RD Sharma Solutions: Ratio, Proportion & Unitary Method (Exercise 9.1) Notes | EduRev

Mathematics (Maths) Class 6

Class 6 : RD Sharma Solutions: Ratio, Proportion & Unitary Method (Exercise 9.1) Notes | EduRev

 Page 1


 
 
 
 
 
 
Exercise 9.1                                                                                  page: 9.5 
1. Express each of the following in the language of ratios: 
(i) In a class, the number of girls in the merit list of the board examination is two times that of boys. 
(ii) The number of students passing mathematics test is 2/3 of the number that appeared. 
Solution: 
 
(i) Ratio of the number of girls to that of boys in the merit list is 2: 1. 
 
(ii) Ratio of the number of students passing a mathematics test to that of total students appearing in the test is 2: 3. 
 
2. Express the following ratios in language of daily life: 
(i) The ratio of the number of bad pencils to that of good pencils produced in a factory is 1: 9. 
(ii) In India, the ratio of the number of villages to that of cities is about 2000: 1. 
Solution: 
 
(i) The number of bad pencils produced in a factory is 1/9 of the number of good pencils produced in the factory. 
 
(ii) The number of villages is 2000 times that of cities in India. 
 
3. Express each of the following ratios in its simplest form: 
(i) 60: 72 
(ii) 324: 144 
(iii) 85: 391 
(iv) 186: 403 
Solution: 
 
(i) 60: 72  
It can be written as 60/72 
We know that the HCF of 60 and 72 is 12 
By dividing the term by 12 we get 
(60/72) × (12/12) = 5/6  
So we get 60: 72 = 5: 6 
 
(ii) 324: 144 
It can be written as 324/144 
We know that the HCF of 324 and 144 is 36 
By dividing the term by 36 we get 
(324/144) × (36/36) = 9/4  
So we get 324: 144 = 9: 4 
 
(iii) 85: 391 
It can be written as 85/391 
We know that the HCF of 85 and 391 is 17 
By dividing the term by 17 we get 
(85/391) × (17/17) = 5/23 
So we get 85: 391 = 5: 23 
 
(iv) 186: 403 
It can be written as 186/403 
Page 2


 
 
 
 
 
 
Exercise 9.1                                                                                  page: 9.5 
1. Express each of the following in the language of ratios: 
(i) In a class, the number of girls in the merit list of the board examination is two times that of boys. 
(ii) The number of students passing mathematics test is 2/3 of the number that appeared. 
Solution: 
 
(i) Ratio of the number of girls to that of boys in the merit list is 2: 1. 
 
(ii) Ratio of the number of students passing a mathematics test to that of total students appearing in the test is 2: 3. 
 
2. Express the following ratios in language of daily life: 
(i) The ratio of the number of bad pencils to that of good pencils produced in a factory is 1: 9. 
(ii) In India, the ratio of the number of villages to that of cities is about 2000: 1. 
Solution: 
 
(i) The number of bad pencils produced in a factory is 1/9 of the number of good pencils produced in the factory. 
 
(ii) The number of villages is 2000 times that of cities in India. 
 
3. Express each of the following ratios in its simplest form: 
(i) 60: 72 
(ii) 324: 144 
(iii) 85: 391 
(iv) 186: 403 
Solution: 
 
(i) 60: 72  
It can be written as 60/72 
We know that the HCF of 60 and 72 is 12 
By dividing the term by 12 we get 
(60/72) × (12/12) = 5/6  
So we get 60: 72 = 5: 6 
 
(ii) 324: 144 
It can be written as 324/144 
We know that the HCF of 324 and 144 is 36 
By dividing the term by 36 we get 
(324/144) × (36/36) = 9/4  
So we get 324: 144 = 9: 4 
 
(iii) 85: 391 
It can be written as 85/391 
We know that the HCF of 85 and 391 is 17 
By dividing the term by 17 we get 
(85/391) × (17/17) = 5/23 
So we get 85: 391 = 5: 23 
 
(iv) 186: 403 
It can be written as 186/403 
 
 
 
 
 
 
We know that the HCF of 186 and 403 is 31 
By dividing the term by 31 we get 
(186/403) × (31/31) = 6/13  
So we get 186: 403 = 6: 13 
 
