{8}{9}.......(1)$

$\frac{24}{27}=\frac{8}{9}.......(2)$

As we can see (1) and (2) are equal So, They are in proportion.i.e.

$8:9::24:27$

Hence the statement is True.

(e) $5.2:3.9::3:4$

$\frac{5.2}{3.9}=\frac{4}{3}.......(1)$

$\frac{3}{4}=\frac{3}{4}.......(2)$

As we can see (1) and (2) are not equal So, They are not in proportion.

Hence the statement is False.

(f) $0.9:0.36::10:4$

$\frac{0.9}{0.36}=\frac{10}{4}.......(1)$

$\frac{10}{4}=\frac{10}{4}.......(2)$

As we can see (1) and (2) are equal So, They are in proportion.i.e.

$0.9:0.36::10:4$

Hence the statement is True.

Question: 3 Are the following statements true?

(a) $40$ persons : $200$ persons = $Rs.15:Rs.75$

(b) $7.5$ litres : $15$ litres = $5\; kg:10\; kg$

(d) $32\; m:64\; m=6\; sec:12\; sec$

(e) $45\; km:60\; km=$ $12$ hours : $15$ hours

Answer: (a) $40$ persons : $200$ persons = $Rs.15:Rs.75$

$\frac{40}{200}=\frac{1}{5}.........(1)$

$\frac{15}{75}=\frac{1}{5}.........(2)$

As we can see (1) is equal to (2), They are in proportion.

Hence The statement is True.

(b) $7.5$ litres : $15$ litres = $5\; kg:10\; kg$

$\frac{7.5}{15}=\frac{1}{2}.........(1)$

$\frac{5}{10}=\frac{1}{2}.........(2)$

As we can see (1) is equal to (2), They are in proportion.

Hence The statement is True.

$\frac{99}{45}=\frac{11}{5}.........(1)$

$\frac{44}{20}=\frac{11}{5}.........(2)$

As we can see (1) is equal to (2), They are in proportion.

Hence The statement is True.

(d) $32\; m:64\; m=6\; sec:12\; sec$

$\frac{32}{64}=\frac{1}{2}.........(1)$

$\frac{6}{12}=\frac{1}{2}.........(2)$

As we can see (1) is equal to (2), They are in proportion.

Hence The statement is True.

(e) $45\; km:60\; km=$ $12$ hours : $15$ hours

$\frac{45}{60}=\frac{3}{4}.........(1)$

$\frac{12}{15}=\frac{4}{5}.........(2)$

As we can see (1) is not equal to (2), They are not in proportion.

Hence the statement is False.

Question: 4 Determine if the following ratios form a proportion. Also, write the middle terms and extreme terms where the ratios form a proportion.

(a) $25\; cm:1\; m\; and\; Rs.40:Rs.160$

(b) $39$ litres : $65$ litres and $6$ bottles : $10$ bottles

(d) $200\; mL:2.5\; litre\; and\; Rs.4:Rs.50$

Answer: (a) $25\; cm:1\; m\; and\; Rs.40:Rs.160$

$\frac{25}{100}=\frac{1}{4}...........(1)$

$\frac{40}{160}=\frac{1}{4}...........(2)$

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) $39$ litres: litres and $6$ bottles : $10$ bottles

$\frac{39}{65}=\frac{3}{5}...........(1)$

$\frac{6}{10}=\frac{3}{5}...........(2)$

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.

$\frac{2}{80}=\frac{1}{40}...........(1)$

$\frac{25}{626}=\frac{1}{25}...........(2)$

As we can see (1) and (2) are not equal, they are not in proportion.

(d) $200\; mL:2.5\; litre\; and\; Rs.4:Rs.50$

$\frac{200}{2500}=\frac{2}{25}...........(1)$

$\frac{4}{50}=\frac{2}{50}...........(2)$

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.

NCERT Class 6 Maths Chapter 12 Ratio and Proportion 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

NCERT Class 6 Maths Chapter 12 Ratio and Proportion Exercise 12.3

Question: 1 If the cost of $7\; m$ of cloth is $Rs.1470,$ find the cost of $5\; m$ of cloth.

Answer: Given,

Cost of 7 m cloth = Rs 1470

Cost of 1 m cloth :

$=\frac{1470}{7}=Rs\:210$

So,

Cost of 5 m cloth :

$=Rs\:210\times5=Rs\:1050$

Hence the cost of 5 m cloth is Rs 1050.

Question: 2 Ekta earns $Rs.3000$ in $10$ days. How much will she earn in $30$ days?

Answer: Given

Amount of money earned in 10 days:

$=Rs \:3000$

So,

Amount of money earned in 1 day :

$=\frac{3000}{10}=Rs\:300$

So,

Amount of Money earned in 30 days :

$30\times\:300=Rs\:9000$

Hence Ekta will earn 9000 Rs in 30 days.

Question: 3 If it has rained $276\; mm$ in the last $3\; days,$ days, how many cm of rain will fall in one full week $(7\; days)$ ? Assume that the rain continues to fall at the same rate.

