Page 1 Exercise 9.3 page: 9.14 1. Which of the following statements are true? (i) 16: 24 = 20: 30 (ii) 21: 6 = 35: 10 (iii) 12: 18 = 28: 12 (iv) 51: 58 = 85: 102 (v) 40 men: 200 men = Rs 5: Rs 25 (vi) 99 kg: 45 kg = Rs 44: Rs 20 Solution: (i) 16: 24 = 20: 30 It can be written as 16/24 = 20/30 Dividing 16/24 by 4/4 and 20/30 by 5/5 (16/24) ÷ (4/4) = (20/30) ÷ (5/5) On further calculation 4/6 = 4/6 We get 2/3 = 2/3 Hence, 16: 24 = 20: 30 is true. (ii) 21: 6 = 35: 10 It can be written as 21/6 = 35/10 Dividing 21/6 by 3/3 and 35/10 by 5/5 (21/6) ÷ (3/3) = (35/10) ÷ (5/5) On further calculation 7/2 = 7/2 Hence, 21: 6 = 35: 10 is true. (iii) 12: 18 = 28: 12 It can be written as 12/18 = 28/12 On further calculation 6/9 ? 14/6 Hence, 12: 18 = 28: 12 is false. (iv) 51: 58 = 85: 102 It can be written as 51/58 = 85/102 On further calculation 51/58 ? 5/6 Hence, 51: 58 = 85: 102 is false. (v) 40 men: 200 men = Rs 5: Rs 25 Page 2 Exercise 9.3 page: 9.14 1. Which of the following statements are true? (i) 16: 24 = 20: 30 (ii) 21: 6 = 35: 10 (iii) 12: 18 = 28: 12 (iv) 51: 58 = 85: 102 (v) 40 men: 200 men = Rs 5: Rs 25 (vi) 99 kg: 45 kg = Rs 44: Rs 20 Solution: (i) 16: 24 = 20: 30 It can be written as 16/24 = 20/30 Dividing 16/24 by 4/4 and 20/30 by 5/5 (16/24) ÷ (4/4) = (20/30) ÷ (5/5) On further calculation 4/6 = 4/6 We get 2/3 = 2/3 Hence, 16: 24 = 20: 30 is true. (ii) 21: 6 = 35: 10 It can be written as 21/6 = 35/10 Dividing 21/6 by 3/3 and 35/10 by 5/5 (21/6) ÷ (3/3) = (35/10) ÷ (5/5) On further calculation 7/2 = 7/2 Hence, 21: 6 = 35: 10 is true. (iii) 12: 18 = 28: 12 It can be written as 12/18 = 28/12 On further calculation 6/9 ? 14/6 Hence, 12: 18 = 28: 12 is false. (iv) 51: 58 = 85: 102 It can be written as 51/58 = 85/102 On further calculation 51/58 ? 5/6 Hence, 51: 58 = 85: 102 is false. (v) 40 men: 200 men = Rs 5: Rs 25 It can be written as 40/200 = 5/25 We get 40/200 = 1/5 and 5/25 = 1/5 Hence, 40 men: 200 men = Rs 5: Rs 25 is true. (vi) 99 kg: 45 kg = Rs 44: Rs 20 It can be written as 99/45 = 44/20 Dividing the fraction by 9 (99/45) ÷ (9/9) = (44/20) ÷ (9/9) On further calculation 11/5 = 11/5 Hence, 99 kg: 45 kg = Rs 44: Rs 20 is true. 2. Find which of the following are in proportion: (i) 8, 16, 6, 12 (ii) 6, 2, 4, 3 (iii) 150, 250, 200, 300 Solution: (i) 8, 16, 6, 12 We know that 8: 16 = 8/16 = 1/2 6: 12 = 6/12 = 1/2 So we get 8/16 = 6/12 Therefore, 8, 16, 6, 12 are in proportion. (ii) 6, 2, 4, 3 We know that 6: 2 = 6/2 = 3/1 4: 3 = 4/3 So we get 3/1 ? 4/3 Therefore, 6, 2, 4, 3 are not in proportion. (iii) 150, 250, 200, 300 We know that 150: 250 = 150/250 = 3/5 200: 300 = 200/300 = 4/6 = 2/3 So we get 3/5 ? 2/3 Therefore, 150, 250, 200, 300 are not in proportion. 