4. Find the ratio of the following in the simplest form: 
(i) 75 paise to Rs 3 
(ii) 35 minutes to 45 minutes 
(iii) 8 kg to 400 gm 
(iv) 48 minutes to 1 hour 
(v) 2 metres to 35 cm 
(vi) 35 minutes to 45 seconds 
(vii) 2 dozen to 3 scores 
(viii) 3 weeks to 3 days 
(ix) 48 min to 2 hours 40 min 
(x) 3 m 5 cm to 35 cm 
Solution: 
 
(i) 75 paise to Rs 3 
It can be written as  
75 paise to Rs 3 = 75 paise: Rs 3 
We know that 1 Rs = 100 paise 
So we get 
75 paise to Rs 3 = 75 paise: 300 paise  
Dividing the two terms by HCF 75 
75 paise to Rs 3 = 1: 4 
 
(ii) 35 minutes to 45 minutes 
It can be written as  
35 minutes to 45 minutes = 35 minutes: 45 minutes 
Dividing the two terms by HCF 5 
35 minutes to 45 minutes = 7: 9 
 
(iii) 8 kg to 400 gm 
It can be written as  
8 kg to 400 gm = 8 kg: 400 gm 
We know that 1 kg = 1000 gm 
So we get 
8 kg to 400 gm = 8000 gm: 400 gm 
Dividing the two terms by HCF 400 
8 kg to 400 gm = 20: 1 
 
(iv) 48 minutes to 1 hour 
It can be written as  
48 minutes to 1 hour = 48 minutes: 1 hour 
We know that 1 hour = 60 minutes 
So we get 
48 minutes to 1 hour = 48 minutes: 60 minutes 
Dividing the two terms by HCF 12 
48 minutes to 1 hour = 4: 5 
Page 3


 
 
 
 
 
 
Exercise 9.1                                                                                  page: 9.5 
1. Express each of the following in the language of ratios: 
(i) In a class, the number of girls in the merit list of the board examination is two times that of boys. 
(ii) The number of students passing mathematics test is 2/3 of the number that appeared. 
Solution: 
 
(i) Ratio of the number of girls to that of boys in the merit list is 2: 1. 
 
(ii) Ratio of the number of students passing a mathematics test to that of total students appearing in the test is 2: 3. 
 
2. Express the following ratios in language of daily life: 
(i) The ratio of the number of bad pencils to that of good pencils produced in a factory is 1: 9. 
(ii) In India, the ratio of the number of villages to that of cities is about 2000: 1. 
Solution: 
 
(i) The number of bad pencils produced in a factory is 1/9 of the number of good pencils produced in the factory. 
 
(ii) The number of villages is 2000 times that of cities in India. 
 
3. Express each of the following ratios in its simplest form: 
(i) 60: 72 
(ii) 324: 144 
(iii) 85: 391 
(iv) 186: 403 
Solution: 
 
(i) 60: 72  
It can be written as 60/72 
We know that the HCF of 60 and 72 is 12 
By dividing the term by 12 we get 
(60/72) × (12/12) = 5/6  
So we get 60: 72 = 5: 6 
 
(ii) 324: 144 
It can be written as 324/144 
We know that the HCF of 324 and 144 is 36 
By dividing the term by 36 we get 
(324/144) × (36/36) = 9/4  
So we get 324: 144 = 9: 4 
 
(iii) 85: 391 
It can be written as 85/391 
We know that the HCF of 85 and 391 is 17 
By dividing the term by 17 we get 
(85/391) × (17/17) = 5/23 
So we get 85: 391 = 5: 23 
 
(iv) 186: 403 
It can be written as 186/403 
 
 
 
 
 
 
We know that the HCF of 186 and 403 is 31 
By dividing the term by 31 we get 
(186/403) × (31/31) = 6/13  
So we get 186: 403 = 6: 13 
 
4. Find the ratio of the following in the simplest form: 
(i) 75 paise to Rs 3 
(ii) 35 minutes to 45 minutes 
(iii) 8 kg to 400 gm 
(iv) 48 minutes to 1 hour 
(v) 2 metres to 35 cm 
(vi) 35 minutes to 45 seconds 
(vii) 2 dozen to 3 scores 
(viii) 3 weeks to 3 days 
(ix) 48 min to 2 hours 40 min 
(x) 3 m 5 cm to 35 cm 
Solution: 
 
