The document RD Sharma Solutions -Page No.9.5 & 9.6, Ratio Proportion And Unitary Method, Class 6, Maths Class 6 Notes | EduRev is a part of the Class 6 Course RD Sharma Solutions for Class 6 Mathematics.

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**Question 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 student passing mathematics test is 2/3 of the number that appeared.**

(i) The ratio of the number of girls in the merit list of the board examination to the number of boys in that list is 2 : 1.

(ii) The ratio of the number of students passing mathematics test to the total number of students appeared is 2 : 3.

**Question 2: Express the following ratios in language of daily life:(i) The ratio of the number of bad pencils to that 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.**

**ANSWER:** (i) The ratio of the number of bad pencils to that of good pencils produced in a factory is 1 : 9 means out of 10 or (9 + 1) pencils, 9 pencils are good and 1 is bad.

(ii) In India, the number of villages is 2,000 times that of the cities.

**Question 3: Express each of the of the following rations in its simplest from:**

(ii) 324:144

(iii) 85:391

(iv) 186:403

**ANSWER: **(i) 60 : 72 = 5 : 6 (dividing by 12)

(ii) 324 : 144 = 9 : 4 (dividing by 36)

(iii) 85 : 391 = 5 : 23 (dividing by 17)

(iv) 186 : 403 = 6 : 13 (dividing by 31)

**Question 4: Find the ratio of the following in the simplest form:**

(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 hour 40 min

(x) 3 m 5 cm to 35 cm.

**ANSWER:**

(i) âˆµ Rs. 1 = 100 paise

âˆ´ 75 : 300 = 1 : 4

(ii) 35 : 45 = 7 : 9

(iii) âˆµ 1 kg = 1000 gm

âˆ´ 8000 : 400 = 20 : 1

(iv) âˆµ 1 Hour = 60 minute

âˆ´48 : 60 = 4 : 5

(v) âˆµ 1 meter = 100 cm

âˆ´ 200 : 35 = 40 : 7

(vi) âˆµ 1 min = 60 sec.

âˆ´ 35Ã—60 : 45 = 140 : 3

(vii) âˆµ 1 dozen = 12

âˆ´ 1 score = 20

or 3 score = 3 Ã— 20 = 60

âˆ´ 24 : 60 = 2 : 5.

(viii) âˆµ 1 week = 7 days

âˆ´ 21 : 3 = 7 : 1

(ix) âˆµ 1 hour = 60 minute

âˆ´ 2 hour 40 min = 2 Ã— 60 + 40 = 160

âˆ´ 48 : 160 = 3 : 10

(x) âˆµ 1 meter = 100 cm

âˆ´ 3 m 5 cm = 3 Ã—100 + 5 = 305 cm

âˆ´ 305 : 35 = 61 : 7

**Question 5: Find the ratio of**

(ii) 10 metres to 25 cm.

(iii) 25 paisa to Rs 60

(iv) 10 litres to 0.25 litre

**ANSWER:** (i) The ratio of 3.2 metres to 56 metres = 3.2 : 56 = 0.4 : 7 = 2 : 35

(ii) The ratio of 10 metres to 25 cm = 1000 : 25 = 40 : 1

(iii) The ratio of 25 paisa to Rs 60 = 25 : 6000 = 1 : 240

(iv) The ratio of 10 litres to 0.25 litre = 10 : 0.25 = 40 : 1

**Question 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.**

**ANSWER:** Ratio of the number of boys to that of the girls is 1168 : 1095 = 16 : 15 (dividing by 73)

**Question 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:**

(ii) Avinash's income to their total income.

**ANSWER: **Avinash's income = Rs. 12000

Avinash's wife income = Rs. 15000

Total income = 12000 + 15000 = Rs. 27000

(i) Ratio of Avinash's income to the income of his wife = 12000 : 15000 = 4 : 5

(ii) Ratio of Avinash's income to their total income = 12000 : 27000 = 4 : 9

**Question 8: Of the 72 persons working in an office, 28 are men and the remaining are women. Find the ratio of the number of:**

(ii) men to the total number persons

(iii) persons to that of women.

**ANSWER:**

Total number of persons = 72

Number of men = 28

Number of women = 72 âˆ’- 28 = 44

(i) Ratio of men to that of women = 28 : 44 = 7 : 11

(ii) Ratio of men to the total number of persons = 28 : 72 = 7 : 18

(iii) Ratio of persons to that of women = 72 : 44 = 18 : 11

**Question 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?**

**ANSWER:**

Length of the steel tape = 10 m

= 10Ã—100 cm10Ã—100 cm = 1000 cm

Breadth of the steel tape = 2.4 cm

**Question 10: An office opens at 9 a.m. and closed at 5 p.m. with a lunch interval of 30 minutes. What is the ratio of lunch interval to the total period in office?**

**ANSWER:**

Total period in office = 9 a.m. to 12 p.m. and 12 p.m. to 5 p.m.

= 3 hours + 5 hours = 8 hours

âˆµ 1 hour = 60 minutes

âˆ´ 8 hours = 8 Ã— 60 = 480 minutes

Ratio of lunch interval to total period = 30 : 480 = 1 : 16 (dividing by 30)

**Question 11: A bullock-cart travels 24 km in 3 hours and a train travels 120 km in 2 hours. Find the ratio fo their speeds.**

**ANSWER:**

Distance covered by bullock-cart = 24 km

Time taken = 3 hours

Speed of bullock-cart = 24/3=8 km/h

Distance covered by train = 120 km

Time taken = 2 hours

Speed of train = 120/2=60 km/h

Ratio for their speeds = Speed of bullock-cart : Speed of train = 8 : 60

= 2 : 15

**Question 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:**

(ii) her income to her expenditure

(iii) her savings to her expenditure.

**ANSWER:**

Income of Margarette per month = Rs. 955

Saving of Margarette per month = Rs. 185

Expenditure of Margarette per month = 955âˆ’-185 = Rs. 770

(i) Ratio of her saving to her income = 185 : 955 = 37 : 191

(ii) Ratio of her income to her expenditure = 955 : 770 = 191 : 154

(iii) Ratio of her saving to her expenditure = 185 : 770 = 37 : 154

**(i) âˆµ Rs. 1 = 100 paise âˆ´ 75 : 300 = 1 : 4(ii) 35 : 45 = 7 : 9(iii) âˆµ 1 kg = 1000 gm âˆ´ 8000 : 400 = 20 : 1(iv) âˆµ 1 Hour = 60 minute âˆ´48 : 60 = 4 : 5(v) âˆµ 1 meter = 100 cm âˆ´ 200 : 35 = 40 : 7(vi) âˆµ 1 min = 60 sec. âˆ´ 35Ã—60 : 45 = 140 : 3(vii) âˆµ 1 dozen = 12 âˆ´ 1 score = 20 or 3 score = 3 Ã— 20 = 60 âˆ´ 24 : 60 = 2 : 5.(viii) âˆµ 1 week = 7 days âˆ´ 21 : 3 = 7 : 1(ix) âˆµ 1 hour = 60 minute âˆ´ 2 hour 40 min = 2 Ã— 60 + 40 = 160 âˆ´ 48 : 160 = 3 : 10(x) âˆµ 1 meter = 100 cm âˆ´ 3 m 5 cm = 3 Ã—100 + 5 = 305 cm âˆ´ 305 : 35 = 61 : **