Ratio Proportion
Chapter 12
Exercise 12.1
EX 12.1 QUESTION 1.
There are 20 girls and 15 boys in a class.
(a) What is the ratio of number of girls to the number boys?
(b) What is the ratio of number of girls to the total number of students in the class?
Solution:
Number of girls = 20 girls
Number of boys = 15 boys
Total number of students = 20 + 15= 35
(a) The ratio of girls to that of boys = 20 / 15 = 4 / 3 = 4 : 3
(b) The ratio of the girls to total students = 20 / 20 + 15 = 4 / 7 = 4 : 7
EX 12.1 QUESTION 2.
Solution:
Total Number of students in the class = 30
Number of students liking football = 6
Number of students liking cricket = 12
Number of students liking tennis = 30 – 6 -12 = 30 – 18 = 12
(a) Ratio of number of students like football that of tennis= 6 / 12 = 1 / 2 = 1 : 2
(b) Ratio of number of students like cricket to that of total students = 12 / 30 = 2 / 5 = 2 : 5
EX 12.1 QUESTION 3.
See the figure and find the ratio of
Solution:
Total number of figures = 7
Number of triangles = 3
Number of circles = 2
Number of squares = 2
(a) The ratio of the number of triangles to that of circles = 3 / 2 = 3 : 2
(b) The ratio of the number of squares to all the figures = 2 / 7 = 2 : 7
(c) The ratio of the number of circles to all the figures = 2 / 7 = 2 : 7
EX 12.1 QUESTION 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.
Solution:
In one hour distance travelled by Hamid = 9 km.
In one hour distance travelled by Akhtar = 12 km.
Speed of Hamid = 9 km / hr
Speed of Akhtar = 12 km / hr
∴ The ratio of the speed of Hamid to that Speed of Akhtar = 9 / 12 = 3 / 4 = 3 : 4
EX 12.1 QUESTION 5.
Fill in the following blanks:
15 / 18 = ☐ / 6 = 10 / ☐ = ☐ / 30 [Are these equivalent ratios?]
Solution:
15 / 18 = (5 × 3) / (6 × 3)
= 5 / 6
5 / 6 = (5 × 2) / (6 × 2)
= 10 / 12
5 / 6 = (5 ×5) / (6 × 5)
= 25 / 30
15 / 18 = 5 / 6 = 10 / 12 = 25 / 30
Yes, these equivalent ratios.
EX 12.1 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
Solution:
(a) 81 / 108
= 3 / 4 = 3 : 4
(b) 98 / 63
= 14 / 9 = 14 : 9
(c) 33 / 121
= 3 / 11 = 3 : 11
(d) 30 / 45
= 2 / 3 = 2 : 3
EX 12.1 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
Solution:
(a) 30 minutes to 1.5 hours
1.5 hours = 90 minutes [1 hour = 60 min.]
The ratio of 30 minutes to 1.5 hours = 30 : 90
= 30 / 90 = 1 / 3
= 1 : 3
(b) 40 cm to 1.5 m
1.5 m = 1.5 x 100 = 150 cm [1 m = 100 cm]
The ratio of 40 cm to 1.5 m = 40 : 150
= 40 / 150 = 4 / 15
= 4 : 15
(c) 55 paise to ₹ 1
₹ 1 = 100 paise
The ratio of 55 paise to ₹ 1 = 55 : 100
= 55 / 100 = 11 / 20
= 11 : 20
(d) 500 ml to 2 litres
2 litre = 2000 ml [1 litre = 1000 ml]
The ratio of 500 ml to 2 litres = 500 : 2000
500 / 2000 = 1 / 4
= 1 : 4
EX 12.1 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.
Solution:
Total earning = ₹ 1,50,000
Total saving = ₹ 50,000
Money spent by Seema = ₹ 150000 – ₹ 50000 = ₹ 100000
(a) Ratio of money earned to money saved = 150000 / 50000 = 15 / 5
= 3 / 1 = 3 : 1
(b) Ratio of money saved to money spent = 50000 / 100000 = 5 / 10
= 1 / 2 = 1 : 2
EX 12.1 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.
