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
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