Worksheet on Ratio of Two or More Quantities

Practice the questions given in the worksheet on ratio of two or more quantities.

Here the questions are related how to divide a quantity into two parts in a given ratio and similarly, to divide a quantity into three parts in a given ratio.

1. Divide 3570 in the ratio 2\(\frac{1}{5}\) : \(\frac{3}{5}\).

2. If a : b = 3 : 8 and c : d = 4 : 9 then find a : d.

3. If x : y = 2 : 3 and y : z = 9 : 8 then find the duplicate ratio of x : z.

4. Divide $ 2880 in the ratio \(\frac{1}{5}\) : \(\frac{2}{15}\) : 1\(\frac{2}{3}\).

5.  If x : y = 12 : 5 and y : z = 15 : 8 then find the reciprocal ratio of x : z.

6. If x : y = 3 : 4 and y : z = 5 : 6, find: (i) x : z (ii) x : y : z

7. If j : k = 7 : 8, k : l = 15 : 4 and l : m = 16 : 21 then find m : j.

8. If p : q = \(\frac{1}{3}\) : \(\frac{1}{2}\) and q : r = \(\frac{1}{4}\) : \(\frac{1}{5}\), find (i) p : r (ii) p : q : r.

9. If a : b = 2 : 5, b : c = 15 : 8 and c : k = 3 : 2 then find the triplicate ratio of a :  k.

10. Find x such that the ratio (28 + k) : (40 + k) = 3 : 4.

11. What should be added to both terms of 17 : 29 so that the ratio becomes 5 : 8?

12. What should be subtracted from both the terms of 19 : 39 So that the ratio becomes 3 : 7?

13. The angles of a triangle are in the ratio 3 : 5 : 10. Find the angles.

14. Find p if (3p + 1) : (5p - 4) is the duplicate ratio of 5 : 6.

15. Find m if (m + 1) : (m - 2) is the reciprocal ratio of 10 : 13.

16. If x : y = 4 : 5 and y : z = 2 : 15, find (i) x : y (ii) x : y : z

17. If a : b = 4 : 7, find the ratios:

(i) (4a + 7b) : (5a - b)

(ii) (3a - b) : (a + b)

18. If x : y : z = 1 : 3 : 5 and z = 25, find x and y.

19. If x : y = 5 : 3, find (5x + 8y) : (6x - 7y).

20. If (4a + 5b) : (a + 3b) = 2 : 1 then find a : b.

21. If (a + b) : (a - b) is equal to the duplicate ratio of 3 : 1 then find a : b.

22. If y(2x - y) : x(6x - y) = 1 : 6 then find ratio then find the ratio y : x.

23. If x : y : z = \(\frac{1}{5}\) : \(\frac{2}{25}\) : \(\frac{3}{5}\) and y = 24, find x and z.

24.  If (a^2 + b^2) : ab = 5 : 2 then find the ratio (a + 2b) : (2a +b).

25. If (m + 3n) : (5m - 2n) = (4m + n) : (8m - 4n), where m ≠ 0, n ≠ 0 then find n : m.

26. If 2x = 5y = 4z, find x : y : z.

27. If the reciprocal ratio of (2x + y) : (x - y) is the ratio (x + 2y) : (3x - 2y) then find the duplicate ratio of a : b.

Answers for worksheet on ratio of two or more quantities are given below.

Answers:

1. $ 2805 and $ 765

2. 1 : 6

3. 9 : 16

4. $ 288, $ 192 and $ 2400

5. 2 : 9

6. (i) 5 : 8

(ii) 15 : 20 : 24

7. 2 : 5

8. (i) 5 : 6

(ii) 10 : 15 : 12

9. 729 : 512

10. 8

11. 3

12. 4

13. 30°, 50° and 100°

14. 8

15. 12

16. (i) 6 : 1

(ii) 12 : 2 : 15

17. (i) 5 : 1

(ii) 5 : 11

18. x : 5, y = 15

19. 49 : 9

20. 1 : 2

21. 5 : 4

22. 2 : 3 or 3 : 2

23. x = 60, z = 180.

24. 4 : 5 or 5 : 4

25. 3 : 2 or 4 : 5

26. 10 : 4 : 5

27. 100 : 1

● Ratio and proportion

• Basic Concept of Ratios
• Important Properties of Ratios
• Ratio in Lowest Term
  
• Types of Ratios
• Comparing Ratios
• Arranging Ratios
  
• Dividing into a Given Ratio
  
• Divide a Number into Three Parts in a Given Ratio
• Dividing a Quantity into Three Parts in a Given Ratio
  
• Problems on Ratio
  
• Worksheet on Ratio in Lowest Term
  
• Worksheet on Types of Ratios
  
• Worksheet on Comparison on Ratios
• Worksheet on Ratio of Two or More Quantities
  
• Worksheet on Dividing a Quantity in a Given Ratio
• Word Problems on Ratio
  
• Proportion
  
• Definition of Continued Proportion
  
• Mean and Third Proportional
  
• Word Problems on Proportion
  
• Worksheet on Proportion and Continued Proportion
  
• Worksheet on Mean Proportional
  
• Properties of Ratio and Proportion

10th Grade Math

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