Solution:
Number of teachers = 102
Number of students = 3300
The ratio of teachers to that of students = 102 / 3300 = 17 / 550
= 17 : 550
EX 12.1 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.
Solution:
Total number of students in school = 4320
Number of girls in school = 2300
Therefore the number of boys in school = 4320 – 2300
= 2020
(a) The ratio of the number of girls to the total number of students = 2300 / 4320
= 115 / 216 = 115 : 216
(b) The ratio of the number of boys to the number of girls = 2020 / 2300
= 101 / 115 = 101 : 115
(c) The ratio of the number of boys to the total number of students = 2020 / 4320
= 101 / 216 = 101 : 216
EX 12.1 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.
Solution:
Total number of students = 1800
Number of students opting basketball = 750
Number of students who opted cricket = 800
Number of remaining students who opted table tennis = 1800 – (750 + 800)
= 1800 – 1550 = 250
(а) The ratio of the number of students opted basketball to the number of students who opted table tennis
=750 / 250 = 3 / 1 = 3 : 1
(b) The ratio of the number of students who opted cricket to the number of students opting basketball
= 800 / 750 = 16 / 15 = 16 : 15
(c) The ratio of the number of students who opted basketball to the total number of students
= 750 / 1800 = 5 / 12 = 5 : 12
EX 12.1 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.
Solution:
Cost of a dozen pens = ₹ 180
Cost of 1 pen = 180 / 12 = ₹ 15
Cost of 8 ball pens = ₹ 56
Cost of 1 ball pen = 56 / 8 = ₹ 7
Hence, the required ratio = 15 : 7
EX 12.1 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.
| Breadth of the hall (in metres) | 10 | ☐ | 40 |
| Length of the hall (in metres) | 25 | 50 | ☐ |
Solution:
The ratio of breadth to length = 2 : 5
Other ratios are = 2 / 5 x 10 / 10 = 20 / 50 ,.2 / 5 x 20 / 20 = 40 / 100
| Breadth of the hall (in metres) | 10 | 20 | 40 |
| Length of the hall (in metres) | 25 | 50 | 100 |
EX 12.1 QUESTION 14.
Divide 20 pens between Sheela and Sangeeta in the ratio of 3 : 2.
Solution:
The ratio between Sheela and Sangeeta = 3 : 2
Total terms = 3 + 2 = 5
Total number of pen = 20
∴ The part of Sheela =
The part of Sangeeta =
Thus, Sheela gets = 3 / 5 x 20 = 12 pens
Sangeeta gets = 2 / 5 x 20 = 8 pens.
EX 12.1 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?
Solution:
The ratio of the age of Shreya to that of Bhoomika = 15 : 12 = 15 / 12 = 5 / 4 = 5 : 4
Hence, the mother wants to divide ₹ 36 in the ratio of 5: 4
Shreya gets = 5 / 9 x 36 = ₹ 20
Bhoomika gets = 4 / 9 x 36 = ₹ 16
EX 12.1 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.
Solution:
The present age of father = 42 years.
The present age of his son = 14 years.
(a) The ratio of the present age of father to the present age of the son
= 42 / 14 = 3 /1 = 3 : 1
(b) (b) When son was 12 years old, i.e., 14 – 12 = 2 years ago father’s age = 42 – 2 = 40 years.
The ratio of the father’s age to the son’s age =40 / 12 = 10 / 3 = 10 : 3
(c) Age of father after 10 years = 42 + 10 = 52 years
Age of father after 10 years = 12 + 10 = 22 years
Therefore the ratio of their ages = 52 / 24 = 13 / 6 = 13 : 6
(d) When father was 30 years,
i.e., before 42 – 30 = 12 years
Age of son was = 14 – 12 = 2 years
∴ ratio = 30 / 2 = 15 / 1 = 15 : 1