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NCERT Solutions For Class 6 Maths Chapter 12 - Ratio and Proportion

NCERT Solutions for Class 6 Maths offer comprehensive explanations for the questions found within the NCERT textbooks endorsed by the Central Board of Secondary Education (CBSE). Orchids the international school provides these NCERT Class 6 Maths Solutions on a chapter-by-chapter basis, aiming to assist students in resolving any uncertainties and acquiring a profound comprehension of the subject matter. These resources, including NCERT Solutions, are conveniently accessible in PDF format, allowing students to download them for offline learning.

NCERT Solutions for Maths Ratio and Proportion

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Access Answers to NCERT Solutions For Class 6 Maths Chapter 12 - Ratio and Proportion

Introduction

Question 1 :

 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 / 108 = (3 × 3 × 3 × 3) / (2 × 2 × 3 × 3 × 3)

= 3 / 4

(b) 98 / 63 = (14 × 7) / (9 × 7)

= 14 / 9

(c) 33 / 121 = (3 × 11) / (11 × 11)

= 3 / 11

(d) 30 / 45 = (2 × 3 × 5) / (3 × 3 × 5)

= 2 / 3

 


Question 2 :

Fill in the following blanks.

15 / 18 = ☐ / 6 = 10 / ☐ = ☐ / 30 [Are these equivalent ratios?]

 

Answer :

15 / 18 = (5 × 3) / (6 × 3)

= 5 / 6

5 / 6 = (5 × 2) / (6 × 2)

= 10 / 12

5 / 6 = (5 × 5) / (6 × 5)

= 25 / 30

Hence, 5, 12 and 25 are the numbers which come in the blanks, respectively.

Yes, all are equivalent ratios.

 


Question 3 :

 There are 20 girls and 15 boys in a class.

(a) What is the ratio of the number of girls to the number of boys?

(b) What is the ratio of the number of girls to the total number of students in the class?

 

Answer :

Given

Number of girls = 20 girls

Number of boys = 15 boys

The total number of students = 20 + 15

= 35

(a) The ratio of the number of girls to the number of boys = 20 / 15 = 4 / 3

(b) The ratio of the number of girls to the total number of students = 20 / 35 = 4 / 7

 


Question 4 :

Out of 30 students in a class, 6 like football, 12 like cricket and the remaining like tennis. Find the ratio of

NCERT Solutions for Class 6 Maths Chapter 12 Exercise 12.1 - 1

(a) The number of students liking football to the number of students liking tennis.

(b) The number of students liking cricket to the total number of students.

 

Answer :

Given

The number of students who like football = 6

The number of students who like cricket = 12

The number of students who like tennis = 30 – 6 – 12

= 12

(a) Ratio of the number of students liking football to the number of students liking tennis

= 6 / 12 = 1 / 2

(b) Ratio of the number of students liking cricket to the total number of

= 12 / 30

= 2 / 5

 


Question 5 :

 See the figure and find the ratio of

NCERT Solutions for Class 6 Maths Chapter 12 Exercise 12.1 - 2

(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 :

Given in the figure

The number of triangles = 3

The number of circles = 2

The number of squares = 2

The total number of figures = 7

(a) The ratio of the number of triangles to the number of circles inside the rectangle

= 3 / 2

(b) The ratio of the number of squares to all the figures inside the rectangle

= 2 / 7

(c) The ratio of the number of circles to all the figures inside the rectangle

= 2 / 7

 


Question 6 :

Distances traveled by Hamid and Akhtar in an hour are 9 km and 12 km. Find the ratio of the speed of Hamid to the speed of Akhtar.

 

Answer :

We know that the speed of a certain object is the distance travelled by that object in an hour

Distance travelled by Hamid in one hour = 9 km

Distance travelled by Akhtar in one hour = 12 km

Speed of Hamid = 9 km/hr

Speed of Akhtar = 12 km/hr

The ratio of the speed of Hamid to the speed of Akhtar = 9 / 12 = 3 / 4

 


Question 7 :

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 :

Money earned by Seema = ₹ 150000

Money saved by Seema = ₹ 50000

Money spent by Seema = ₹ 150000 – ₹ 50000 = ₹ 100000

(a) The ratio of the money earned to money saved = 150000 / 50000 = 15 / 5

= 3 / 1

(b) The ratio of the money saved to money spent = 50000 / 100000 = 5 / 10

= 1 / 2

 


Question 8 :

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

The number of teachers in a school = 102

The number of students in a school = 3300

The ratio of the number of teachers to the number of students = 102 / 3300

= (2 × 3 × 17) / (2 × 3 × 550)

= 17 / 550

 


Question 9 :

 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 :

