Exercise 3.1

Exercise 3.1

1. Fill in the blanks.

(i) Ratio of ₹ 3 to ₹ 5 = 3 : 5.

(ii) Ratio of 3m to 200cm = 3 : 2. [200cm = 2m].

(iii) Ratio of 5 km 400 m to 6 km = 9:10. [54:60].

(iv) Ratio of 75 paise to ₹ 2 = 3 : 8. [75 : 200].

2. Say whether the following statements are True or False.

(i) The ratio of 130 cm to 1 m is 13 : 10. [True]

(ii) One of the terms in a ratio cannot be 1. [False]

3. Find the simplified form of the following ratios.

(i) 15 : 20 (ii) 32 : 24 (iii) 7 : 15 (iv) 12 : 27 (v) 75 : 100

Solution:

(i) 15 : 20

Fractional form = (15 ÷ 5) / (20 ÷ 5) = 3 / 4

Simplest form = 3 : 4

(ii) 32 : 24

Fractional form = [32 ÷ 8] / [24 ÷ 8] = 4 / 3

Simplest form = 4 : 3

(iii) 7 : 15

Fractional form = 7 / 15 (No common divisor)

Simplest form = 7 : 15

(iv) 12 : 27

Fractional form = [12 ÷  3] / [27 ÷  3] = 4 / 9

Simplest form = 4 : 9

(v) 75: 100

Fractional form = [75 ÷  25]  / [100 ÷ 25]  = 3 / 4

Simplest form = 3 : 4

4. Akilan walks 10 km in an hour while Selvi walks 6 km in an hour. Find the simplest ratio of the distance covered by Akilan to that of Selvi.

Solution:

Akilan walks in an hour = 10 km

Selvi walks in an hour = 6 km

Ratio of distance covered by both = 10 : 6

Simplest form:

[10 ÷ 2]  / [6 ÷  2] = 5 / 3

Distance covered by Akilan and Selvi = 5 : 3

5. The cost of parking a bicycle is ₹ 5 and the cost of parking a scooter is ₹ 15. Find the simplest ratio of the parking cost of a bicycle to that of a scooter.

Solution:

Parking cost of a bicycle = Rs. 5

Parking cost of a scooter = Rs.15

Simplest ratio of bicycle to scooter

[5 ÷  5] / [15 ÷  5] = 1 / 3  

Ratio of bicycle to scooter = 1 : 3

6. Out of 50 students in a class, 30 are boys. Find the ratio of

(i) number of boys to the number of girls.

(ii) number of girls to the total number of students.

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

Solution:

Total No. of students = 50

No. of boys = 30

No. of girls = 50 − 30

= 20 girls

(i) number of boys to the number of girls.

boys : girls = 30 : 20

Simplest form = [30 ÷ 10] / [20 ÷ 10] = 3 / 2

boys : girls = 3:2

(ii) number of girls to the total number of students.

girls : total students = 20 : 50

Simplest form =  [20 ÷ 10] / [50 ÷ 10] = 2 / 5

girls : students = 2 : 5

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

boys : total students = 30 : 50

Simplest form = [30 ÷ 10] / [50 ÷ 10] = 3 / 5

boys : students = 3 : 5

Objective Type Questions

7. The ratio of ₹ 1 to 20 paise is __________.

(a) 1 : 5

(b) 1 : 2

(c) 2 : 1

(d) 5 : 1

Answer: (d) 5 : 1

8. The ratio of 1 m to 50 cm is __________.

(a) 1 : 50

(b) 50 : 1

(c) 2 : 1

(d) 1 : 2

Answer: (c) 2 : 1

9. The length and breadth of a window are in 1m and 70 cm respectively. The ratio of the length to the breadth is ____________.

(a) 1 : 7

(b) 7 : 1

(c) 7 : 10

(d) 10 : 7

Answer: (d) 10:7

10. The ratio of the number of sides of a triangle to the number of sides of a rectangle is

(a) 4 : 3

(b) 3 : 4

(c) 3 : 5

(d) 3 : 2

Answer: (b) 3 : 4

11. If Azhagan is 50 years old and his son is 10 years old then the simplest ratio between the age of Azhagan to his son is

(a) 10 : 50

(b) 50 : 10

(c) 5 : 1

(d) 1 : 5

Answer: (c) 5 : 1

Answers:

Exercise 3.1

1) (i) 3 : 5 (ii) 3 : 2 (iii) 9 : 10 (iv) 3 : 8

2) (i) True (ii) False

3) (i) 3 : 4 (ii) 4 : 3 (iii) 7 : 15 (iv) 4 : 9 (v) 3 : 4

4) 5 : 3

5) 1 : 3

6) (i) 3 : 2 (ii) 2 : 5 (iii) 3 : 5

7) (d) 5 : 1

8) (c) 2 : 1

9) (d) 10 : 7

10. (b) 3 : 4

11. (c) 5 : 1