Haryana State Board HBSE 6th Class Maths Solutions Chapter 12 Ratio and Proportion Ex 12.2 Textbook Exercise Questions and Answers.
Haryana Board 6th Class Maths Solutions Chapter 12 Ratio and Proportion Exercise
12.2
Question 1.
Determine if the following are in proportion :
(a) 15, 45, 40, 120
(b) 33, 121, 9, 96
(c) 24, 28, 36, 48
(d) 32, 48, 70, 210
(e) 4, 6, 8, 12
(f) 33, 44, 75, 100.
Solution:
(a) Ratio of 15 to 45 = \(\frac{15}{45}=\frac{1}{3}\) = 1 : 3
Ratio of 40 to 120 = \(\frac{40}{120}=\frac{1}{3}\) =1:3
Since, 15 : 45 = 40 : 120
∴ 15, 45, 40, 120 are in proportion.
(b) Ratio of 33 to 121 = \(\frac{33}{121}=\frac{3}{11}\) = 3 : 11
Ratio of 9 to 96 = \(\frac{9}{96}=\frac{3}{32}\) = 3 : 32
Since, 33 : 121 ≠ 9 : 96
∴ 33, 121, 9, 96 are not in proportion.
(c) Ratio of 24 to 28 = \(\frac{24}{28}=\frac{6}{7}\) = 6 : 7
Ratio of 36 to 48 = \(\frac{36}{48}=\frac{3}{4}\)
Since, 24 : 28 ≠ 36 : 48
∴ 24, 28, 36, 48 are not in proportion.
(d) Ratio of 32 to 48 = \(\frac{32}{48}=\frac{2}{3}\) =2:3
Ratio of 70 to 210 = \(\frac{70}{210}=\frac{1}{3}\) =1:3
Since, 32 : 48 ≠ 70 : 210
∴ 32, 48, 70, 210 are not in proportion.
(e) Ratio of 4 to 6 = \(\frac{4}{6}=\frac{2}{3}\) = 2:3
Ratio of 8 to 12 = \(\frac{8}{12}=\frac{2}{3}\) = 2 : 3
Since, 4 : 6 = 8 : 12
∴ 4, 6, 8, 12 are in proportion.
(f) Ratio of 33 to 44 = \(\frac{33}{44}=\frac{3}{4}\) = 3 : 4
Ratio of 75 to 100 = \(\frac{75}{100}=\frac{3}{4}\) = 3:4
Since, 33 : 44 = 75 : 100
33, 44, 75, 100 are in proportion.
Question 2.
Write true (T) or false (F) against each of the following statements :
(a) 16: 24:: 20: 30
(b) 21: 6:: 35:10
(c) 12:18:: 28:12
(d) 8: 9:: 24: 27
(e) 5.2: 3.9:: 3: 4
(f) 0.9 : 0.36:: 10: 4
Solution:
(a)
Product of extreme terms = 16 x 30 = 480
Product of middle terms = 24 x 20 = 480
∵ Product of extreme terms
= Product of middle terms
∴ 16 : 24 :: 20 : 30 is true.
(b)
Product of extreme terms = 21 x 10 = 210
Product of middle terms = 6 x 35 = 210
∵ Product of extreme terms
= Product of middle terms
∴ 21 : 6 :: 35 : 10 is true.
(c) 12 : 18 :: 28 : 12
Product of extreme terms = 12 x 12 = 144 Product of middle terms = 18 x 28 = 504
∵ Product of extreme terms
∴ Product of middle terms 12 : 18 :: 28 : 12 is false.
(d) 8:9 :: 24:27
Product of extreme terms = 8 x 27 = 216
Product of middle terms = 9 x 24 = 216
∵ Product of extreme terms = Product of middle terms
∴ 8:9 :: 24 : 27 is true.
(e) 5.2 : 3.9 :: 3 : 4
Product of extreme terms = 5.2 x 4 = 20.8
Product of middle terms = 3.9 x 3 = 11.7
∵ Product of extreme terms * Product of middle terms
∴ 5.2 : 3.9 :: 3 : 4 is false.
(f) 0.9 : 0.36 :: 10 : 4
Product of extreme terms = 0.9 x 4 = 3.6
Product of middle terms = 0.36 x 10 = 3.6
∵ Product of extreme terms = Product of middle terms
∴ 0.9 : 0.36 :: 10 : 4 is true.