3. Find x in the following proportions: (i) x: 6 = 55: 11 (ii) 18: x = 27: 3 (iii) 7: 14 = 15: x Page 3 Exercise 9.3 page: 9.14 1. Which of the following statements are true? (i) 16: 24 = 20: 30 (ii) 21: 6 = 35: 10 (iii) 12: 18 = 28: 12 (iv) 51: 58 = 85: 102 (v) 40 men: 200 men = Rs 5: Rs 25 (vi) 99 kg: 45 kg = Rs 44: Rs 20 Solution: (i) 16: 24 = 20: 30 It can be written as 16/24 = 20/30 Dividing 16/24 by 4/4 and 20/30 by 5/5 (16/24) ÷ (4/4) = (20/30) ÷ (5/5) On further calculation 4/6 = 4/6 We get 2/3 = 2/3 Hence, 16: 24 = 20: 30 is true. (ii) 21: 6 = 35: 10 It can be written as 21/6 = 35/10 Dividing 21/6 by 3/3 and 35/10 by 5/5 (21/6) ÷ (3/3) = (35/10) ÷ (5/5) On further calculation 7/2 = 7/2 Hence, 21: 6 = 35: 10 is true. (iii) 12: 18 = 28: 12 It can be written as 12/18 = 28/12 On further calculation 6/9 ? 14/6 Hence, 12: 18 = 28: 12 is false. (iv) 51: 58 = 85: 102 It can be written as 51/58 = 85/102 On further calculation 51/58 ? 5/6 Hence, 51: 58 = 85: 102 is false. (v) 40 men: 200 men = Rs 5: Rs 25 It can be written as 40/200 = 5/25 We get 40/200 = 1/5 and 5/25 = 1/5 Hence, 40 men: 200 men = Rs 5: Rs 25 is true. (vi) 99 kg: 45 kg = Rs 44: Rs 20 It can be written as 99/45 = 44/20 Dividing the fraction by 9 (99/45) ÷ (9/9) = (44/20) ÷ (9/9) On further calculation 11/5 = 11/5 Hence, 99 kg: 45 kg = Rs 44: Rs 20 is true. 2. Find which of the following are in proportion: (i) 8, 16, 6, 12 (ii) 6, 2, 4, 3 (iii) 150, 250, 200, 300 Solution: (i) 8, 16, 6, 12 We know that 8: 16 = 8/16 = 1/2 6: 12 = 6/12 = 1/2 So we get 8/16 = 6/12 Therefore, 8, 16, 6, 12 are in proportion. (ii) 6, 2, 4, 3 We know that 6: 2 = 6/2 = 3/1 4: 3 = 4/3 So we get 3/1 ? 4/3 Therefore, 6, 2, 4, 3 are not in proportion. (iii) 150, 250, 200, 300 We know that 150: 250 = 150/250 = 3/5 200: 300 = 200/300 = 4/6 = 2/3 So we get 3/5 ? 2/3 Therefore, 150, 250, 200, 300 are not in proportion. 3. Find x in the following proportions: (i) x: 6 = 55: 11 (ii) 18: x = 27: 3 (iii) 7: 14 = 15: x (iv) 16: 18 = x: 96 Solution: (i) x: 6 = 55: 11 It can be written as x/6 = 55/11 We get x/6 = 5/1 On further calculation x = 5 (6) = 30 (ii) 18: x = 27: 3 It can be written as 18/x = 27/3 We get 18/x = 9/1 On further calculation x = 18/9 = 2 (iii) 7: 14 = 15: x It can be written as 7/14 = 15/x We get 1/2 = 15/x On further calculation x = 15 (2) = 30 (iv) 16: 18 = x: 96 It can be written as 16/18 = x/96 We get 8/9 = x/96 On further calculation x = 8/9 (96) = 256/3 4. Set up all proportions from the numbers 9, 150, 105, 1750. Solution: The proportions from the numbers are 9: 150 = 3: 50 9: 105 = 3: 35 9: 1750 150: 9 = 50: 3 150: 105 = 10: 7 150: 1750 = 3: 35 105: 9 = 35: 3 105: 150 = 7: 10 105: 1750 = 3: 50 1750: 9 1750: 150 = 35: 3 Page 4 Exercise 9.3 page: 9.14 1. Which of the following statements are true? (i) 16: 24 = 20: 30 (ii) 21: 6 = 35: 10 (iii) 12: 18 = 28: 12 (iv) 51: 58 = 85: 102 (v) 40 men: 200 men = Rs 5: Rs 25 (vi) 99 kg: 45 kg = Rs 44: Rs 20 Solution: (i) 16: 24 = 20: 30 It can be written as 16/24 = 20/30 Dividing 16/24 by 4/4 and 20/30 by 5/5 (16/24) ÷ (4/4) = (20/30) ÷ (5/5) On further calculation 4/6 = 4/6 We get 2/3 = 2/3 Hence, 16: 24 = 20: 30 is true. (ii) 21: 6 = 35: 10 It can be written as 21/6 = 35/10 Dividing 21/6 by 3/3 and 35/10 by 5/5 (21/6) ÷ (3/3) = (35/10) ÷ (5/5) On further calculation 7/2 = 7/2 Hence, 21: 6 = 35: 10 is true. (iii) 12: 18 = 28: 12 It can be written as 12/18 = 28/12 On further calculation 6/9 ? 