The ratio of two quantities of the same kind and in the same units is a fraction that shows how many times one quantity is of the other. This exercise has questions based on ratio and their comparison by difference and division. RD Sharma Solutions Class 6 help students understand the steps followed in converting the given ratio to its simplest form. The students can download RD Sharma Solutions for Class 6 Maths Chapter 9 Ratio, Proportion and Unitary Method Exercise 9.1 PDF, which is given here.
RD Sharma Solutions for Class 6 Maths Chapter 9: Ratio, Proportion and Unitary Method Exercise 9.1
Access answers to Maths RD Sharma Solutions for Class 6 Chapter 9: Ratio, Proportion and Unitary Method Exercise 9.1
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.
10. An office opens at 9 am and closes at 5 pm with a lunch interval of 30 minutes. What is the ratio of lunch interval to the total period in office?
Solution:
Duration of office = 9 am to 5 pm = 8 hours
Lunch interval = 30 minutes
So the ratio of lunch interval to the period in office = 30 minutes/8 hours
We know that 1 hour = 60 minutes
Ratio of lunch interval to the period in office = 30/ (8 × 60) = 30/480
Dividing the two terms by HCF 30
Ratio of lunch interval to the period in office = (30/480) × (30/30) = 1: 16
Hence, the ratio of lunch interval to the total period in office is 1: 16.
11. A bullock-cart travels 24 km in 3 hours and a train travels 120 km in 2 hours. Find the ratio of their speeds.
Solution:
Distance travelled by bullock-cart = 24 km in 3 hours
Distance travelled by train = 120 km in 2 hours
It can be written as
Distance travelled by bullock-cart = 24 km/ 3 = 8 km
Distance travelled by train = 120 km/2 = 60 km
So the ratio of their speeds = 8/60
Dividing the two terms by HCF 4
Ratio of their speeds = (8/60) × (4/4) = 2:15
Hence, the ratio of their speeds is 2: 15.
12. Margarette works in a factory and earns Rs 955 per month. She saves Rs 185 per month from her earnings. Find the ratio of:
(i) her savings to her income
(ii) her income to her expenditure
(iii) her savings to her expenditure.
Solution:
Margarette monthly income = Rs 955
Margarette monthly savings = Rs 185
Margarette expenditure = 955 – 185 = Rs 770
(i) her savings to her income = 185/955
Dividing the two terms by HCF 5
Her savings to her income = (185/955) × (5/5) = 37: 191
(ii) her income to her expenditure = 955/770 = 191: 154
(iii) her savings to her expenditure = 185/770 = 37: 154
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