Given

The total number of students = 4320

The number of girls = 2300

The number of boys = 4320 – 2300

= 2020

(a) The ratio of the number of girls to the total number of students = 2300 / 4320

= (2 × 2 × 5 × 115) / (2 × 2 × 5 × 216)

= 115 / 216

(b) The ratio of the number of boys to the number of girls = 2020 / 2300

= (2 × 2 × 5 × 101) / (2 × 2 × 5 × 115)

= 101 / 115

(c) The ratio of the number of boys to the total number of students = 2020 / 4320

= (2 × 2 × 5 × 101) / (2 × 2 × 5 × 216)

= 101 / 216

 


Question 10 :

Out of 1800 students in a school, 750 opted basketball, 800 opted cricket and the 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 :

(a) The ratio of the number of students who opted basketball to the number of students who opted table tennis = 750 / 250 = 3 / 1

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

= 800 / 750 = 16 / 15

(c) The ratio of the number of students who opted basketball to the total number of students

= 750 / 1800 = 25 / 60 = 5 / 12

 


Question 11 :

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

 

Answer :

The cost of a dozen pens = ₹ 180

The cost of 1 pen = 180 / 12

= ₹ 15

The cost of 8 ball pens = ₹ 56

The cost of 1 ball pen = 56 / 8

= ₹ 7

Hence, the required ratio is 15 / 7.

 


Question 12 :

Consider the statement: The 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.

The breadth of the hall (in metres)

10

 

40

The length of the hall (in metres)

25

50

 

 

Answer :

(i) Length = 50 m

Breadth / 50 = 2 / 5

By cross multiplication,

5× Breadth = 50 × 2

Breadth = (50 × 2) / 5

= 100 / 5

= 20 m

(ii) Breadth = 40 m

40 / Length = 2 / 5

By cross multiplication,

2 × Length = 40 × 5

Length = (40 × 5) / 2

Length = 200 / 2

Length = 100 m

 


Question 13 :

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

Answer :

Terms of 3: 2 = 3 and 2

The sum of these terms = 3 + 2

= 5

Now, Sheela will get 3 / 5 of the total pens, and Sangeeta will get 2 / 5 of the total pens.

The number of pens Sheela has = 3 / 5 × 20

= 3 × 4

= 12

The number of pens Sangeeta has = 2 / 5 × 20

= 2 × 4

= 8

 


Question 14 :

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

NCERT Solutions for Class 6 Maths Chapter 12 Exercise 12.1 - 3

 

 

Answer :

Ratio of ages = 15 / 12

= 5 / 4

Hence, the mother wants to divide ₹ 36 in the ratio of 5: 4.

Terms of 5: 4 are 5 and 4

The sum of these terms = 5 + 4

= 9

Here, Shreya will get 5 / 9 of the total money, and Bhoomika will get 4 / 9 of the total money.

The amount Shreya gets = 5 / 9 × 36

= 20

The amount Bhoomika gets = 4 / 9 × 36

= 16

Therefore, Shreya will get ₹ 20, and Sangeeta will get ₹ 16.

 


Question 15 :

 Present age of the father is 42 years, and that of his son is 14 years. Find the ratio of

(a) Present age of the 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 the father after 10 years to the age of the son after 10 years.

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

 

Answer :

(a) Present age of father = 42 years

Present age of son = 14 years

Required ratio 42 / 14

= 3 / 1

(b) The son was 12 years old 2 years ago. So, the age of the father 2 years ago will be

= 42 – 2 = 40 years

Required ratio = 40 / 12 = (4 × 10) / (4 × 3) = 10 / 3

(c) After ten years age of the father = 42 + 10 = 52 years

After 10 years age of the son = 14 + 10 = 24 years

Required ratio = 52 / 24 = (4 × 13) / (4 × 6)

= 13 / 6

(d) 12 years ago, age of the father was 30.

At that time, the age of the son = 14 – 12

= 2 years

Required ratio = 30 / 2 = (2 × 15) / 2

= 15 / 1



 


Question 16 :

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) 30 minutes to 1.5 hours

30 min = 30 / 60

= 0.5 hours

Required ratio = (0.5 × 1) / (0.5 × 3)

= 1 / 3

(b) 40 cm to 1.5 m

1.5 m = 150 cm

Required ratio = 40 / 150

= 4 / 15

(c) 55 paise to ₹ 1

₹ 1 = 100 paise

Required ratio = 55 / 100 = (11 × 5) / (20 × 5)

= 11 / 20

(d) 500 ml to 2 litres

1 litre = 1000 ml

2 litre = 2000 ml

Required ratio = 500 / 2000 = 5 / 20 = 5 / (5 × 4)

= 1 / 4

 


Ratio

Question 1 :

Are the following statements true?