(i) 75 paise to Rs 3 
It can be written as  
75 paise to Rs 3 = 75 paise: Rs 3 
We know that 1 Rs = 100 paise 
So we get 
75 paise to Rs 3 = 75 paise: 300 paise  
Dividing the two terms by HCF 75 
75 paise to Rs 3 = 1: 4 
 
(ii) 35 minutes to 45 minutes 
It can be written as  
35 minutes to 45 minutes = 35 minutes: 45 minutes 
Dividing the two terms by HCF 5 
35 minutes to 45 minutes = 7: 9 
 
(iii) 8 kg to 400 gm 
It can be written as  
8 kg to 400 gm = 8 kg: 400 gm 
We know that 1 kg = 1000 gm 
So we get 
8 kg to 400 gm = 8000 gm: 400 gm 
Dividing the two terms by HCF 400 
8 kg to 400 gm = 20: 1 
 
(iv) 48 minutes to 1 hour 
It can be written as  
48 minutes to 1 hour = 48 minutes: 1 hour 
We know that 1 hour = 60 minutes 
So we get 
48 minutes to 1 hour = 48 minutes: 60 minutes 
Dividing the two terms by HCF 12 
48 minutes to 1 hour = 4: 5 
 
 
 
 
 
 
(v) 2 metres to 35 cm 
It can be written as  
2 metres to 35 cm = 2 metres: 35 cm 
We know that 1 m = 100 cm 
So we get 
2 metres to 35 cm = 200 cm: 35 cm 
Dividing the two terms by HCF 5 
2 metres to 35 cm = 40: 7 
 
(vi) 35 minutes to 45 seconds 
It can be written as  
35 minutes to 45 seconds = 35 minutes: 45 seconds 
We know that 1 minute = 60 seconds 
So we get 
35 minutes to 45 seconds = 2100 seconds: 45 seconds 
Dividing the two terms by HCF 15 
35 minutes to 45 seconds = 140: 3 
 
(vii) 2 dozen to 3 scores 
It can be written as  
2 dozen to 3 scores = 2 dozen: 3 scores 
We know that 1 dozen = 12 score = 20 
So we get 
2 dozen to 3 scores = 24: 60 
Dividing the two terms by HCF 12 
2 dozen to 3 scores = 2: 5 
 
(viii) 3 weeks to 3 days 
It can be written as  
3 weeks to 3 days = 3 weeks: 3 days 
We know that 1 week = 7 days 
So we get 
3 weeks to 3 days = 21 days: 3 days 
Dividing the two terms by HCF 3 
3 weeks to 3 days = 7: 1 
 
(ix) 48 min to 2 hours 40 min 
It can be written as  
48 min to 2 hours 40 min = 48 min: 2 hours 40 min 
We know that 1 hour = 60 minutes 
So we get 
48 min to 2 hours 40 min = 48 min: 160 min 
Dividing the two terms by HCF 16 
48 min to 2 hours 40 min = 3: 10 
 
(x) 3 m 5 cm to 35 cm 
It can be written as  
3 m 5 cm to 35 cm = 3 m 5 cm: 35 cm 
We know that 1 m = 100 cm 
So we get 
Page 4


 
 
 
 
 
 
Exercise 9.1                                                                                  page: 9.5 
1. Express each of the following in the language of ratios: 
(i) In a class, the number of girls in the merit list of the board examination is two times that of boys. 
(ii) The number of students passing mathematics test is 2/3 of the number that appeared. 
Solution: 
 
(i) Ratio of the number of girls to that of boys in the merit list is 2: 1. 
 
(ii) Ratio of the number of students passing a mathematics test to that of total students appearing in the test is 2: 3. 
 
2. Express the following ratios in language of daily life: 
(i) The ratio of the number of bad pencils to that of good pencils produced in a factory is 1: 9. 
(ii) In India, the ratio of the number of villages to that of cities is about 2000: 1. 
Solution: 
 
(i) The number of bad pencils produced in a factory is 1/9 of the number of good pencils produced in the factory. 
 
(ii) The number of villages is 2000 times that of cities in India. 
 
