| Chapter 12 Exercise 12.1 Chapter 12 Exercise 12.3 |
NCERT Answers for Class 6 Maths Chapter 12 |
Ratio and Proportion Exercise 12.2
Page 255
Ex 12.2 Class 6 Maths 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
Answer
(a) 15, 45, 40, 120
15 / 45 = 1 / 3
40 / 120 = 1 / 3
Hence, 15: 45 = 40:120
∴ These are in a proportion
(b) 33, 121, 9, 96
33 / 121 = 3 / 11
9 / 96 = 3 / 32
Hence 33:121 ≠ 9: 96
∴ These are not in a proportion
(c) 24, 28, 36, 48
24 / 28 = 6 / 7
36 / 48 = 3 / 4
Hence, 24: 28 ≠ 36:48
∴ These are not in a proportion
(d) 32, 48, 70, 210
32 / 48 = 2 / 3
70 / 210 = 1 / 3
Hence, 32: 48 ≠ 70: 210
∴ These are not in a proportion
(e) 4, 6, 8, 12
4 / 6 = 2 / 3
8 / 12 = 2 / 3
Hence 4: 6 = 8: 12
∴ These are in a proportion
(f) 33, 44, 75, 100
33/ 44 = 3/ 4
75 / 100 = 3 / 4
Hence, 33:44 = 75: 100
∴ These are in a proportion
Ex 12.2 Class 6 Maths 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
Answer
(a) 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 Class 6 Maths 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
Answer
(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 Class 6 Maths 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
Answer
(a) 25 cm : 1 m and ₹ 40 : ₹ 160
25 cm = 25 / 100 m
= 0.25 m
0.25 / 1 = 1 / 4
40 / 160 = 1 / 4
Yes, these are in a proportion
Middle terms are 1 m, ₹ 40 and Extreme terms are 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 are 65 litres, 6 bottles and Extreme terms are 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
1 litre = 1000 ml
2.5 litre = 2500 ml
200 / 2500 = 2 / 5
4 / 50 = 2 / 25
Yes, these are in a proportion
Middle terms arte 2.5 litres, ₹ 4 and Extreme terms are 200 ml, ₹ 50