 

(a) 40 persons : 200 persons = ₹ 15 : ₹ 75

 

(b) 7.5 litres : 15 litres = 5 kg : 10 kg

 

(c) 99 kg : 45 kg = ₹ 44 : ₹ 20

 

(d) 32 m : 64 m = 6 sec : 12 sec

 

(e) 45 km : 60 km = 12 hours : 15 hours

 

Answer :

(a) 40 persons : 200 persons = ₹ 15 : ₹ 75

40 / 200 = 1 / 5

15 / 75 = 1 / 5

Hence, it is true.

(b) 7.5 litres : 15 litres = 5 kg : 10 kg

7.5 / 15 = 1 / 2

5 / 10 = 1 / 2

Hence, it is true.

(c) 99 kg : 45 kg = ₹ 44 : ₹ 20

99 / 45 = 11 / 5

44 / 20 = 11 / 5

Hence, it is true.

(d) 32 m : 64 m = 6 sec : 12 sec

32 / 64 = 1 / 2

6 / 12 = 1 / 2

Hence, it is true.

(e) 45 km : 60 km = 12 hours : 15 hours

45 / 60 = 3 / 4

12 / 15 = 4 / 5

Hence, it is false.

 


Question 2 :

Write True (T) or False ( F ) against each of the following statements.

 

(a) 16 : 24 :: 20 : 30

 

(b) 21: 6 :: 35 : 10

 

(c) 12 : 18 :: 28 : 12

 

(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

16 / 24 = 2 / 3

20 / 30 = 2 / 3

Hence, 16: 24 = 20: 30

Therefore, it is true.

(b) 21: 6:: 35: 10

21 / 6 = 7 / 2

35 / 10 = 7 / 2

Hence, 21: 6 = 35: 10

Therefore, it is true.

(c) 12: 18 :: 28: 12

12 / 18 = 2 / 3

28 / 12 = 7 / 3

Hence, 12: 18 ≠ 28:12

Therefore, it is false.

(d) 8: 9:: 24: 27

We know that = 24 / 27 = (3 × 8) / (3 × 9)

= 8 / 9

Hence, 8: 9 = 24: 27

Therefore, it is true.

(e) 5.2: 3.9:: 3: 4

As 5.2 / 3.9 = 4/3

Hence, 5.2: 3.9 ≠ 3: 4

Therefore, it is false.

(f) 0.9: 0.36:: 10: 4

0.9 / 0.36 = 90 / 36

= 10 / 4

Hence, 0.9: 0.36 = 10: 4

Therefore, it is true.

 


Question 3 :

Determine if the following are in proportion.

 

(a) 15, 45, 40, 120

 

(b) 33, 121, 9, 96

 

(c) 24, 28, 36, 48

 

(d) 32, 48, 70, 210

 

(e) 4, 6, 8, 12

 

(f) 33, 44, 75, 100

 

Answer :

(a) 15, 45, 40, 120

15 / 45 = 1 / 3

40 / 120 = 1 / 3

Hence, 15: 45 = 40:120

∴ These are in proportion.

(b) 33, 121, 9, 96

33 / 121 = 3 / 11

9 / 96 = 3 / 32

Hence, 33:121 ≠ 9: 96

∴ These are not in proportion.

(c) 24, 28, 36, 48

24 / 28 = 6 / 7

36 / 48 = 3 / 4

Hence, 24: 28 ≠ 36:48

∴ These are not in proportion.

(d) 32, 48, 70, 210

32 / 48 = 2 / 3

70 / 210 = 1 / 3

Hence, 32: 48 ≠ 70: 210

∴ These are not in proportion.

(e) 4, 6, 8, 12

4 / 6 = 2 / 3

8 / 12 = 2 / 3

Hence, 4: 6 = 8: 12

∴ These are in proportion.

(f) 33, 44, 75, 100

33/ 44 = 3/ 4

75 / 100 = 3 / 4

Hence, 33:44 = 75: 100

∴ These are in proportion.

 


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 ₹ 40 : ₹ 160

 

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

 

(c) 2 kg : 80 kg and 25 g : 625 g

 

(d) 200 mL : 2.5 litre and ₹ 4 : ₹ 50

 

Answer :

(a) 25 cm : 1 m and ₹ 40 : ₹ 160

25 cm = 25 / 100 m

= 0.25 m

0.25 / 1 = 1 / 4

40 / 160 = 1 / 4

Yes, these are in proportion.

Middle terms are 1 m, ₹ 40, and Extreme terms are 25 cm, ₹ 160.

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

39 / 65 = 3 /5

6 / 10 = 3 / 5

Yes, these are in proportion.