3. Express each of the following ratios in its simplest form: 
(i) 60: 72 
(ii) 324: 144 
(iii) 85: 391 
(iv) 186: 403 
Solution: 
 
(i) 60: 72  
It can be written as 60/72 
We know that the HCF of 60 and 72 is 12 
By dividing the term by 12 we get 
(60/72) × (12/12) = 5/6  
So we get 60: 72 = 5: 6 
 
(ii) 324: 144 
It can be written as 324/144 
We know that the HCF of 324 and 144 is 36 
By dividing the term by 36 we get 
(324/144) × (36/36) = 9/4  
So we get 324: 144 = 9: 4 
 
(iii) 85: 391 
It can be written as 85/391 
We know that the HCF of 85 and 391 is 17 
By dividing the term by 17 we get 
(85/391) × (17/17) = 5/23 
So we get 85: 391 = 5: 23 
 
(iv) 186: 403 
It can be written as 186/403 
 
 
 
 
 
 
We know that the HCF of 186 and 403 is 31 
By dividing the term by 31 we get 
(186/403) × (31/31) = 6/13  
So we get 186: 403 = 6: 13 
 
4. Find the ratio of the following in the simplest form: 
(i) 75 paise to Rs 3 
(ii) 35 minutes to 45 minutes 
(iii) 8 kg to 400 gm 
(iv) 48 minutes to 1 hour 
(v) 2 metres to 35 cm 
(vi) 35 minutes to 45 seconds 
(vii) 2 dozen to 3 scores 
(viii) 3 weeks to 3 days 
(ix) 48 min to 2 hours 40 min 
(x) 3 m 5 cm to 35 cm 
Solution: 
 
(i) 75 paise to Rs 3 
It can be written as  
75 paise to Rs 3 = 75 paise: Rs 3 
We know that 1 Rs = 100 paise 
So we get 
75 paise to Rs 3 = 75 paise: 300 paise  
Dividing the two terms by HCF 75 
75 paise to Rs 3 = 1: 4 
 
(ii) 35 minutes to 45 minutes 
It can be written as  
35 minutes to 45 minutes = 35 minutes: 45 minutes 
Dividing the two terms by HCF 5 
35 minutes to 45 minutes = 7: 9 
 
(iii) 8 kg to 400 gm 
It can be written as  
8 kg to 400 gm = 8 kg: 400 gm 
We know that 1 kg = 1000 gm 
So we get 
8 kg to 400 gm = 8000 gm: 400 gm 
Dividing the two terms by HCF 400 
8 kg to 400 gm = 20: 1 
 
(iv) 48 minutes to 1 hour 
It can be written as  
48 minutes to 1 hour = 48 minutes: 1 hour 
We know that 1 hour = 60 minutes 
So we get 
48 minutes to 1 hour = 48 minutes: 60 minutes 
Dividing the two terms by HCF 12 
48 minutes to 1 hour = 4: 5 
 
 
 
 
 
 
(v) 2 metres to 35 cm 
It can be written as  
2 metres to 35 cm = 2 metres: 35 cm 
We know that 1 m = 100 cm 
So we get 
2 metres to 35 cm = 200 cm: 35 cm 
Dividing the two terms by HCF 5 
2 metres to 35 cm = 40: 7 
 
(vi) 35 minutes to 45 seconds 
It can be written as  
35 minutes to 45 seconds = 35 minutes: 45 seconds 
We know that 1 minute = 60 seconds 
So we get 
35 minutes to 45 seconds = 2100 seconds: 45 seconds 
Dividing the two terms by HCF 15 
35 minutes to 45 seconds = 140: 3 
 
(vii) 2 dozen to 3 scores 
It can be written as  
2 dozen to 3 scores = 2 dozen: 3 scores 
We know that 1 dozen = 12 score = 20 
So we get 
2 dozen to 3 scores = 24: 60 
Dividing the two terms by HCF 12 
2 dozen to 3 scores = 2: 5 
 
(viii) 3 weeks to 3 days 
It can be written as  
3 weeks to 3 days = 3 weeks: 3 days 
We know that 1 week = 7 days 
So we get 
3 weeks to 3 days = 21 days: 3 days 
Dividing the two terms by HCF 3 
3 weeks to 3 days = 7: 1 
 