Answer: Given

The measure of rain in 3 days :

$=276\; mm$

So,

The measure of rain in 1 day :

$=\frac{276}{3}=92\; mm$

And Hence,

The measure of rain in 7 days :

$=7\times92=644\; mm$

Therefore, 644 mm rain will fall in a week.

Question: 4(a) Cost of 5 kg of wheat is $Rs. 91.50.$

What will be the cost of $8\; kg$ of wheat?

Answer: Given,

The cost of 5 kg of wheat:

$=Rs \:91.50$

So,

The cost of 1 kg of wheat :

$=\frac{91.50}{5}=Rs\:18.30$

And Hence,

The cost of 8 kg of wheat :

$=8\times\:18.30=Rs\:146.40$

Therefore, the cost of 8 kg of wheat is Rs 146.40.

Question: 4(b) Cost of $5\; kg$ of wheat is $Rs.91.50.$

What quantity of wheat can be purchased in $Rs.183?$

Answer: Given,

The cost of 5 kg of wheat:

$=Rs \:91.50$

So,

The cost of 1 kg of wheat :

$=\frac{91.50}{5}=Rs\:18.30$

So, The amount of wheat which can be bought in Rs 183:

$=\frac{183}{18.3}=10kg$

Hence 10 kg of wheat can be bought in Rs 183.

Question: 5 The temperature dropped $15$ degree celsius in the last $30$ days. If the rate of temperature drop remains the same, how many degrees will the temperature drop in the next ten days?

Answer: Temperature drop in 30 days :

$=15^o$

So, Temperature drop in 1 day :

$=\frac{15}{30}=\frac{1}{2}=0.5^o$

And Hence, The Temperature drop in 10 days :

$=10\times0.5^o=5^o$

Hence if the temperature rate remains the same, there will be a drop of 5 degrees in the next 10 days.

Question: 6 Shaina pays $Rs.15000$ as rent for 3 months. How much does she has to pay for a whole year, if the rent per month remains same?

Answer: Given

Rent of 3 months :

$=Rs \:15000$

So,

Rent of 1 month :

$=\frac{15000}{3}=Rs \:5000$

And Hence Using unity principle

Rent of 1 year (12 months ) :

$=12\times\:5000=Rs\:60000$

Therefore, The total rent for one year is Rs 60000.

Question: 7 Cost of 4 dozen bananas is $Rs.180.$ How many bananas can be purchased for $Rs.90?$

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 :

$=\frac{48}{180}=\frac{4}{15}$

So, the number of bananas we can buy in Rs 90:

$=90\times\frac{4}{15}=24$

Hence we can buy 24 bananas in Rs 90.

Question: 8 The weight of 72 books is $9\; kg.$ What is the weight of 40 such books?

Answer: Given,

The weight of 72 books = 9 kg

So, The weight of 1 book :

$=\frac{9}{72}=\frac{1}{8}kg$

And hence,

The weight of 40 such books:

$=40\times\frac{1}{8}=5kg$

Hence, the weight of 40 books will be 5 kg.

Question: 9 A truck requires $108\; litres$ of diesel for covering a distance of $594\; km$ .How much diesel will be required by the truck to cover a distance of $1650\; km?$

Answer: Given

Diesel requires for covering 594 km = 108 litres

So,

Diesel requires for covering 1 km :

$=\frac{108}{594}=\frac{2}{11}L$

And hence,

Diesel requires for covering 1650 km :

$=1650\times\frac{2}{11}=300L$

Hence The truck will require 300 litres of diesel to cover the distance of 1650 km.

Question: 10 Raju purchases $10$ pens for $Rs.150$ and Manish buys $7$ pens for $Rs.84.$ Can you say who got the pens cheaper?

Answer: Cost of Raju's 10 pens = Rs 150

Cost of Raju's 1 pen :

$=\frac{150}{10}=Rs \:15$

And

Cost of Manish's 7 pens = Rs 84

Cost of Manish's 1 pen;

$=\frac{84}{7}=Rs \:12$

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 $42$ runs in $6$ overs and Anup made $63$ runs in $7$ overs. Who made more runs per over?

Answer: Anish's Case:

runs in 6 overs = 42

So, runs in 1 over:

$=\frac{42}{6}=7$

Anup's Case:

Run in 7 overs = 63

So, Runs in 1 over :

$=\frac{63}{7}=9$

As we can see Anup made more runs per over.

Ratio and Proportion Class 6 Maths Chapter 12-Topics

Ratio
Proportion
Unitary Method

Also Check

NCERT Books and NCERT Syllabus

NCERT Solutions for Class 6 Mathematics Chapter Wise

Chapters No.	Chapters Name
Chapter - 1	Knowing Our Numbers
Chapter - 2	Whole Numbers
Chapter - 3	Playing with Numbers
Chapter - 4	Basic Geometrical Ideas
Chapter - 5	Understanding Elementary Shapes
Chapter - 6	Integers
Chapter - 7	Fractions
Chapter - 8	Decimals
Chapter - 9	Data Handling
Chapter -10	Mensuration
Chapter -11	Algebra
Chapter -12	Ratio and Proportion
Chapter -13	Symmetry
Chapter -14	Practical Geometry

Key Features of NCERT Solutions for Class 6 Maths Chapter 12:

Expertly Crafted Solutions: The NCERT Solutions for class 6 chapter 12 maths are skillfully developed to offer clear and accurate explanations for all the problems and concepts discussed in the chapter.

