CBSE Important Questions Class 6 Maths Chapter 12

Important Questions Class 6 Maths Chapter 12 – Ratio and Proportion

Maths is an important subject that is taught in school. Chapter 12 of Class 6 Maths is about ratios and proportions. The ratio is a way of comparison. It is a unitless comparison between measures. On the other hand, when two ratios are equal, they are called proportions. 

The chapter deals with the basic ideas of ratio and proportion. It teaches students how to calculate ratios and the different relations between them. It also gives the idea about proportion. Students must practice questions from this chapter because the concepts are new to them.

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Important Questions Class 6 Maths Chapter 12 – With Solutions

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Question 1. There are a total of 20 girls and 15 boys in the classroom.

(i) What is the final ratio of the number of girls present to the number of boys?

(ii) What is the final ratio of the number of girls present to the total number of students present in the class?

Answer 1 :

Given,

Number of girls present = 20 girls

Number of boys present = 15 boys

Total number of students present = 20 + 15

= 35

(i) Ratio of the number of girls present to the number of boys is = 20 / 15 = 4 / 3

(ii) Ratio of the number of girls present to the total number of students is = 20 / 35 = 4 / 7

Question 2. Out of 30 (thirty) students in a class, six students like football, 12 students like cricket and the remaining students like tennis. Find the ratio of 

(i) Number of students that like football to number of students liking tennis.

(ii) Number of students liking cricket to total number of students.

Answer 2:

The number of students who like football is = 6

The number of students who like cricket is = 12

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

= 12

(i) Ratio of the Number of students that like football to the number of students that like tennis

= 6 / 12 = 1 / 2

(ii) Ratio of the Number of students who like cricket to the total number of students who are

= 12 / 30

= 2 / 5

Question 3. In a year, Seema earns around ₹ 1,50,000 and saves ₹ 50,000. So, find the ratio of

(i) Money that Seema earns to the money she saves

(ii) Money that she saves to the money she spends.

Answer 3:

Money earned by Seema is = ₹ 150000

Money saved by her is = ₹ 50000

The Money spent by her = ₹ 150000 – ₹ 50000 = ₹ 100000

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

= 3 / 1

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

= 1 / 2

Question 4. Find the ratio of the following statements:

(i) 81 to 108

(ii) 98 to 63

(iii) 33 km to 121 km

(iv) 30 minutes to 45 minutes

Answer 4:

(i) 81 / 108 is equal to = (3 × 3 × 3 × 3) / (2 × 2 × 3 × 3 × 3)

= 3 / 4

(ii) 98 / 63 = (14 × 7) / (9 × 7)

= 14 / 9

(iii) 33 / 121 = (3 × 11) / (11 × 11)

= 3 / 11

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

= 2 / 3

Question 5. Find the ratio of the following statements:

(i) 30 minutes to 1.5 hours

(ii) 40 cm to 1.5 m

(iii) 55 paise to ₹ 1

(iv) 500 ml to 2 litres

Answer:

(i) 30 minutes to 1.5 hours

30 min = 30 / 60

= 0.5 hours

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

= 1 / 3

(ii) 40 cm to 1.5 m

1.5 m = 150 cm

Required ratio = 40 / 150

= 4 / 15

(iii) 55 paise to ₹ 1

₹ 1 = 100 paise

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

= 11 / 20

(iv) 500 ml to 2 litres

1 litre = 1000 ml

2 litre = 2000 ml

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

= 1 / 4

Question 6. There is a total of 102 teachers in a school of 3300 no students. Find the final ratio of the number of teachers present to the number of students.

Answer:

Given

Total number of teachers in a school = 102

The total number of students in a school is = 3300

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

= (2 × 3 × 17) / (2 × 3 × 550)

= 17 / 550

Question 7. In a college, out of 4320 students present, 2300 students are girls. And the rest are boys. Find the ratio of

(i) Number of girls to the total number of students.

(ii) Number of boys to the number of girls.

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

Answer:

It is Given

The total number of students is = 4320

Number of girls present = 2300

Number of boys present = 4320 – 2300

= 2020

(i) Ratio of the Number of girls present to the total number of students present = 2300 / 4320

= (2 × 2 × 5 × 115) divided by (2 × 2 × 5 × 216), which will become, 

= 115 / 216

(ii) Ratio of the Number of boys present to the number of girls present = 2020 / 2300

= (2 × 2 × 5 × 101) divided by (2 × 2 × 5 × 115)

= 101 / 115

(iii) Ratio of the Number of boys present to the total number of students present = 2020 / 4320

= (2 × 2 × 5 × 101) divided by (2 × 2 × 5 × 216)

= 101 / 216

Question 8. Out of 1800 students present in a school, 750 students opted for basketball, 800 students opted for cricket, and the remaining students opted for table tennis. If a student can choose only one single game, then find the ratio of

(i) Number of students who opted for the sport basketball to the number of students who chose the sport table tennis.

