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Class 6 Exam  >  Class 6 Notes  >  Mathematics (Maths) Class 6  >  RD Sharma Solutions: Ratio, Proportion & Unitary Method (Exercise 9.3)

Ratio, Proportion & Unitary Method (Exercise 9.3) RD Sharma Solutions | Mathematics (Maths) Class 6 PDF Download

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 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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RD Sharma Solutions: Ratio, Proportion & Unitary Method (Exercise 9.3) Notes

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RD Sharma Solutions: Ratio, Proportion & Unitary Method (Exercise 9.3) Class 6 Questions

The "RD Sharma Solutions: Ratio, Proportion & Unitary Method (Exercise 9.3) Class 6 Questions" guide is a valuable resource for all aspiring students preparing for the Class 6 exam. It focuses on providing a wide range of practice questions to help students gauge their understanding of the exam topics. These questions cover the entire syllabus, ensuring comprehensive preparation. The guide includes previous years' question papers for students to familiarize themselves with the exam's format and difficulty level. Additionally, it offers subject-specific question banks, allowing students to focus on weak areas and improve their performance.

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