14/6 Hence, 12: 18 = 28: 12 is false. (iv) 51: 58 = 85: 102 It can be written as 51/58 = 85/102 On further calculation 51/58 ? 5/6 Hence, 51: 58 = 85: 102 is false. (v) 40 men: 200 men = Rs 5: Rs 25 It can be written as 40/200 = 5/25 We get 40/200 = 1/5 and 5/25 = 1/5 Hence, 40 men: 200 men = Rs 5: Rs 25 is true. (vi) 99 kg: 45 kg = Rs 44: Rs 20 It can be written as 99/45 = 44/20 Dividing the fraction by 9 (99/45) ÷ (9/9) = (44/20) ÷ (9/9) On further calculation 11/5 = 11/5 Hence, 99 kg: 45 kg = Rs 44: Rs 20 is true. 2. Find which of the following are in proportion: (i) 8, 16, 6, 12 (ii) 6, 2, 4, 3 (iii) 150, 250, 200, 300 Solution: (i) 8, 16, 6, 12 We know that 8: 16 = 8/16 = 1/2 6: 12 = 6/12 = 1/2 So we get 8/16 = 6/12 Therefore, 8, 16, 6, 12 are in proportion. (ii) 6, 2, 4, 3 We know that 6: 2 = 6/2 = 3/1 4: 3 = 4/3 So we get 3/1 ? 4/3 Therefore, 6, 2, 4, 3 are not in proportion. (iii) 150, 250, 200, 300 We know that 150: 250 = 150/250 = 3/5 200: 300 = 200/300 = 4/6 = 2/3 So we get 3/5 ? 2/3 Therefore, 150, 250, 200, 300 are not in proportion. 3. Find x in the following proportions: (i) x: 6 = 55: 11 (ii) 18: x = 27: 3 (iii) 7: 14 = 15: x (iv) 16: 18 = x: 96 Solution: (i) x: 6 = 55: 11 It can be written as x/6 = 55/11 We get x/6 = 5/1 On further calculation x = 5 (6) = 30 (ii) 18: x = 27: 3 It can be written as 18/x = 27/3 We get 18/x = 9/1 On further calculation x = 18/9 = 2 (iii) 7: 14 = 15: x It can be written as 7/14 = 15/x We get 1/2 = 15/x On further calculation x = 15 (2) = 30 (iv) 16: 18 = x: 96 It can be written as 16/18 = x/96 We get 8/9 = x/96 On further calculation x = 8/9 (96) = 256/3 4. Set up all proportions from the numbers 9, 150, 105, 1750. Solution: The proportions from the numbers are 9: 150 = 3: 50 9: 105 = 3: 35 9: 1750 150: 9 = 50: 3 150: 105 = 10: 7 150: 1750 = 3: 35 105: 9 = 35: 3 105: 150 = 7: 10 105: 1750 = 3: 50 1750: 9 1750: 150 = 35: 3 1750: 105 = 50: 3 Hence, the proportions that are formed are 9: 150 :: 105: 1750 150: 9 :: 1750: 105 1750: 150 :: 105: 9 9: 105 :: 150: 1750 5. Find the other three proportions involving terms of each of the following: (i) 45: 30 = 24: 16 (ii) 12: 18 = 14: 21 Solution: (i) 45: 30 = 24: 16 can be written as 3: 2 in simplest form So the other three proportions involving terms are 45: 24 = 30: 16 can be written as 15: 8 in simplest form 30: 45 = 16: 24 can be written as 2: 3 in simplest form 16: 30 = 24: 45 can be written as 8: 15 in simplest form (ii) 12: 18 = 14: 21 can be written as 2: 3 in simplest form So the other three