Middle terms are 65 litres, 6 bottles, and Extreme terms are 39 litres, 10 bottles.

(c) 2 kg : 80 kg and 25 g : 625 g

2 / 80 = 1 / 40

25 / 625 = 1 / 25

No, these are not in proportion.

(d) 200 mL : 2.5 litre and ₹ 4 : ₹ 50

1 litre = 1000 ml

2.5 litre = 2500 ml

200 / 2500 = 2 / 25

4 / 50 = 2 / 25

Yes, these are in proportion.

Middle terms are 2.5 litres, ₹ 4, and Extreme terms are 200 ml, ₹ 50.




Proportion

Question 1 :

If the cost of 7 m of cloth is ₹ 1470, find the cost of 5 m of cloth.

 

Answer :

Given

Cost of 7 m cloth = ₹ 1470

Cost of 1 m cloth = 1470 / 7

= ₹ 210

So, cost of 5 m cloth = 210 × 5 = 1050

∴ Cost of 5 m cloth is ₹ 1050

 


Question 2 :

Ekta earns ₹ 3000 in 10 days. How much will she earn in 30 days?

 

Answer :

Money earned by Ekta in 10 days = ₹ 3000

Money earned in one day by her = 3000 / 10

= ₹ 300

So, money earned by her in 30 days = 300 × 30

= ₹ 9000

 


Question 3 :

If it has rained 276 mm in the last 3 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 :

Measure of rain in 3 days = 276 mm

Measure of rain in one day = 276 / 3

= 92 mm

So, measure of rain in one week, i.e. 7 days = 92 × 7

= 644 mm

= 644 / 10

= 64.4 cm

 


Question 4 :

Cost of 5 kg of wheat is ₹ 91.50.

(a) What will be the cost of 8 kg of wheat?

(b) What quantity of wheat can be purchased in ₹ 183?

 

Answer :

(a) Cost of 5 kg wheat = ₹ 91.50.

Cost of 1 kg wheat = 91.50 / 5

= ₹ 18.3

So, the cost of 8 kg wheat = 18.3 × 8

= ₹ 146.40

(b) Wheat purchased in ₹ 91.50 = 5 kg

Wheat purchased in ₹ 1 = 5 / 91.50 kg

So, wheat purchased in ₹ 183 = (5 / 91.50) × 183

= 10 kg

 


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 = 150 C

Temperature drop in 1 day = 15 / 30

= (1 / 2)0 C

So, temperature drop in next 10 days = (1 / 2) × 10

= 50 C

∴ The temperature drop in the next 10 days will be 50 C

 


Question 6 :

Shaina pays ₹ 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 :

Rent paid by Shaina in 3 months = ₹ 15000

Rent for 1 month = 15000 / 3

= ₹ 5000

So, rent for 12 months, i.e. 1 year = 5000 × 12

= ₹ 60,000

∴ Rent paid by Shaina in 1 year is ₹ 60,000

 


Question 7 :

 Cost of 4 dozen bananas is ₹ 180. How many bananas can be purchased for ₹ 90?

 

Answer :

Number of bananas bought in₹ 180 = 4 dozens

= 4 × 12

= 48 bananas

Number of bananas bought in ₹ 1 = 48 / 180

So, number of bananas bought in ₹ 90 = (48 / 180) × 90

= 24 bananas

∴ 24 bananas can be purchased for ₹ 90

 


Question 8 :

The weight of 72 books is 9 kg. What is the weight of 40 such books?

 

Answer :

Weight of 72 books = 9 kg

Weight of 1 book = 9 / 72

= 1 / 8 kg

So, weight of 40 books = (1 / 8) × 40

= 5 kg

∴ Weight of 40 books is 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 :

Diesel required for 594 km = 108 litres

Diesel required for 1 km = 108 / 594

= 2 / 11 litre

So, diesel required for 1650 km = (2 / 11) × 1650

= 300 litres

∴ Diesel required by the truck to cover a distance of 1650 km is 300 litres

 


Question 10 :

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

 

Answer :

Pens purchased by Raju for ₹ 150 = 10 pens

Cost of 1 pen = 150 / 10

= ₹ 15

Pens purchased by Manish for ₹ 84 = 7 pens

Cost of 1 pen = 84 / 7

= ₹ 12

∴ Pens purchased by Manish are cheaper than Raju

 


Question 11 :

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

 

Answer :

Runs made by Anish in 6 overs = 42

Runs made by Anish in 1 over = 42 / 6

= 7

Runs made by Anup in 7 overs = 63

Runs made by Anup in 1 over = 63 / 7

= 9

∴ Anup scored more runs than Anish.

 


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