Worksheet on Proportions

In worksheet on proportions the questions are related to the basic concept of proportion, continued proportion, finding mean proportional between the numbers and also word problems on proportion. Recall the topic proportion and then practice the questions on proportion.

1. Check if each of the following is in proportion. 

(a) 6, 21, 12, 4 

(b) 4, 3, 6, 45 

(c) 5, 8, 200, 125 

(d) 30, 16, 45, 25 

(e) 18, 8, 54, 24 

(f) 6, 8, 24, 30 

2. Find the value of x in the following.

(a) 6 : 9 :: x : 15

(b) x : 7 :: 12 : 21

(c) 4 : x :: 8 : 14

(d) x : 3 :: 0.4 : 0.5

(e) \(\frac{1}{3}\) ∶ \(\frac{1}{4}\) : : \(\frac{1}{9}\) : x

(f) 9 : x :: 6 : 10

(g) 2 : 7 :: x : 42

(h) 30 : 25 :: 42 : x

(i) x : 1.5 :: 6.3 : 4.5

3. Find the fourth proportional to

(a) 18, 54, 6

(b) 30, 32, 42

(c) 4, 3, 6

(d) 2, 6, 1

(e) 32, 24, 8

4. Find the third proportional to

(a) 2, 4

(b) 3, 9

(c) 36, 42

(d) 16, 36

(e) 14, 28

(f) 48, 96

5. Find the mean proportional between

(a) 36 and 4

(b) 1.2 and 0.3 

(c) 25 and 9

(d) 24 and 54

(e) \(\frac{1}{9}\) and 4

6. The first, second and fourth terms of the proportion are 9, 21, 77. Find the third term.

7. The second, third and fourth terns of the proportion are 27, 35, 63. Find the first term.

8. In the school library, the ratio of science books to social studies books is the same as the ratio of social studies books to math books. If there are 450 books in science and 300 books in social studies, find the number of books on math.

9. If 4 books cost $28, what will the cost of 20 books be?

10. The ratio of length and breadth of a playground is 3 : 2. Find the length if breadth is 36 m.

11. In a proportion, the first, third and fourth terms are 80, 30 and 24 respectively. Find the second term.

12. Find the mean proportion of the following.

(i) 5, 20

(ii) 49, 36

13. If 25, 35 and x are in continued proportion, find the value of x.

14. In a proportion, the first, second and third terms are 9500, 7500 and 665, respectively. Find the fourth term.

Answers for the worksheet on proportions are given below to check the exact answers of the questions.

Answers:

1. (a) No

(b) No

(c) No

(d) No

(e) Yes

(f) No

2. (a) 10

(b) 4

(c) 7

(d) 2.4

(e) \(\frac{1}{12}\)

(f) 15

(g) 12

(h) 35

(i) 2.1

3. (a) 18

(b) 37\(\frac{1}{3}\)

(c) 4.5

(d) 3

(e) 6

4. (a) 8

(b) 27

(c) 49

(d) 81

(e) 56

(f) 192

5. (a) 12

(b) 0.6

(c) 15

(d) 36

(e) \(\frac{2}{3}\)

6. 33

7. 15

8. 200

9. $ 140

10. 54 m

11. 64

12. (i) 10

(ii) 42

13. x = 49

14. Fourth term = 525

● Ratios and Proportions - Worksheets

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Worksheet on Proportions

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