# NCERT Solutions For Class 6 Maths Chapter 12 : Ratio And Proportion

**NCERT Solutions For Class 6 Maths Chapter 12 Ratio And Proportion** comprises exercise wise solved questions of Ratio and Proportion concept. These study materials are available in PDF format for greater assistance, prepared by our experts. Students can easily download the PDF file and study offline as well. These NCERT Solutions for Class 6 Maths are prepared as per the CBSE syllabus, prescribed by the board.Chapter 12 Ratio ProportionExercise 12.1

## NCERT Solutions for Class 6 Chapter 12: Ratio and Proportion Download PDF

Further, students can also have a look at other NCERT Solutions, notes and preparation tips available on the website for attaining strong preparation of the exams. To get an idea of the types of questions asked from Ratio and Proportion, students are advised to solve sample papers and previous year question papers as well.

### Exercises of NCERT Solutions Class 6 Maths Chapter 12 โ Ratio and Proportion

## Access NCERT Solutions for Class 6 Chapter 12: Ratio and Proportion

**Exercise 12.1 page no: 251**

**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?**

**Solutions:**

Given

Number of girls = 20 girls

Number of boys = 15 boys

Total number of students = 20 + 15

= 35

(a) Ratio of number of girls to number of boys = 20 / 15 = 4 / 3

(b) Ratio of number of girls to total number of students = 20 / 35 = 4 / 7

**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.**

**Solutions:**

Given

Number of students who like football = 6

Number of students who like cricket = 12

Number of students who like tennis = 30 โ 6 โ 12

= 12

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

= 6 / 12 = 1 / 2

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

= 12 / 30

= 2 / 5

**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.**

**Solutions:**

Given in the figure

Number of triangles = 3

Number of circles = 2

Number of squares = 2

Total number of figures = 7

(a) Ratio of number of triangles to the number of circles inside the rectangle

= 3 / 2

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

= 2 / 7

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

= 2 / 7

**4. Distance 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.**

**Solutions:**

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

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

**5. Fill in the following blanks:**

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

**Solutions:**

15 / 18 = (5 ร 3) / (6 ร 3)

= 5 / 6

5 / 6 = (5 **ร **2) / (6 ร 2)

= 10 / 12

5 / 6 = (5 **ร **5) / (6 ร 5)

= 25 / 30

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

Yes, all are equivalent ratios.

**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**

**Solutions:**

(a) 81 / 108 = (3 **ร **3 ร 3 ร 3) / (2 **ร **2 ร 3 ร 3 ร 3**)**

= 3 / 4

(b) 98 / 63 = (14 **ร **7) / (9 ร 7)

= 14 / 9

(c) 33 / 121 = (3 **ร **11) / (11 ร 11)

= 3 / 11

(d) 30 / 45 = (2 **ร **3 ร 5) / (3 ร 3 ร 5)

= 2 / 3

**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 โน 1**

**(d) 500 ml to 2 litres**

**Solutions:**

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

30 min = 30 / 60

= 0.5 hours

Required ratio = (0.5 **ร **1**) / **(0.5 ร 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 โน 1

โน 1 = 100 paise

Required ratio = 55 / 100 = (11 **ร **5) / (20 ร 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 **ร **4)

**= **1 / 4

**8. In a year, Seema earns โน 1,50,000 and saves โน 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.**

**Solutions:**

Money earned by Seema** = **โน 150000

Money saved by her = โน 50000

Money spent by her = โน 150000 โ โน 50000 = โน 100000

(a) Ratio of money earned to money saved = 150000 / 50000 = 15 / 5

= 3 / 1

(b) Ratio of money saved to money spent = 50000 / 100000 = 5 / 10

= 1 / 2

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

**Solutions:**

Given

Number of teachers in a school = 102

Number of students in a school = 3300

Ratio of number of teachers to the number of students = 102 / 3300

= (2 ร 3 ร 17) / (2 ร 3 ร 550)