(ii) Number of students who opted for the sport cricket to the number of students opting for the sport basketball.

(iii) Number of students who opted for the sport basketball to the total number of students.

Answers :

(i) Ratio of the Number of students who opted for the sport basketball to the number of students that opted for the sport table tennis = 750 / 250 = 3 / 1

(ii) Ratio of the Number of students who opted for the sport cricket to the number of students opting for basketball

= 800 / 750 = 16 / 15

(iii) Ratio of the Number of students who opted for the sport basketball to the total number of students

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

Question 9. Divide 20 pens between Sheela and Seema in a ratio of 3: 2.

Answer:

Terms of 3: 2 = 3 and 2

Sum of these terms = 3 + 2

= 5

Hence Sheela will get 3 / 5 of the total pens, and Seema will get 2 / 5 of the total pens.

Number of pens present with Sheela = 3 / 5 × 20

= 3 × 4

= 12 pens

Number of pens having Seema = 2 / 5 × 20

= 2 × 4

= 8 pens

Question 10. A Mother wants to divide ₹ 36 between her two daughters, Shreya and Bhavna, in the ratio of their respective ages. If the age of Shreya is 15 years and the age of Bhavna is 12 years, find how much money Shreya and Bhavna will receive.

Answer :

The ratio of ages of Shreya and bhavna = 15 / 12

= 5 / 4

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

Terms of 5: 4 are denoted as 5 and 4

The Sum of these terms will be = 5 + 4

= 9

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

The amount Shreya get = 5 / 9 × 36

= 20

The amount Bhavna get = 4 / 9 × 36

= 16

Therefore Shreya will get ₹ 20, and Bhavna will get ₹ 16

Question 11. The present age of the father is 42 (forty-two) years, and that of his son is 14 years. Hence Find the ratio of

(i) Present age of the father to the present age of the son

(ii) Age of the father to the age of his son, when the son was 12 years old.

(iii) Age of the father to the age of the son after 10 (ten) years.

(iv) Age of the father to the age of his son, when the father was 30 (thirty) years old, will be.

Answer:

(i) Present age of father = 42 years

The present age of son = is 14 years

Required ratio 42 / 14

= 3 / 1

(ii) The son was 12 years old two years ago. Hence the age of the father two years ago will be,

= 42 – 2 = 40 years

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

(iii) After ten years the age of father will be = 42 + 10 = 52 years

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

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

= 13 / 6

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

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

= 2 years

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

= 15 / 1

Question 12.  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

Answers :

(a) 15, 45, 40, 120

15 / 45 = 1 / 3

40 / 120 = 1 / 3

Hence, 15: 45 = 40:120

∴ These are in a proportion

(b) 33, 121, 9, 96

33 / 121 = 3 / 11

9 / 96 = 3 / 32

Hence 33:121 ≠ 9: 96

∴ These are not in a 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 a proportion

(e) 4, 6, 8, 12

4 / 6 = 2 / 3

8 / 12 = 2 / 3

Hence 4: 6 = 8: 12

∴ These are in a proportion

(f) 33, 44, 75, 100

33/ 44 = 3/ 4

75 / 100 = 3 / 4

Hence, 33:44 = 75: 100

∴ These are in proportion.

Question 13. Are the following statements true?

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

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

(iii) 99 kg : 45 kg = ₹ 44 : ₹ 20

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

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

Answer:

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

40 / 200 = 1 / 5

15 / 75 = 1 / 5

Hence, True

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

7.5 / 15 = 1 / 2

5 / 10 = 1 / 2

Hence, True

(iii) 99 kg : 45 kg = ₹ 44 : ₹ 20

99 / 45 = 11 / 5

44 / 20 = 11 / 5

Hence, True

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

32 / 64 = 1 / 2

6 / 12 = 1 / 2

Hence, True

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

45 / 60 = 3 / 4

12 / 15 = 4 / 5

Hence, False

Question 14. Determine if the following ratios form a proportion. Also, write the middle terms and the extreme terms where the ratios form a proportion.

(i) 25 cm : 1 m and ₹ 40 : ₹ 160

(ii)39 litres: 65 litres and six bottles : 10 bottles

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

(i) 200 mL : 2.5 litre and ₹ 4 : ₹ 50

Answer:

(i) 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 a definite proportion.

