Worksheet on Ratio and Proportion

Math worksheet on ratio and proportion encourage the students to practice more questions and think more about it. The questions are related to express the ratios in the simplest form, simplify the ratio, compare the ratios, arranging the ratios in the ascending order or descending order, proportion and also mean proportional between the numbers.

1. Express each of the following ratios in the simplest form. 

(a) 5.6 m to 28 cm

(b) dozen to a score 

(c) score to a gross 

(d) 6 hours to a day 

(e) 20 litres to 0.75 litres 

(f) 1728 : 2400 

2. Simplify the following ratios. 

(a) 1/4 : 1/6 : 1/8

(b) 3.6 : 4.5

(c) 3²/₃ : 4¹/₂

(d) 3 : 2.4 : 2¹/₄

3. Compare the following ratios.

(a) 5 : 7 and 4 : 3

(b) 1/3 : 1/4 and 1/5 ∶ 1/4

(c) 2¹/₂ : 3¹/₃ and 0.3 : 1

(d) 2³/₄ : 1²/₃ and 1.2 : 1.5

4. Arrange the following in ascending order.

(a)  3 : 8, 5 : 6, 1 : 3,

(b)   17 : 20, 7 : 10, 4 : 5

(c)  5 : 14, 7 : 10, 3 : 7, 1 : 5

5. In the ratio 3 : 5, the consequent is 15. Find the antecedent.

6. Divide 3000 among P, Q, R in the ratio 2 : 3 : 5

7. Which of the following statements are true?

(a) 25 : 35 = 45 : 55

(b) 105 : 30 = 49 : 14

(c) 45 : 48 = 60 : 64

(d) 2/3 : 7/9 = 3/4 : 5/6

(e) 4.2 : 12.6 = 1.5 : 4.5

(f) 12 : 18 = 28 : 12

8. Determine if the following ratios form a proportion.

(a) 25 cm : 1 m = $40 : $160

(b) 200 ml : 2.5 l = $4 : $50

(c) 32 m : 64 m = 7 seconds : 14 seconds

(d) 6.5 litres : 13 litres = 50 kg : 10 kg

9. Find the value of x in each of the following.

(a) 4, 5, x, 480

(b) 9, 21, 33, x

(c) x, 28, 20, 4

(d) 15, x, 27, 63

(e) x, 30, 60

(f) 6, x, 24

10. Find the fourth proportional to

(a) 5.6, 2.1, 1.6, x

(b) 3/4, 15/16, 2/4, x

(c) 5³/₅, 3¹/₂, 2, x

(d) 8, 6, 4, x

11. Find the third proportional to

(a) 9, 6, x

(b) 0.2, 0.4, x

(c) 9/16, 3/5, x 

(d) 6, 12, x

12. Find the mean proportional between

(a) 9 and 4 

(b) 1.6 and 0.4

(c) 1⁴/₅ and ⁴/₅

13. Multiple Choice Questions (MCQ) on Ratio and Proportion:

   Tick (✔) the correct option.

(a) If 8, m, 6, 54 are in proportion, then the value of m is

(i) 49

(ii) 72

(iii) 63

(iv) 36

(b) If 72 : x = 57 : 95, then the value of x is

(i) 76

(ii) 95

(iii) 120

(iv) 114

(c) If 65 : x :: 35 : 42, then the value of x is

(i) 78

(ii) 63

(ii) 54

(iv) 60

(d) Two numbers are in ratio 3 : 5. If sum of the numbers is 288, the larger one is

(i) 110

(ii) 75

(iii) 108

(iv) 180

14. State True or False:

(i) A ratio is a fraction. It cannot be an integer.

(ii) A ratio of whose terms have no common factor other than 1 is said to be in the simplest form.

(iii) If the cost of 9 toys is $ 274.50, the cost of 5 toys will be $ 152.75.

(iv) The ratio of the height of James and Michael is 6 : 5. If James is 1.5 m tall, then Michael's height is 1.8 m

15. The number of male and female in a office are 520 and 650 respectively. Find the ratio of female to the total number of employees.

16. Two number are in the ratio 5 : 7. If sum of the numbers is 840, find them.

17. The length of a swimming pool is 26 m and its breadth is 15.6 m. Find the ratio of its length to its breadth.

18. If 30 bed covers cost $ 70, what is the cost of 6 dozen bed covers?

19. 23 kg of sugar costs Rs. 333.50. What is the cost of 12 kg sugar?

20. A web designer earned $ 53200 in 28 months. How much does he earn in 6 months?

21. If a dozen of eggs costs Rs. 90.84, how many eggs can be bought for Rs. 166.54?

22. Find x in the following proportions

(i) 6 : 15 = 2 : x

(ii) 2 : 4 = x : 10

(iii) x : 3 = 8 : 12

23. If the cost of 17 metres carpet is $ 340, find the cost of 11 metres.

24. Alexander can type 2820 words in one hour. How many words can he type in 15 minutes?

Answers for the math worksheet on ratio and proportion are given below to check the exact answers of the questions.

Answers:

1. (a) 20 : 1

(b) 3 : 5

(c) 5 : 36

(d) 1 : 4

(e) 80 : 3

(f) 18 : 25

2. (a) 6 : 4 : 3

(b) 4 : 5

(c) 22 : 27

(d) 20 : 16 : 15

3. (a) 5 : 7 < 4 : 3

(b) 1/3 ∶ 1/4 > 1/5 : 1/4

(c) 2¹/₂ : 3¹/₃ > 0.3 : 1

(d) 2³/₄ : 1²/₃ > 1. 2 : 1.5

4. (a) 1 : 3, 3 : 8, 5 : 6

(b) 7 : 10, 4 : 5, 17 : 20

(c) 1 : 5, 5 : 14, 3 : 7, 7 : 10

5. 9

6. $600, $900, $1500

7. (b) true

(c) true

(e) true

8. (a) (b) (c) in proportion

9. (a) 384

(b) 77

(c) 140

(d) 35

(e) 15

(f) 12

10. (a) 0.6

(b) 5/8

(c) 5/4

(d ) 3

11. (a) 4

(b) 0.8

(c) 16/25

(d) 24

12. (a) 6

(b) 0.8

(c) 6/5

13. (a) → (ii) 72

(b) → (iii) 120

(c) → (i) 78

(d) → (iv) 180

14. (i) False

(ii) True

(iii) False

(iv) False

15. 5 : 9

16. 350 and 490

17. 5 : 3

18. $ 168

19. Rs. 174

20. $ 11400

21. 22 eggs

22. (i) x = 5

(ii) x = 5

(iii) x = 2

23. $ 220

24. 705 words 

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