Ratio Proportion
Chapter 12
Exercise 12.2
EX 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) 15, 45, 40, 120
15 / 45 = 1 / 3 = 1 : 3
40 / 120 = 1 / 3 = 1 : 3
Since 15: 45 = 40:120
∴ 15, 45, 40, 120 are in a proportion
(b) 33, 121, 9, 96
33 / 121 = 3 / 11 = 3 : 11
9 / 96 = 3 / 32 = 3 : 32
Since 33:121 ≠ 9: 96
∴ 33, 121, 9, 96 are not in a proportion
(c) 24, 28, 36, 48
24 / 28 = 6 / 7 = 6 : 7
36 / 48 = 3 / 4 = 3 : 4
Since, 24: 28 ≠ 36:48
∴ 24, 28, 36, 48 are not in a proportion
(d) 32, 48, 70, 210
32 / 48 = 2 / 3 = 2 : 3
70 / 210 = 1 / 3 = 1 : 3
Since, 32: 48 ≠ 70: 210
∴ 32, 48, 70, 210 are not in a proportion
(e) 4, 6, 8, 12
4 / 6 = 2 / 3 = 2 : 3
8 / 12 = 2 / 3 = 2 : 3
Since, 4: 6 = 8: 12
∴ 4, 6, 8, 12are in a proportion
(f) 33, 44, 75, 100
33/ 44 = 3/ 4 = 3 : 4
75 / 100 = 3 / 4 = 3 : 4
Since, 33:44 = 75: 100
∴ 33, 44, 75, 100 are in a proportion
EX 12.2 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:
16: 24 :: 20: 30
16 / 24 = 2 / 3
20 / 30 = 2 / 3
Hence, 16: 24 = 20: 30
Therefore True
(b) 21: 6:: 35: 10
21 / 6 = 7 / 2
35 / 10 = 7 / 2
Hence, 21: 6 = 35: 10
Therefore True
(c) 12: 18 :: 28: 12
12 / 18 = 2 / 3
28 / 12 = 7 / 3
Hence, 12: 18 ≠ 28:12
Therefore False
(d) 8: 9:: 24: 27
We know that = 24 / 27 = (3 × 8) / (3 × 9)
= 8 / 9
Hence, 8: 9 = 24: 27
Therefore True
(e) 5.2: 3.9:: 3: 4
As 5.2 / 3.9 = 3 / 4
Hence, 5.2: 3.9 ≠ 3: 4
Therefore False
(f) 0.9: 0.36:: 10: 4
0.9 / 0.36 = 90 / 36
= 10 / 4
Hence, 0.9: 0.36 = 10: 4
Therefore True
EX 12.2 QUESTION 3.
Are the following statements true?
(a) 40 persons : 200 persons = ₹ 15 : ₹ 75
(b) 7.5 litres : 15 litres = 5 kg : 10 kg
(c) 99 kg : 45 kg = ₹ 44 : ₹ 20
(d) 32 m : 64 m = 6 sec : 12 sec
(e) 45 km : 60 km = 12 hours : 15 hours
Solutions:
(a) 40 persons : 200 persons = ₹ 15 : ₹ 75
40 / 200 = 1 / 5
15 / 75 = 1 / 5
Hence, True
(b) 7.5 litres : 15 litres = 5 kg : 10 kg
7.5 / 15 = 1 / 2
5 / 10 = 1 / 2
Hence, True
(c) 99 kg : 45 kg = ₹ 44 : ₹ 20
99 / 45 = 11 / 5
44 / 20 = 11 / 5
Hence, True
(d) 32 m : 64 m = 6 sec : 12 sec
32 / 64 = 1 / 2
6 / 12 = 1 / 2
Hence, True
(e) 45 km : 60 km = 12 hours : 15 hours
45 / 60 = 3 / 4
12 / 15 = 4 / 5
Hence, False
EX 12.2 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 ₹ 40 : ₹ 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 ₹ 4 : ₹ 50
Solutions:
(a) 25 cm : 1 m and ₹ 40 : ₹ 160
25 cm = 25 cm / 100 cm [ 1 m = 100 cm]
= 1 / 4
40 / 160 = 1 / 4
Yes, these are in a proportion
Middle terms = 1 m, ₹ 40 and Extreme terms = 25 cm, ₹ 160
(b) 39 litres : 65 litres and 6 bottles : 10 bottles
39 / 65 = 3 /5
6 / 10 = 3 / 5
Yes, these are in a proportion
Middle terms a= 65 litres, 6 bottles and Extreme terms = 39 litres, 10 bottles
(c) 2 kg : 80 kg and 25 g : 625 g
2 / 80 = 1 / 40
25 / 625 = 1 / 25
No, these are not in a proportion
(d) 200 mL : 2.5 litre and ₹ 4 : ₹ 50
2.5 litre = 2500 ml [1 litre = 1000 ml]
200 / 2500 = 2 / 5
4 / 50 = 2 / 25
Yes, these are in a proportion
Middle terms = 2.5 litres, ₹ 4 and Extreme terms = 200 ml, ₹ 50