(ix) 48 min to 2 hours 40 min 
It can be written as  
48 min to 2 hours 40 min = 48 min: 2 hours 40 min 
We know that 1 hour = 60 minutes 
So we get 
48 min to 2 hours 40 min = 48 min: 160 min 
Dividing the two terms by HCF 16 
48 min to 2 hours 40 min = 3: 10 
 
(x) 3 m 5 cm to 35 cm 
It can be written as  
3 m 5 cm to 35 cm = 3 m 5 cm: 35 cm 
We know that 1 m = 100 cm 
So we get 
 
 
 
 
 
 
3 m 5 cm to 35 cm = 305 cm: 35 cm 
Dividing the two terms by HCF 5 
3 m 5 cm to 35 cm = 61: 7 
 
5. Find the ratio of  
(i) 3.2 metres to 56 metres 
(ii) 10 metres to 25 cm 
(iii) 25 paise to Rs 60 
(iv) 10 litres to 0.25 litre 
Solution: 
 
(i) 3.2 metres to 56 metres 
It can be written as 
3.2 metres to 56 metres = 3.2 metres: 56 metres 
Dividing the two terms by HCF 1.6 
3.2 metres to 56 metres = 2: 35 
 
(ii) 10 metres to 25 cm 
It can be written as 
10 metres to 25 cm = 10 m: 25 cm 
We know that 1 m = 100 cm 
10 metres to 25 cm = 1000 cm: 25 cm 
Dividing the two terms by HCF 25 
10 metres to 25 cm = 40: 1 
 
(iii) 25 paise to Rs 60 
It can be written as 
25 paise to Rs 60 = 25 paise: Rs 60 
We know that 1 Rs = 100 paise 
25 paise to Rs 60 = 25 paise: 6000 paise 
Dividing the two terms by HCF 25  
25 paise to Rs 60 = 1: 240 
 
(iv) 10 litres to 0.25 litre 
It can be written as 
10 litres to 0.25 litre = 10 litres: 0.25 litre 
Dividing the two terms by HCF 0.25 
10 litres to 0.25 litre = 40: 1 
 
6. The number of boys and girls in a school are 1168 and 1095 respectively. Express the ratio of the number 
of boys to that of the girls in the simplest form. 
Solution: 
 
No. of boys = 1168 
No. of girls = 1095 
So the ratio of the number of boys to that of the girls = 1168: 1095 
Dividing the two terms by HCF 73 
Ratio of number of boys to that of the girls = 16: 15 
 
Hence, the ratio of the number of boys to that of girls in simplest form is 16: 15. 
Page 5


 
 
 
 
 
 
Exercise 9.1                                                                                  page: 9.5 
1. Express each of the following in the language of ratios: 
(i) In a class, the number of girls in the merit list of the board examination is two times that of boys. 
(ii) The number of students passing mathematics test is 2/3 of the number that appeared. 
Solution: 
 
(i) Ratio of the number of girls to that of boys in the merit list is 2: 1. 
 
(ii) Ratio of the number of students passing a mathematics test to that of total students appearing in the test is 2: 3. 
 
2. Express the following ratios in language of daily life: 
(i) The ratio of the number of bad pencils to that of good pencils produced in a factory is 1: 9. 
(ii) In India, the ratio of the number of villages to that of cities is about 2000: 1. 
Solution: 
 
(i) The number of bad pencils produced in a factory is 1/9 of the number of good pencils produced in the factory. 
 
(ii) The number of villages is 2000 times that of cities in India. 
 
3. Express each of the following ratios in its simplest form: 
(i) 60: 72 
(ii) 324: 144 
(iii) 85: 391 
(iv) 186: 403 
Solution: 
 
(i) 60: 72  
It can be written as 60/72 
We know that the HCF of 60 and 72 is 12 
By dividing the term by 12 we get 
(60/72) × (12/12) = 5/6  
So we get 60: 72 = 5: 6 
 
(ii) 324: 144 
It can be written as 324/144 
We know that the HCF of 324 and 144 is 36 
By dividing the term by 36 we get 
(324/144) × (36/36) = 9/4  
So we get 324: 144 = 9: 4 
 
