NCERT Solutions Class 6th Maths 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) 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

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) 16 : 24 :: 20 : 30
Product of the extreme terms = 16 x 30 = 480
Product of the middle terms = 24 x 20 = 480
∴ The given statement (a) → (T)

(B) 21 : 6 :: 35 : 10
Product of the extreme terms = 21 x 10 = 210
Product of the middle terms = 6 x 35 = 210
∴ The given statement (b) → (T)

(C) 12 : 18 :: 28 : 12
Product of the extreme terms = 12 x 12 = 144
Product of the middle terms = 18 x 28 = 504
Since 144 ≠ 504
∴ The given statement (c) → (F)

(D) 8 : 9 :: 24 : 27
Product of the extreme terms = 8 x 27 = 216
The product of the middle terms = 9 x 24 = 216
The given statement (d) → (T)

(E) 5.2 : 3.9 :: 3 : 4
Product of the extreme terms = 5.2 x 4 = 20.8
Product of the middle terms = 3.9 x 3 = 11.7
Since 20.8 ≠ 11.7
The given statement (e) → (F)

(F) 0.9 : 0.36 :: 10 : 4
Product of the extreme terms = 0.9 x 4 = 3.6
Product of the middle terms = 0.36 x 10 = 3.6
∴ The given statement (f) → (T)

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

Solution – 

(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

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 litres and ₹ 4 : ₹ 50

Solution – 

(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