Conceptual Clarity: The NCERT Maths book Class 6 Chapter 12 solutions aim to enhance students' conceptual understanding by presenting complex topics in a simplified and easy-to-understand manner.

Comprehensive Coverage: The Maths Class 6 Chapter 12 solutions cover all the important topics and subtopics, ensuring that students grasp the complete essence of the chapter.

Exam-Focused Approach: The NCERT Class 6 Maths Chapter 12 solutions are designed with a focus on exam preparation, equipping students with essential tools and techniques to tackle questions effectively and score well in their exams.

NCERT Solutions for Class 6 - Subject Wise

NCERT Solutions for Class 6 Maths

NCERT Solutions for Class 6 Science

Benefits of NCERT Solutions for Class 6 Maths Chapter 12 Ratio and Proportion-

You will get NCERT Solutions for this chapter very easily.
You will get some new way to solve some specific problems.
All the questions in CBSE NCERT solutions for Class 6 Maths chapter 12 ratio and proportion are explained in a step-by-step manner so it will be very easy for you to understand the concept. Students can practice ratio and proportion questions for class 6 from PDF provided at careers360 website.
It is going to help you with your homework as all the practice questions given below every topic are also covered in this article.
It will help you understand the concept as well as solving some real-life problems.

Happy learning!

Also Read

NCERT Solutions for Class 6 Science Chapter 3 Fibre to Fabric

NCERT Solutions for Class 6 Science Chapter 2 Components of Food

NCERT Solutions for Class 6 Science Chapter 1 Food Where Does It Come From

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes

NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry

NCERT Solutions for Class 6 Maths Chapter 13 Symmetry

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Option 1) $0.34\; J$	Option 2) $0.16\; J$
Option 3) $1.00\; J$	Option 4) $0.67\; J$

Option 1) $2,000 \; J - 5,000\; J$	Option 2) $200 \, \, J - 500 \, \, J$
Option 3) $2\times 10^{5}J-3\times 10^{5}J$	Option 4) $20,000 \, \, J - 50,000 \, \, J$

Option 1) $K/2\,$	Option 2) $\; K\;$
Option 3) $zero\;$	Option 4) $K/4$

Option 1) $11.2\, L\, H_{2(g)}$ at STP is produced for every mole $HCL_{(aq)}$ consumed	Option 2) $6L\, HCl_{(aq)}$ is consumed for ever $3L\, H_{2(g)}$ produced
Option 3) $33.6 L\, H_{2(g)}$ is produced regardless of temperature and pressure for every mole Al that reacts	Option 4) $67.2\, L\, H_{2(g)}$ at STP is produced for every mole Al that reacts .

Option 1) 0.02	Option 2) 3.125 × 10^-2
Option 3) 1.25 × 10^-2	Option 4) 2.5 × 10^-2

Option 1) decrease twice	Option 2) increase two fold
Option 3) remain unchanged	Option 4) be a function of the molecular mass of the substance.

Option 1) Molality	Option 2) Weight fraction of solute
Option 3) Fraction of solute present in water	Option 4) Mole fraction.

Option 1) twice that in 60 g carbon	Option 2) 6.023 × 10²²
Option 3) half that in 8 g He	Option 4) 558.5 × 6.023 × 10²³

Option 1) less than 3	Option 2) more than 3 but less than 6
Option 3) more than 6 but less than 9	Option 4) more than 9

NCERT Solutions for Class 6 Maths Chapter 12 Ratio and Proportion

NCERT Solutions for Class 6 Maths Chapter 12 Ratio and Proportion - Important Formulae

NCERT Solutions for Class 6 Maths Chapter 12 Ratio and Proportion - Important Points

NCERT Solutions for Class 6 Maths Chapter 12 Ratio and Proportion

NCERT Class 6 Maths Chapter 12 Ratio and Proportion Topic 12.2 Ratio

NCERT Class 6 Maths Chapter 12 Ratio and Proportion Exercise 12.1

NCERT Class 6 Maths Chapter 12 Ratio and Proportion Topic 12.3 Proportion

NCERT Class 6 Maths Chapter 12 Ratio and Proportion Exercise 12.2

NCERT Class 6 Maths Chapter 12 Ratio and Proportion Topic 12.4 Unitary Method

NCERT Class 6 Maths Chapter 12 Ratio and Proportion Exercise 12.3

Ratio and Proportion Class 6 Maths Chapter 12-Topics

NCERT Solutions for Class 6 Mathematics Chapter Wise

Key Features of NCERT Solutions for Class 6 Maths Chapter 12:

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Benefits of NCERT Solutions for Class 6 Maths Chapter 12 Ratio and Proportion-

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