Middle terms are said to be 1 m, ₹ 40, and Extreme terms are found to be 25 cm, ₹ 160

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

39 / 65 = 3 /5

6 / 10 = 3 / 5

Yes, these are in definite proportion

Middle terms are said to be 65 litres, 6 bottles, and the Extreme terms are 39 litres, 10 bottles.

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

2 / 80 = 1 / 40

25 / 625 = 1 / 25

No, these are not in a definite proportion

(iv) 200 mL : 2.5 litre and ₹ 4 : ₹ 50

1 litre = 1000 ml

2.5 litre = 2500 ml

200 / 2500 = 2 / 5

4 / 50 = 2 / 25

Yes, these are in definite proportion

Middle terms are said to be 2.5 litres, ₹ 4 and the Extreme terms are 200 ml, ₹ 50

Question 15. Esha earns ₹ 3000 in 10 (ten) days. How much will she earn in 30 (thirty) days?

Answer:

Money earned by Esha in 10 days = ₹ 3000

Money earned by her in one day = 3000 / 10

= ₹ 300

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

= ₹ 9000

Question 16. If it has rained 276 mm in the previous 3 days, how many cm of rain will fall in the next one full week (7 days)? Assuming that the rain continues to fall in the same rate.

Answer:

Measure of rain in the previous 3 days = 276 mm

Measure of rain in one single day = 276 / 3

= 92 mm

So, a measure of rain in one week which is, 7 days = 92 × 7

= 644 mm

= 644 / 10

= 64.4 cm

Question 17. The Cost of 5 kg of wheat is ₹ 91.50.

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

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

Answer

(i) Cost of 5 kg wheat is = ₹ 91.50.

Cost of 1 kg wheat is = 91.50 / 5

= ₹ 18.3

So, cost of 8 kg wheat is = 18.3 × 8

= ₹ 146.40

(ii) Wheat purchased in ₹ 91.50 is = 5 kg

Wheat purchased in ₹ 1 is = 5 / 91.50 kg

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

= 10 kg

Question 18. Shreya pays ₹ 15000 as rent for 3 months. How much does Shreya have to pay for a whole year, given that the rent per month remains the same?

Answer:

Rent paid by Shreya in 3 months = ₹ 15000

Rent for 1 month is = 15000 / 3

= ₹ 5000

So, rent for 12 months which is 1 year, becomes = 5000 × 12

= ₹ 60,000

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

Question 19. The cost of 4 dozen bananas is ₹ 180. How many bananas can be purchased for ₹ 90?

Answers

Number of bananas that are bought in ₹ 180 = 4 dozens

= 4 × 12

= 48 bananas

The number of bananas bought in ₹ 1 is = 48 / 180

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

= 24 bananas

∴ 24 bananas can be purchased for ₹ 90

Question 20. The weight of 72 books is 9 kg. So What is the weight of 40 such books?

Answers:

The weight of 72 books is = 9 kilograms.

The weight of 1 book is = 9 / 72

= 1 / 8 kg

So, the weight of 40 books becomes = (1 / 8) × 40

= 5 kg

∴ The weight of 40 books is 5 kilograms.

Question 21. A truck requires at least 108 litres of Diesel to cover a distance of at least 594 km. So How much Diesel will be required by the same truck to cover a distance of around 1650 km?

Answers:

The diesel required for 594 km is = 108 litres

Diesel required for 1 km is = 108 / 594

= 2 / 11 litre

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

= 300 litres

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

Benefits of Solving Important Questions Class 6 Maths Chapter 12

Practice is very important for students. It clears their concepts and generates interest in the subject matter. Many students fear maths because they do not understand the subject matter. Practice is really important to clear their doubts and boost confidence. The experts of Extramarks have made the Important Questions Class 6 Maths Chapter 12 to help students solve questions. There will be multiple benefits to solving the questions. These are-

• The experts have collected the questions from sources like textbook exercises, CBSE sample papers, NCERT exemplars and important reference books. They have included a few questions from CBSE past years’ question papers so that students may have an idea regarding questions in exams. Thus, the Maths Class 6 Chapter 12 Important Questions will help students solve questions regularly.
• The experts have solved the questions too. They have given a step-by-step solution to each question so that students can easily understand the solution. Thus, the students can follow the answers if they cannot solve a question. They can check their answers with the experts’ answers too. Experienced professionals have further checked the answers to ensure the best quality of content for students. Thus, the Important Questions Class 6 Maths Chapter 12 will guide students thoroughly.
• Practice helps students in many ways, such as it helps them to build confidence in the subject. We see many students are afraid of Maths. It is simply because their concepts need to be clarified. Practice helps a lot to clear the doubts. So, the Class 6 Maths Chapter 12 Important Questions will build the habit of solving questions regularly among students. This habit will surely help students to make progress in the subject.

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