Ratio, Proportion and Unitary Method - Exercise 9.3 Class 6 Notes | EduRev

Mathematics (Maths) Class 6

Class 6 : Ratio, Proportion and Unitary Method - Exercise 9.3 Class 6 Notes | EduRev

 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: 2 
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