Page No.9.5 & 9.6, Ratio Proportion And Unitary Method, Class 6, Maths RD Sharma Solutions | RD Sharma Solutions for Class 6 Mathematics PDF Download

PAGE NO 9.5:

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.

ANSWER:

(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.

PAGE NO 9.6:

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.

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)

ANSWER:

(i) ∵ Rs. 1 = 100 paise    
∴ 75  : 300 = 1 : 4

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

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

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

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

ANSWER:

Total number of persons = 72
Number of men = 28
Number of women = 72 −- 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

ANSWER:

Length of the steel tape = 10 m
= 10×100 cm10×100 cm = 1000 cm
Breadth of the steel tape = 2.4 cm

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
∵ 1 hour = 60 minutes
∴ 8 hours = 8 × 60 = 480 minutes
Ratio of lunch interval to total period = 30 : 480 = 1 : 16 (dividing by 30)

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 

ANSWER:

Income of Margarette per month = Rs. 955
Saving of Margarette per month = Rs. 185
Expenditure of Margarette per month = 955−-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) ∵ Rs. 1 = 100 paise     ∴ 75  : 300 = 1 : 4(ii)  35 : 45 = 7 : 9(iii) ∵ 1 kg = 1000 gm    ∴ 8000 : 400 = 20 : 1(iv) ∵ 1 Hour = 60 minute     ∴48 : 60 = 4 : 5(v) ∵ 1 meter = 100 cm    ∴ 200 : 35 = 40 : 7(vi) ∵ 1 min = 60 sec.     ∴ 35×60 : 45 = 140 : 3(vii) ∵ 1 dozen = 12      ∴ 1 score = 20   or 3 score = 3 × 20 = 60   ∴ 24 : 60 = 2 : 5.(viii) ∵ 1 week = 7 days      ∴ 21 : 3 = 7 : 1(ix) ∵ 1 hour = 60 minute     ∴ 2 hour 40 min = 2 × 60 + 40 = 160     ∴ 48 : 160 = 3 : 10(x) ∵ 1 meter = 100 cm     ∴ 3 m 5 cm = 3 ×100 + 5 = 305 cm    ∴ 305 : 35 = 61 :