proportions involving terms are 12: 14 = 18: 21 can be written as 6: 7 in simplest form 21: 18 = 14: 12 can be written as 7: 6 in simplest form 18: 12 = 21: 14 can be written as 3: 2 in simplest form 6. If 4, x, 9 are in continued proportion, find the value of x. Solution: We know that 4, x, 9 are in continued proportion It can be written as 4: x :: x: 9 We get 4/x = x/9 On further calculation x 2 = 9 (4) = 36 So we get x = 6 7. If in a proportion, the first, second and fourth terms are 32, 112 and 217 respectively, find the third term. Solution: It is given that in a proportion the first, second and fourth terms are 32, 112 and 217 Consider x as the third term We can write it as 32: 112 :: x: 217 On further calculation 32/112 = x/217 So we get x = 32/112 (217) = 62 Page 5 Exercise 9.3 page: 9.14 1. Which of the following statements are true? (i) 16: 24 = 20: 30 (ii) 21: 6 = 35: 10 (iii) 12: 18 = 28: 12 (iv) 51: 58 = 85: 102 (v) 40 men: 200 men = Rs 5: Rs 25 (vi) 99 kg: 45 kg = Rs 44: Rs 20 Solution: (i) 16: 24 = 20: 30 It can be written as 16/24 = 20/30 Dividing 16/24 by 4/4 and 20/30 by 5/5 (16/24) ÷ (4/4) = (20/30) ÷ (5/5) On further calculation 4/6 = 4/6 We get 2/3 = 2/3 Hence, 16: 24 = 20: 30 is true. (ii) 21: 6 = 35: 10 It can be written as 21/6 = 35/10 Dividing 21/6 by 3/3 and 35/10 by 5/5 (21/6) ÷ (3/3) = (35/10) ÷ (5/5) On further calculation 7/2 = 7/2 Hence, 21: 6 = 35: 10 is true. (iii) 12: 18 = 28: 12 It can be written as 12/18 = 28/12 On further calculation 6/9 ? 14/6 Hence, 12: 18 = 28: 12 is false. (iv) 51: 58 = 85: 102 It can be written as 51/58 = 85/102 On further calculation 51/58 ? 5/6 Hence, 51: 58 = 85: 102 is false. (v) 40 men: 200 men = Rs 5: Rs 25 It can be written as 40/200 = 5/25 We get 40/200 = 1/5 and 5/25 = 1/5 Hence, 40 men: 200 men = Rs 5: Rs 25 is true. (vi) 99 kg: 45 kg = Rs 44: Rs 20 It can be written as 99/45 = 44/20 Dividing the fraction by 9 (99/45) ÷ (9/9) = (44/20) ÷ (9/9) On further calculation 11/5 = 11/5 Hence, 99 kg: 45 kg = Rs 44: Rs 20 is true. 2. Find which of the following are in proportion: (i) 8, 16, 6, 12 (ii) 6, 2, 4, 3 (iii) 150, 250, 200, 300 Solution: (i) 8, 16, 6, 12 We know that 8: 16 = 8/16 = 1/2 6: 12 = 6/12 = 1/2 So we get 8/16 = 6/12 Therefore, 8, 16, 6, 12 are in proportion. (ii) 6, 2, 4, 3 We know that 6: 2 = 6/2 = 3/1 4: 3 = 4/3 So we get 3/1 ? 4/3 Therefore, 6, 2, 4, 3 are not in proportion. (iii) 150, 250, 200, 300 We know that 150: 250 = 150/250 = 3/5 200: 300 = 200/300 = 4/6 = 2/3 So we get 3/5 ? 2/3 Therefore, 150, 250, 200, 300 are not in proportion. 