= 17 / 550

**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.**

**Solutions:**

Given

Total number of students = 4320

Number of girls = 2300

Number of boys = 4320 โ 2300

= 2020

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

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

= 115 / 216

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

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

= 101 / 115

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

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

= 101 / 216

**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.**

**Solutions:**

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

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

= 800 / 750 = 16 / 15

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

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

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

**Solutions:**

Cost of a dozen pens** = **โน 180

Cost of 1 pen = 180 / 12

= โน 15

Cost of 8 ball pens = โน 56

Cost of 1 ball pen = 56 / 8

= โน 7

Hence, required ratio is 15 / 7

**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.**

Breadth of the hall (in metres) | 10 | 40 | |

Length of the hall (in metres) | 25 | 50 |

**Solutions:**

**(i) **Length = 50 m

Breadth / 50 = 2 / 5

By cross multiplication

5ร breadth = 50 ร 2

Breadth = (50 ร 2) / 5

= 100 / 5

= 20 m

(ii) Breadth = 40 m

40 / Length = 2 / 5

By cross multiplication

2 ร Length = 40 ร 5

Length = (40 ร 5) / 2

Length = 200 / 2

Length = 100 m

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

**Solutions:**

Terms of 3: 2 = 3 and 2

Sum of these terms = 3 + 2

= 5

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

Number of pens having with Sheela = 3 / 5 ร 20

= 3 ร 4

= 12

Number of pens having with Sangeeta = 2 / 5 ร 20

= 2 ร 4

= 8

**15. Mother wants to divide โน 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.**

**Solutions:**

Ratio of ages = 15 / 12

= 5 / 4

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

Terms of 5: 4 are 5 and 4

Sum of these terms = 5 + 4

= 9

Here Shreya will get 5 / 9 of total money and Sangeeta will get 4 / 9 of total money

The amount Shreya get** = **5 / 9 ร 36

= 20

The amount Sangeeta get = 4 / 9 ร 36

= 16

Therefore Shreya will get โน 20 and Sangeeta will get โน 16

**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.**

**Solutions:**

**(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 father 2 years ago will be

= 42 โ 2 = 40 years

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

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

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

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

= 13 / 6

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

At that time age of son = 14 โ 12

= 2 years

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

= 15 / 1

Exercise 12.2 page no: 255

**1. 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**

**Solutions:**

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

15 / 45 = 1 / 3

40 / 120 = 1 / 3

Hence, 15: 45 = 40:120

โด These are in a proportion

(b) 33, 121, 9, 96

33 / 121 = 3 / 11

9 / 96 = 3 / 32

Hence 33:121 โ 9: 96

โด These are not in a proportion

(c) 24, 28, 36, 48

24 / 28 = 6 / 7

36 / 48 = 3 / 4

Hence, 24: 28 โ 36:48

โด These are not in a proportion

(d) 32, 48, 70, 210

32 / 48 = 2 / 3

70 / 210 = 1 / 3

Hence, 32: 48 โ 70: 210

โด These are not in a proportion

(e) 4, 6, 8, 12

4 / 6 = 2 / 3

8 / 12 = 2 / 3

Hence 4: 6 = 8: 12

โด These are in a proportion

(f) 33, 44, 75, 100

33/ 44 = 3/ 4

75 / 100 = 3 / 4

Hence, 33:44 = 75: 100

โด These are in a proportion

**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**

**Solutions:**

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

16 / 24 = 2 / 3

20 / 30 = 2 / 3

Hence, 16: 24 = 20: 30

Therefore True

(b) 21: 6:: 35: 10

21 / 6 = 7 / 2

35 / 10 = 7 / 2

Hence, 21: 6 = 35: 10

Therefore True

(c) 12: 18 :: 28: 12

12 / 18 = 2 / 3

28 / 12 = 7 / 3

Hence, 12: 18 โ 28:12

Therefore False

(d) 8: 9:: 24: 27

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

= 8 / 9

Hence, 8: 9 = 24: 27

Therefore True

(e) 5.2: 3.9:: 3: 4

As 5.2 / 3.9 = 3 / 4

Hence, 5.2: 3.9 โ 3: 4

Therefore False

(f) 0.9: 0.36:: 10: 4

0.9 / 0.36 = 90 / 36

= 10 / 4

Hence, 0.9: 0.36 = 10: 4

Therefore True

**3. Are the following statements true?**

**(a) 40 persons : 200 persons = โน 15 : โน 75**

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

**(c) 99 kg : 45 kg = โน 44 : โน 20**

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

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

**Solutions:**

**(a) **40 persons : 200 persons = โน 15 : โน 75

40 / 200 = 1 / 5

15 / 75 = 1 / 5

Hence, True

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

7.5 / 15 = 1 / 2

5 / 10 = 1 / 2

Hence, True

(c) 99 kg : 45 kg = โน 44 : โน 20

99 / 45 = 11 / 5

44 / 20 = 11 / 5

Hence, True

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

32 / 64 = 1 / 2

6 / 12 = 1 / 2

Hence, True

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

45 / 60 = 3 / 4

12 / 15 = 4 / 5

Hence, False

**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 โน 40 : โน 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 โน 4 : โน 50**