(iii) 85: 391 
It can be written as 85/391 
We know that the HCF of 85 and 391 is 17 
By dividing the term by 17 we get 
(85/391) × (17/17) = 5/23 
So we get 85: 391 = 5: 23 
 
(iv) 186: 403 
It can be written as 186/403 
 
 
 
 
 
 
We know that the HCF of 186 and 403 is 31 
By dividing the term by 31 we get 
(186/403) × (31/31) = 6/13  
So we get 186: 403 = 6: 13 
 
4. Find the ratio of the following in the simplest form: 
(i) 75 paise to Rs 3 
(ii) 35 minutes to 45 minutes 
(iii) 8 kg to 400 gm 
(iv) 48 minutes to 1 hour 
(v) 2 metres to 35 cm 
(vi) 35 minutes to 45 seconds 
(vii) 2 dozen to 3 scores 
(viii) 3 weeks to 3 days 
(ix) 48 min to 2 hours 40 min 
(x) 3 m 5 cm to 35 cm 
Solution: 
 
(i) 75 paise to Rs 3 
It can be written as  
75 paise to Rs 3 = 75 paise: Rs 3 
We know that 1 Rs = 100 paise 
So we get 
75 paise to Rs 3 = 75 paise: 300 paise  
Dividing the two terms by HCF 75 
75 paise to Rs 3 = 1: 4 
 
(ii) 35 minutes to 45 minutes 
It can be written as  
35 minutes to 45 minutes = 35 minutes: 45 minutes 
Dividing the two terms by HCF 5 
35 minutes to 45 minutes = 7: 9 
 
(iii) 8 kg to 400 gm 
It can be written as  
8 kg to 400 gm = 8 kg: 400 gm 
We know that 1 kg = 1000 gm 
So we get 
8 kg to 400 gm = 8000 gm: 400 gm 
Dividing the two terms by HCF 400 
8 kg to 400 gm = 20: 1 
 
(iv) 48 minutes to 1 hour 
It can be written as  
48 minutes to 1 hour = 48 minutes: 1 hour 
We know that 1 hour = 60 minutes 
So we get 
48 minutes to 1 hour = 48 minutes: 60 minutes 
Dividing the two terms by HCF 12 
48 minutes to 1 hour = 4: 5 
 
 
 
 
 
 
(v) 2 metres to 35 cm 
It can be written as  
2 metres to 35 cm = 2 metres: 35 cm 
We know that 1 m = 100 cm 
So we get 
2 metres to 35 cm = 200 cm: 35 cm 
Dividing the two terms by HCF 5 
2 metres to 35 cm = 40: 7 
 
(vi) 35 minutes to 45 seconds 
It can be written as  
35 minutes to 45 seconds = 35 minutes: 45 seconds 
We know that 1 minute = 60 seconds 
So we get 
35 minutes to 45 seconds = 2100 seconds: 45 seconds 
Dividing the two terms by HCF 15 
35 minutes to 45 seconds = 140: 3 
 
(vii) 2 dozen to 3 scores 
It can be written as  
2 dozen to 3 scores = 2 dozen: 3 scores 
We know that 1 dozen = 12 score = 20 
So we get 
2 dozen to 3 scores = 24: 60 
Dividing the two terms by HCF 12 
2 dozen to 3 scores = 2: 5 
 
(viii) 3 weeks to 3 days 
It can be written as  
3 weeks to 3 days = 3 weeks: 3 days 
We know that 1 week = 7 days 
So we get 
3 weeks to 3 days = 21 days: 3 days 
Dividing the two terms by HCF 3 
3 weeks to 3 days = 7: 1 
 
(ix) 48 min to 2 hours 40 min 
It can be written as  
48 min to 2 hours 40 min = 48 min: 2 hours 40 min 
We know that 1 hour = 60 minutes 
So we get 
48 min to 2 hours 40 min = 48 min: 160 min 
Dividing the two terms by HCF 16 
48 min to 2 hours 40 min = 3: 10 
 
(x) 3 m 5 cm to 35 cm 
It can be written as  
3 m 5 cm to 35 cm = 3 m 5 cm: 35 cm 
We know that 1 m = 100 cm 
So we get 
 
 
 
 
 
