NCERT Solutions for Class 6 Maths Chapter 12 Ratios and Proportions Ex 12.2

NCERT Solutions for Class 6 Maths Chapter 12 Ratios and Proportions Ex 12.2 are the part of NCERT Solutions for Class 6 Maths (Rationalised Contents). Here you can find the NCERT Solutions for Class 6 Maths Chapter 12 Ratios and Proportions Ex 12.2.

NCERT Solutions for Class 6 Maths Chapter 12 Ratios and Proportions Ex 12.2 (Rationalised Contents)

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

Solution:

Thus, 15 : 45 :: 40 : 120
∴ 15, 45, 40 and 120 are in proportion.

∴ 33, 121, 9 and 96 are not in proportion.

∴ 24, 28, 36 and 48 are not in proportion.

Since 2/3 ≠ 1/3
∴ 32, 48, 70 and 210 are not in proportion.

Thus, 4 : 6 :: 8 : 12
∴ 4, 6, 8 and 12 are in proportion.

Thus, 33 : 44 :: 75 : 100
∴ 33, 44, 75 and 100 are in 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

Solution:
(a) 16 : 24 :: 20 : 30
Product of the extremes = 16 × 30 = 480
Product of the means = 24 × 20 = 480
∴ The given statement is True (T).

(b) 21 : 6 :: 35 : 10
Product of the extremes = 21 × 10 = 210
Product of the means = 6 × 35 = 210
∴ The given statement is True (T).

(c) 12 : 18 :: 28 : 12
Product of the extremes = 12 × 12 = 144
Product of the means = 18 × 28 = 504
Since 144 ≠ 504
∴ The given statement is False (F).

(d) 8 : 9 :: 24 : 27
Product of the extremes = 8 × 27 = 216
The product of the means = 9 × 24 = 216
The given statement is True (T).

(e) 5.2 : 3.9 :: 3 : 4
Product of the extremes = 5.2 × 4 = 20.8
Product of the means = 3.9 × 3 = 11.7
Since 20.8 ≠ 11.7
The given statement is False (F).

(f) 0.9 : 0.36 :: 10 : 4
Product of the extremes = 0.9 × 4 = 3.6
Product of the means = 0.36 × 10 = 3.6
∴ The given statement is True (T).

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

Solution:
(a) 40 persons : 200 persons = ₹15 : ₹75

40 persons : 200 persons

∴ The given statement is true.

(b) 7.5 litres : 15 litres = 5 kg : 10 kg

7.5 litres : 15 litres

∴ The given statement is true.

∴ The given statement is not true.

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 litres and ₹ 4 : ₹ 50

Solution:
(a) 25 cm : 1 m = 25 cm : 100 cm [∵ 1 m = 100 cm]

∴ The given ratios form a proportion.
Extreme terms are 25 cm and ₹ 160.
Middle terms are 1 m and ₹40.