NCERT Solutions for Class 6 Maths Exercise 12.1 of Chapter 12 Ratio and Proportion discuss the concept of ratio. A comparison of two quantities which we observe in our daily activities can be made either as a ratio or a proportion. Illustrative examples are also given in order to enable students to solve problems within the specified duration. These Class 6 Maths NCERT Solutions contain explanations in a comprehensive manner with the aim of making it easy for the students during their exam preparation.
NCERT Solutions for Class 6 Maths Chapter 12 Ratio and Proportion Exercise 12.1
Access NCERT Solutions for Class 6 Chapter 12: Ratio and Proportion Exercise 12.1
1. 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?
Solutions:
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
2. Out of 30 students in a class, 6 like football, 12 like cricket and the remaining like tennis. Find the ratio of
(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.
Solutions:
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
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
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
4. Distances travelled 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.
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
The ratio of the speed of Hamid to the speed of Akhtar = 9 / 12 = 3 / 4
5. Fill in the following blanks.
15 / 18 = ☐ / 6 = 10 / ☐ = ☐ / 30 [Are these equivalent ratios?]
Solutions:
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.
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 × 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
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
Solutions:
(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
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.
Solutions:
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
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
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
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
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
11. 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.
Solutions:
(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
12. 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.
Solutions:
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.
13. 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 |
Solutions:
(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
14. Divide 20 pens between Sheela and Sangeeta in a ratio of 3: 2.
Solutions:
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
15. 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.
Solutions:
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.
16. 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.
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 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
Also, explore –
NCERT Solutions for Class 6 Maths Chapter 12
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