Question 3.
Are the following statements true ?
(a) 40 persons : 200 persons = Rs. 15 : Rs. 75.
(b) 7.5 litres : 15 litres = 5 kg : 10 kg.
(c) 99 kg: 45 kg = Rs. 44: Rs. 20.
(d) 32 m : 64m = 6 sec : 12 sec.
(e) 45 km: 60 km = 12 hours: 15 hours.
Solution:
(a) 40 persons : 200 persons
= \(\frac{40}{200}=\frac{1}{5}\) = 1 : 5
Rs. 15 : Rs. 75
= \(\frac{15}{75}=\frac{1}{5}\) = 1:5
∴ 40 persons : 200 persons = Rs. 15 : Rs. 75 is true.
(b) 7.5 litre : 15 litre
= \(\frac{7.5}{15}=\frac{1}{2}\) = 1:2
5 kg : 10 kg = \(\frac{5}{10}=\frac{1}{2}\) = 1 : 2
∴ 7.5 litre : 15 litre = 5 kg : 10 kg is true.
(c)99 kg : 45 kg = \(\frac{99}{45}=\frac{11}{5}\) =11:5
Rs. 44 : Rs. 20 = \(\frac{44}{20}=\frac{11}{5}\) = 11 : 5
∴ 99 kg : 45 kg = Rs. 44 : Rs. 20 is true.
(d) 32m : 64m = \(\frac{32}{64}=\frac{1}{2}\) = 1 : 2
6 sec : 12 sec = \(\frac{6}{12}=\frac{1}{2}\) = 1 : 2
∴ 32 m : 64 m = 6 sec : 12 sec is true.
(e) 45 km : 60 km = \(\frac{45}{60}=\frac{3}{4}\) = 3 : 4
12 hours : 15 hours = \(\frac{12}{15}=\frac{4}{5}\) = 4:5
∵ 3:4 ≠ 4:5
∴ 45 km : 60 km = 12 hours : 15 hours is false.
Question 4.
Determine if the following ratios form a proportion.
Also write the middle terms and extreme terms where the ratios form a proportion.
(a) 25 cm : 1 m and, Rs. 40: Rs. 160.
(b) 39 litres : 65 litres and 6 bottles : 10 bottles.
(c) 2 kg : 80 kg and 25 g : 625 g.
(d) 200 ml: 2.5 litre and Rs. 4: Rs. 50.
Solution:
(a) 25 cm : 1 m = 25 cm : 100 cm
= \(\frac{25}{100}=\frac{1}{4}\) = 1:4
and Rs. 40 : Rs. 160 = \(\frac{40}{160}=\frac{1}{4}\) = 1 : 4
∴ They are in proportion.
i.e. 25 cm : 1 m :: Rs. 40 : Rs. 160
Here, middle terms are 100 cm and Rs. 40.
And extreme terms are 25 cm and Rs. 160.
(b) 39 litres : 65 litres = \(\frac{39}{65}=\frac{3}{5}\) = 3 : 5
and 6 bottles : 10 bottles = \(\frac{6}{10}=\frac{3}{5}\) =3:5
∴ They are in proportion.
i.e. 39 litres: 65 litres:: 6 bottles: 10 bottles.
Here, middle terms are 65 litres and 6 bottles.
And extreme terms are 39 litres and 10 bottles.
(c) 2 kg : 80 kg = \(\frac{2}{80}=\frac{1}{40}\) = 1 : 40
and 25 g . 625 g = \(\frac{25}{625}=\frac{1}{25}\) = 1:25
∴ 2 kg : 80 kg ≠ 25 g : 625
i.e. they are not in proportion.
(d) 200 ml: 2.5 litre = \(\frac{200}{2500}=\frac{2}{25}\) = 2 : 25
Rs. 4 : Rs. 50 = \(\frac{4}{50}=\frac{2}{25}\) = 2 : 25
∴ They are in proportion,
i.e. 200 ml: 2.5 litres :: Rs. 4 : Rs. 50
Here, middle terms are 2500 ml and Rs. 4.
And extreme terms are 200 ml and Rs. 50.