 
3 m 5 cm to 35 cm = 305 cm: 35 cm 
Dividing the two terms by HCF 5 
3 m 5 cm to 35 cm = 61: 7 
 
5. Find the ratio of  
(i) 3.2 metres to 56 metres 
(ii) 10 metres to 25 cm 
(iii) 25 paise to Rs 60 
(iv) 10 litres to 0.25 litre 
Solution: 
 
(i) 3.2 metres to 56 metres 
It can be written as 
3.2 metres to 56 metres = 3.2 metres: 56 metres 
Dividing the two terms by HCF 1.6 
3.2 metres to 56 metres = 2: 35 
 
(ii) 10 metres to 25 cm 
It can be written as 
10 metres to 25 cm = 10 m: 25 cm 
We know that 1 m = 100 cm 
10 metres to 25 cm = 1000 cm: 25 cm 
Dividing the two terms by HCF 25 
10 metres to 25 cm = 40: 1 
 
(iii) 25 paise to Rs 60 
It can be written as 
25 paise to Rs 60 = 25 paise: Rs 60 
We know that 1 Rs = 100 paise 
25 paise to Rs 60 = 25 paise: 6000 paise 
Dividing the two terms by HCF 25  
25 paise to Rs 60 = 1: 240 
 
(iv) 10 litres to 0.25 litre 
It can be written as 
10 litres to 0.25 litre = 10 litres: 0.25 litre 
Dividing the two terms by HCF 0.25 
10 litres to 0.25 litre = 40: 1 
 
6. The number of boys and girls in a school are 1168 and 1095 respectively. Express the ratio of the number 
of boys to that of the girls in the simplest form. 
Solution: 
 
No. of boys = 1168 
No. of girls = 1095 
So the ratio of the number of boys to that of the girls = 1168: 1095 
Dividing the two terms by HCF 73 
Ratio of number of boys to that of the girls = 16: 15 
 
Hence, the ratio of the number of boys to that of girls in simplest form is 16: 15. 
 
 
 
 
 
 
7. Avinash works as a lecturer and earns Rs 12000 per month. His wife who is a doctor earns Rs 15000 per 
month. Find the following ratios: 
(i) Avinash’s income to the income of his wife. 
(ii) Avinash’s income to their total income. 
Solution: 
 
Avinash salary earned per month = Rs 12000 
Avinash wife salary per month = Rs 15000 
(i) Avinash’s income to the income of his wife = 12000/15000 = 4: 5 
 
(ii) Avinash’s income to their total income = 12000/ (12000 + 15000) = 4: 9 
 
8. Of the 72 persons working in an office, 28 are men and the remaining are women. Find the ratio of the 
number of: 
(i) men to that of women, 
(ii) men to the total number of persons 
(iii) persons to that of women. 
Solution: 
 
No. of persons working in an office = 72 
No. of men = 28 
So the number of women = 72 – 28 = 44 
 
(i) men to that of women = 28: 44 
Multiplying and dividing the equation by HCF 4 
Men to that of women = (28/44) × (4/4) = 7: 11 
 
(ii) men to the total number of persons = 28: 72 
Multiplying and dividing the equation by HCF 4 
Men to the total number of persons = (28/72) × (4/4) = 7: 18 
 
(iii) persons to that of women = 72: 44 
Multiplying and dividing the equation by HCF 4 
Persons to that of women = (72/44) × (4/4) = 18: 11 
 
9. The length of a steel tape for measurements of buildings is 10 m and its width is 2.4 cm. What is the ratio 
of its length to width? 
Solution: 
 
It is given that 
Length of a steel tape = 10 m 
Width of steel tape = 2.4 cm 
So the ratio of its length to width = 10 m/ 2.4 cm 
We know that 1 m = 100 cm 
Ratio of its length to width = 1000 cm/ 2.4 cm 
Dividing the two terms by HCF 0.8 cm 
Ratio of its length to width = 1250: 3 
 
Hence, the ratio of its length to width is 1250: 3. 
 
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Previous Year Questions with Solutions

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Proportion & Unitary Method (Exercise 9.1) Notes | EduRev

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mock tests for examination

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RD Sharma Solutions: Ratio

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Objective type Questions

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Viva Questions

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Semester Notes

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RD Sharma Solutions: Ratio

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MCQs

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