# 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

10th Grade Math

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