ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 8 Ratio and Proportion Ex 8.2
Question 1.
Check whether the given two ratios form a proportion or not:
(i) 4 : 6 and 12 : 18
(ii) 15:45 and 40 :120
(iii) 14 : 4 and 18 : 6
(iv) 12 : 18 and 28 : 12
Solution:
4 : 6 and 12 : 18
Question 2.
Write true (T) or false (F) against each of the following statements:
(i) 16 : 24 = 20 : 30
(ii) 16 : 24 = 30 : 20
(iii) 21 : 6 :: 35 : 10
(iv) 5.2 : 3.9 :: 3 :4
Solution:
(i) 16 : 24 = 20 : 30
2 : 3 = 2 : 3 True
(ii) 16 : 24 = 30 : 20
2 : 3 = 3 : 2 False
(iii) 21 : 6 :: 35 : 10
21 : 6 = 35 : 10
7 : 2 = 7 : 2 True
(iv) 5.2 : 3.9 :: 3 : 4
Question 3.
Find which of the following are in proportion:
(i) 12, 16, 6, 8
(ii) 2, 3, 4, 5
(iii) 18, 10, 9, 5
(iv) 18, 9, 10, 5
Solution:
(i) 12, 16, 6, 8
12: 16 :: 6 : 8
\(\Rightarrow \frac{12}{16}=\frac{6}{8}\)
12 × 8 = 16 × 6 ⇒ 96 = 96
∴ 12 : 16 :: 6 : 8 are in proportion
(ii) 2, 3, 4, 5
2 : 3 :: 4 : 5
\(\Rightarrow \frac{2}{3}=\frac{4}{5}\)
2 × 5 = 3 × 4 ⇒ 10 = 12 not in proportion
(iii) 18, 10, 9, 5
18 : 10 : : 9 : 5
\(\Rightarrow \frac{18}{10}=\frac{9}{5}\)
∴ 18 × 5 = 10 × 9 ⇒ 90 = 90
∴ 18 : 10 :: 9 : 5 are in proportion
(iv) 18, 9, 10, 5
18 : 9 :: 10 : 5
\(\Rightarrow \frac{18}{9}=\frac{10}{5}\)
18 × 5 = 9 × 10
⇒ 90 = 90
∴ 18 : 9 :: 10 : 5 are in proportion
Question 4.
Are the following statements true?
(i) 39 kg : 36 kg = 26 men : 24 men
(ii) 45 km : 60 km = 12 hours : 15 hours
(iii) 40 people : 200 people = ₹1000 : ₹5000
(iv) 7.5 litres: 15 litres = 15 children: 30 children
Solution:
(i) 39 kg : 36 kg = 26 men : 24 men
∴ 39 : 36 = 26 : 24
So, the given statement is true.
(ii) 45 km : 60 km = 12 hours : 15 hours
∴ 45 : 60 ≠ 12 : 15
So, the given statement is false.
(iii) 40 people : 200 people = ₹ 1000 : ₹5000
∴ 40 : 200 = 1000 : 5000
So, the given statement is true.
(iv) 7.5 litres : 15 litres = 15 children : 30 children
∴ 7.5 : 15 = 15 : 30
So, the given statement is true.
Question 5.
Determine if the following ratios form a proportion. Also, write the middle terms and extreme terms when the ratios form a proportion. .
(i) 25 cm : 1 m and ₹40 : ₹ 160
(ii) 39 litres : 65 litres and 6 bottles : 10 bottles
(iii) 2 kg : 80 kg and 30 sec : 5 minutes
(iv) 200 g : 2.5 kg and ₹4 : ₹50
Solution:
(i) ∵ 1 m = 100 cm
∴ 25 cm : 1 m = 25 cm : 100 cm
\(=\frac{1}{4}=1 : 4\)
Since, the two ratio are equal, therefore, the given ratios form a proportion. Middle terms are 1 m and ₹40. Extreme terms are 25 cm and ₹160.
Since the two ratios are equal, therefore, the given ratios form a proportion. Middle terms are 65 litres and 6 bottle. Extreme terms are 39 litres and 10 bottle.
Since the two ratios are not equal, therefore, the given ratios do not form a proportion.
(iv) 2.5 kg = 2.5 × 1000 g = 2500 g
∴ 200 g : 2.5 kg = 200 g : 2500 g
Since, the two ratios are equal, therefore, the given ratios form a proportion. Middle term are 2.5 kg and ₹4. Extreme terms are 200 g and ₹50.