NCERT SOLUTIONS FOR CLASS 6 MATHS EXERCISE 12.1

Find here step by step NCERT Solutions for Class 6 Maths Exercise 12.1 Chapter 12 Ratio & Proportion. NCERT SOLUTIONS FOR CLASS 6 MATHS EXERCISE 12.1 deals with the Idea of Comparison by Division commonly known as Ratio.

Prerequisite / Revise this

Comparison By Division : Ratio

Comparison by Difference – For comparing quantities of the same type, we commonly use the method of taking difference between the quantities.

Comparison by Division – In many situations, a more meaningful comparison between quantities is made by using division, i.e. by seeing how many times one quantity is to the other quantity. This method is known as comparison by ratio.

For comparison by ratio, the two quantities must be in the same unit. If they are not, they should be expressed in the same unit before the ratio is taken.

Order of a Ratio – the order in which quantities are taken to express their ratio is important. The ratio 5 : 2 is different from 2 : 5.

Ratio as a Fraction – A ratio may be treated as a fraction, thus the ratio 5 : 2 may be written as 5/2 .

Equivalent Ratios – Two ratios are equivalent, if the fractions corresponding to them are equivalent. Thus, 5 : 2 is equivalent to 10 : 4 or 20 : 8.

Simplest Form of a Ratio – A ratio can be expressed in its lowest form. For example, ratio 15 : 9 is treated as 15/9 ; in its lowest form 15/9 = 5/3 . Hence, the lowest form of the ratio 15 : 9 is 5 : 3.

Exercise 12.1
Finding Ratio

QUESTION 1

There are 20 girls and 15 boys in a class.
(a) What is the ratio of number of girls to the number of boys?
(b) What is the ratio of number of girls to the total number of students in the class?

ANSWER

(a) Number of girls = 20,

Numbers of boys = 15,

So, ratio of number of girls to the number of boys = \frac{20}{15}
=\frac{4}{3}= 4:3

(b) Total number of students = 20 + 15 = 35,
So

So, ratio of number of girls to the total number of students = \frac{20}{15}
=\frac{4}{3}= 4:3

QUESTION 2

Out of 30 students in a class, 6 like football, 12 like cricket and remaining like tennis. Find the ratio of
(a) Number of students liking football to number of students liking tennis.
(b) Number of students liking cricket to total number of students.

ANSWER

Total number of students in the class = 30,

Number of students who like football = 6,

Number of students who like cricket = 12,

(a) Number of students who like tennis = 30 – (6 + 12)
= 30 – 18 = 12,

So, ratio of number of students liking football to number of students liking tennis = \frac{6}{12}
=\frax{1}{2}= 1:2

(b) Ratio of number of students liking cricket to total number of students =\frac{12}{30}
=\frac{2}{5}=2:5

QUESTION 3

See the figure and find the ratio of

NCERT SOLUTIONS FOR CLASS 6 MATHS EXERCISE 12.1

(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

Inside the rectangle,

Number of circles = 2,
Number of squares = 2,
Number of triangles = 3,
Toatal number of figures = 7,

(a) Ratio of number of triangles to the number of circles inside the rectangle =\frac{3}{2}=3:2

(b) Ratio of number of squares to all the figures inside the rectangle =\frac{2}{7}=2:7

(c) Ratio of number of circles 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

Speed of Hamid = 9 km/hour

Speed of Akhtar = 12 km/hour

So, Ratio of speed of Hamid to to the speed of Akhtar =\frac{9}{12}=3:4

QUESTION 5
Fill in the following blanks:
\frac{15}{18}=\frac{\framebox{}}{6}=\frac{10}{\framebox{}}=\frac{\framebox{}}{30}
[Are these equivalent ratios?]

ANSWER

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

Yes, these are equivalent ratios.

QUESTION 6

Find the ratio of the following :
(a) 81 to 108 (b) 98 to 63
(c) 33 km to 121 km (d) 30 minutes to 45 minutes

ANSWER

(a) 81 to 108 = \frac{81}{108} =\frac{3}{4} = 3:4

(b) 98 to 63 = \frac{98}{63} =\frac{14}{9} = 14:9

(c) 33 km to 121 km = \frac{33}{121} =\frac{3}{11} = 3:11

(d) 30 minutes to 45 minutes = \frac{30}{45} =\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 m
(c) 55 paise to ₹ 1
(d) 500 ml to 2 litres

ANSWER

(a) 1.5 hours = 1.5 × 60 minutes = 90 minutes

So, ratio of 30 minutes to 1.5 hours = \frac{30\, minutes}{90\, minutes} =\frac{1}{3} = 1:3

(b) 1.5 m = 1.5 × 100 cm = 150 cm

So, ratio of 40 cm to 1.5 m = \frac{40\,cm}{150\,cm} =\frac{4}{15} = 4:15

(c) ₹ 1 = 100 paise

So, ratio of 55 paise to ₹ 1 = \frac{55\,paise}{100\,paise} =\frac{11}{20} = 11:20

(d) 2 litres = 2 × 1000 ml = 2000 ml

So, ratio of 500 ml to 2 litres = \frac{500}{2000} =\frac{1}{4} = 1:4

QUESTION 8

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

ANSWER

In a year,
Seema earns = ₹ 1,50,000,
Seema saves = ₹ 50,000
So, money she spends = ₹ (1,50,000 – 50,000) = ₹ 1,00,000

Then,

(a) Ratio of money that Seema earns to the money she saves =\frac{1,50,000}{50,000}
=\frac{3}{1}=3:1

(b) Ratio of money that she saves to the money she spends =\frac{50,000}{1,00,000}
=\frac{1}{2}= 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

Number of teachers = 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

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.
(c) Number of boys to the total number of students.

