NCERT Solutions Class 6 Maths
Chapter – 12 (Ratio and Proportion)
The NCERT Solutions in English Language for Class 6 Mathematics Chapter – 12 Ratio and Proportion Exercise 12.2 has been provided here to help the students in solving the questions from this exercise.
Chapter 12: Ratio and Proportion
Exercise – 12.2
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
Solutions :
(a)
∴ 15 : 45 : : 40 : 120
∴ 15, 45, 40 and 120 are in proportion.
(b)
∴ 33, 121, 9 and 96 are not in a proportion.
(c)
∴ 24, 28, 36 and 48 are not in proportion.
(d)
Since
∴ 32, 48, 70 and 210 are not in proportion.
(e)
∴ 4 : 6 :: 8 : 12
∴ 4, 6, 8 and 12 are in proportion.
(f)
∴ 33 : 44 : : 75 : 100
∴ 33, 44, 75 and 100 are in proportion.
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
Solutions:
(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)
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
∴ Statement (a) is true.
(b) 7.5 litres : 15 litres
∴ Statement (b) is true.
(c)
∴ Statement (c) is true.
(d)
∴ Statement (d) is true.
(e)
∴ Statement (e) is not true.
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
Solutions :
(a) 25 cm : 1 m = 25 cm : 100 cm [∵ 1 m = 100 cm]
Yes, these are in a proportion
Middle terms are 1 m, ₹ 40 and Extreme terms are 25 cm, ₹ 160.
(b)
Yes, these are in a proportion.
Middle terms are 65 litres, 6 bottles and Extreme terms are 39 litres, 10 bottles
(c)
No, these are not in a proportion
(d) 200 mL : 2.5 litres = 2.5 litres = 2.5 x 1000 mL = 2500 mL
Yes, these are in a proportion.
Middle terms are 2.5 litres, ₹ 4 and Extreme terms are 200 ml, ₹ 50.