**Solutions:**

**(a) **25 cm : 1 m and โน 40 : โน 160

25 cm = 25 / 100 m

= 0.25 m

0.25 / 1 = 1 / 4

40 / 160 = 1 / 4

Yes, these are in a proportion

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

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

39 / 65 = 3 /5

6 / 10 = 3 / 5

Yes, these are in a 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 a proportion

(d) 200 mL : 2.5 litre and โน 4 : โน 50

1 litre = 1000 ml

2.5 litre = 2500 ml

200 / 2500 = 2 / 5

4 / 50 = 2 / 25

Yes, these are in a proportion

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

Exercise 12.3 page no: 259

**1. If the cost of 7 m of cloth is โน 1470, find the cost of 5 m of cloth.**

**Solutions:**

Given

Cost of 7 m cloth = โน 1470

Cost of 1 m cloth = 1470 / 7

= โน 210

So, cost of 5 cloth = 210 ร 5 = 1050

โด Cost of 5 m cloth is โน 1050

**2. Ekta earns โน 3000 in 10 days. How much will she earn in 30 days?**

**Solutions:**

Money earned by Ekta in 10 days = โน 3000

Money earned in one day by her = 3000 / 10

= โน 300

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

= โน 9000

**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.**

**Solutions:**

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 ร 7

= 644 mm

= 644 / 10

= 64.4 cm

**4. Cost of 5 kg of wheat is โน 91.50.**

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

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

**Solutions:**

**(a) **Cost of 5 kg wheat = โน 91.50.

Cost of 1 kg wheat = 91.50 / 5

= โน 18.3

So, cost of 8 kg wheat = 18.3 ร 8

= โน 146.40

(b) Wheat purchased in โน 91.50 = 5 kg

Wheat purchased in โน 1 = 5 / 91.50 kg

So, wheat purchased in โน 183 = (5 / 91.50) ร 183

= 10 kg

**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?**

**Solutions:**

Temperature drop in 30 days = 15^{0} C

Temperature drop in 1 day = 15 / 30

= (1 / 2)^{0} C

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

= 5^{0} C

โด The temperature drop in the next 10 days will be 5^{0} C

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

**Solutions:**

Rent paid by Shaina in 3 months = โน 15000

Rent for 1 month = 15000 / 3

**= **โน 5000

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

**= **โน 60,000

โด Rent paid by Shaina in 1 year is โน 60,000

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

**Solutions:**

Number of bananas bought inโน 180 = 4 dozens

= 4 ร 12

= 48 bananas

Number of bananas bought in โน 1 = 48 / 180

So, number of bananas bought in โน 90 = (48 / 180)** ร** 90

= 24 bananas

โด 24 bananas can be purchased in โน 90

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

**Solutions:**

Weight of 72 books = 9 kg

Weight of 1 book = 9 / 72

= 1 / 8 kg

So, weight of 40 books = (1 / 8) ร 40

= 5 kg

โด Weight of 40 books is 5 kg

**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?**

**Solutions:**

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) ร 1650

= 300 litres

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

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

**Solutions:**

Pens purchased by Raju in โน 150 = 10 pens

Cost of 1 pen = 150 / 10

= โน 15

Pens purchased by Manish in โน 84 = 7 pens

Cost of 1 pen = 84 / 7

= โน 12

โด Pens purchased by Manish are cheaper than Raju

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

**Solutions:**

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

โด Anup scored more runs than Anish.

## Frequently Asked Questions on NCERT Solutions for Class 6 Maths Chapter 12

### Explain the golden ratio covered in the Chapter 12 of NCERT Solutions for Class 6 Maths.

Two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities.

### What are equivalent ratios covered in the Chapter 12 of NCERT Solutions for Class 6 Maths.

When the given ratios are equal, then these ratios are called equivalent ratios. Equivalent ratios can be obtained by multiplying and dividing the numerator and denominator with the same number. Example: Ratios 10:30 (=1:3) and 11:33 (=1:3) are equivalent ratios.

### Where can I get the NCERT Solutions for Class 6 Maths Chapter 12?

NCERT Solutions by BYJUโS is the best reference guide for the students to score well in the annual exam. These solutions contain detailed explanations for each and every concept covered in the chapter. Students who find it difficult in solving the exercise wise problems can access the solutions which are available online to get their doubts cleared instantly. The chapter wise and exercise wise solutions are created by the experts at BYJUโS with the aim of helping students irrespective of their intelligence quotient.