ANSWER

Total number of students in a college = 4320,

Number of girls = 2300,

So, number of boys = 4320 – 2300 = 2020

Then,

(a) Ratio of number of girls to the total number of students =\frac{2300}{4320}
=\frac{115}{216}= 115:216

(b) Ratio of number of boys to the number of girls =\frac{2020}{2300}
=\frac{101}{115}= 101:115

(c) Ratio of number of boys to the total number of students =\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.
(c) Number of students who opted basketball to the total number of students.

ANSWER

Total number of students in a school = 1800,

Number of students who opted basketball = 750,

Number of students who opted cricket = 800,

So, number of students who opted tennis = 1800 – (750 + 800) = 250

Then,

(a) Ratio of number of students who opted basketball to the number of students who opted table tennis =\frac{750}{250}
=\frac{3}{1}= 3;1

(b) Ratio of number of students who opted cricket to the number of students who opted basketball =\frac{800}{750}
=\frac{16}{15}= 16:15

(c) Ratio of number of students who opted basketball to the total number of students =\frac{750}{1800}
=\frac{5}{12}= 5:12

QUESTION 12

Cost of a dozen pens is ₹ 180 and cost of 8 ball pens is ₹ 56. Find the ratio of the cost of a pen to the cost of a ball pen.

ANSWER

Cost of a dozen pens = ₹ 180,
So, cost of one pen = ₹ \frac{180}{12}= ₹ 15

Cost of 8 ball pens = ₹ 56,
So, cost of one ball pen = ₹ \frac{56}{8} = ₹ 7

Therefore, the ratio of the cost of a pen to the cost of a ball pen = 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.

NCERT SOLUTIONS FOR CLASS 6 MATHS EXERCISE 12.1

ANSWER

\frac{Breadth}{Length}=\frac{10}{25}=\frac{\framebox{20}}{50}=\frac{40}{\framebox{100}}

QUESTION 14

Divide 20 pens between Sheela and Sangeeta in the ratio of 3 : 2.

ANSWER

Sum of parts = 3 + 2 = 5,

So, Sheela will get = \frac{3}{5}\times 20 =12 pens

and, Sangeeta will get =\frac{2}{5}\times 20 = 8 pens.

QUESTION 15

Mother wants to divide ₹ 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

Age of Shreya = 15 years,
Age of Bhoomika = 12 years,

So, ratio of the age of Shreya to the age of Bhoomika = 15 : 12

Sum of the parts of division = 15 + 12 = 27,

\therefore Shreya will get = ₹ \frac{15}{27}\times 36
= ₹ 5 × 4= ₹ 20,

and Bhoomika will get = ₹ \frac{12}{27}\times 36
= ₹ 4 × 4 = ₹ 16.

QUESTION 16

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 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.

ANSWER

(a) Present age of father = 42 years,
Present age of son = 14 years,
Ratio of present age of father to the present age of son = \frac{42}{14}
= \frac{3}{1} = 3 : 1

(b) 14 – 12 = 2,
So, 2 years ago son was 12 year old,
Then, Age of the father 2 years ago = 42 – 2 = 40 years,
\therefore Ratio of age of father to the age of son, when son was 12 years old = \frac{40}{12}
= \frac{10}{3}= 10 : 3

(c) After 10 years,
Age of father = 42 + 10 = 52 years,
Age of son = 14 + 10 = 24 years,
So, Ratio of age of father after 10 years to the age of son after 10 years = \frac{13}{6} = 13 : 6

(d) 42 – 30 = 12,
So, 12 years ago father was 30 years old,
Then, age of son 12 years ago = 14 – 12 = 2 years,
\therefore Ratio of age of father to the age of son when father was 30 years old = \frac{30}{2}
= \frac{15}{1}=15:1

NCERT SOLUTIONS FOR CLASS 6 MATHS CHAPTER 12

Check NCERT Solutions of other exercises from Class 6 Maths Chapter 12 Ratio & Proportion by clicking the links given below.

Exercise 12.1
Exercise 12.2
Exercise 12.3

We hope NCERT SOLUTIONS FOR CLASS 6 MATHS EXERCISE 12.1 has helped you understand how to find Ratios.

Write in the comment section for any error or any solution related queries from the exercise. [ NCERT SOLUTIONS FOR CLASS 6 MATHS EXERCISE 12.1 ]

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