3. Find x in the following proportions: (i) x: 6 = 55: 11 (ii) 18: x = 27: 3 (iii) 7: 14 = 15: x (iv) 16: 18 = x: 96 Solution: (i) x: 6 = 55: 11 It can be written as x/6 = 55/11 We get x/6 = 5/1 On further calculation x = 5 (6) = 30 (ii) 18: x = 27: 3 It can be written as 18/x = 27/3 We get 18/x = 9/1 On further calculation x = 18/9 = 2 (iii) 7: 14 = 15: x It can be written as 7/14 = 15/x We get 1/2 = 15/x On further calculation x = 15 (2) = 30 (iv) 16: 18 = x: 96 It can be written as 16/18 = x/96 We get 8/9 = x/96 On further calculation x = 8/9 (96) = 256/3 4. Set up all proportions from the numbers 9, 150, 105, 1750. Solution: The proportions from the numbers are 9: 150 = 3: 50 9: 105 = 3: 35 9: 1750 150: 9 = 50: 3 150: 105 = 10: 7 150: 1750 = 3: 35 105: 9 = 35: 3 105: 150 = 7: 10 105: 1750 = 3: 50 1750: 9 1750: 150 = 35: 3 1750: 105 = 50: 3 Hence, the proportions that are formed are 9: 150 :: 105: 1750 150: 9 :: 1750: 105 1750: 150 :: 105: 9 9: 105 :: 150: 1750 5. Find the other three proportions involving terms of each of the following: (i) 45: 30 = 24: 16 (ii) 12: 18 = 14: 21 Solution: (i) 45: 30 = 24: 16 can be written as 3: 2 in simplest form So the other three proportions involving terms are 45: 24 = 30: 16 can be written as 15: 8 in simplest form 30: 45 = 16: 24 can be written as 2: 3 in simplest form 16: 30 = 24: 45 can be written as 8: 15 in simplest form (ii) 12: 18 = 14: 21 can be written as 2: 3 in simplest form So the other three proportions involving terms are 12: 14 = 18: 21 can be written as 6: 7 in simplest form 21: 18 = 14: 12 can be written as 7: 6 in simplest form 18: 12 = 21: 14 can be written as 3: 2 in simplest form 6. If 4, x, 9 are in continued proportion, find the value of x. Solution: We know that 4, x, 9 are in continued proportion It can be written as 4: x :: x: 9 We get 4/x = x/9 On further calculation x 2 = 9 (4) = 36 So we get x = 6 7. If in a proportion, the first, second and fourth terms are 32, 112 and 217 respectively, find the third term. Solution: It is given that in a proportion the first, second and fourth terms are 32, 112 and 217 Consider x as the third term We can write it as 32: 112 :: x: 217 On further calculation 32/112 = x/217 So we get x = 32/112 (217) = 62 8. Show that the following numbers are in continued proportion: (i) 36, 90, 225 (ii) 48, 60, 75 (iii) 16, 84, 441 Solution: (i) 36, 90, 225 Consider the fraction 36/90 By dividing the fraction by 18 We get 36/90 = 2/5 Consider the fraction 90/225 By dividing the fraction by 45 We get 90/225 = 2/5 Hence, 36: 90 :: 90: 225. (ii) 48, 60, 75 Consider the fraction 48/60 By dividing the fraction by 12 We get 48/60 = 4/5 Consider the fraction 60/75 By dividing the fraction by 15 We get 60/75 = 4/5 Hence, 48: 60 :: 60: 75. (iii) 16, 84, 441 Consider the fraction 16/84 By dividing the fraction by 4 We get 16/84 = 4/21 Consider the fraction 84/441 By dividing the fraction by 21 We get 84/441 = 4/21 Hence, 16: 84 :: 84: 441. 9. The ratio of the length of a school ground to its width is 5: 2. Find its length if the width is 40 metres. Solution: It is given that Ratio of length of a school ground to its width = 5: 2Read More

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