ML Aggarwal Ratio and Proportion Exe-8.2 Class 6 ICSE Maths Solutions

ML Aggarwal Ratio and Proportion Exe-8.2 Class 6 ICSE Maths Solutions. We Provide Step by Step Answer of  Exe-8.2 Questions for Ratio and Proportion as council prescribe guideline for upcoming board exam. Visit official Website CISCE for detail information about ICSE Board Class-6.

ML Aggarwal Ratio and Proportion Exe-8.2 Class 6 ICSE Maths Solutions

Board ICSE
Publications Avichal Publishig Company (APC)
Subject Maths
Class 6th
Chapter-8 Ratio and Proportion
Writer ML Aggarwal
Book Name Understanding
Topics Solution of Exe-8.2 Questions
Edition 2023-2024

Ratio and Proportion Exe-8.2

ML Aggarwal Class 6 ICSE Maths Solutions

Page-162

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

Answer:

(i) 4 : 6 and 12 : 18

4/6 and 12/18

2/3 and 2/3

= 2 : 3 and 2 : 3 Yes

(ii) 15:45 and 40 :120

15/45 and 40/120

1/3 and 1/3 Yes

(iii) 14 : 4 and 18 : 6

14/4 and 18/6

7/2 and 3/1

7 : 1 and 3 : 1 No

(iv) 12 : 18 and 28 : 12

12/18 and 28/12

2/3 and 7/3 No


Ratio and Proportion Exe-8.2

ML Aggarwal Class 6 ICSE Maths Solutions

Page-163

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

Answer:

(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 2. Write true (T) or false (F) against each of the following statements:

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

Answer:

(i) 12, 16, 6, 8
12: 16 :: 6 : 8

⇒ 12/16 = 6/8
12 × 8 = 16 × 6 ⇒ 96 = 96
∴ 12 : 16 :: 6 : 8 are in proportion
(ii) 2, 3, 4, 5
2 : 3 :: 4 : 5

⇒ 2/3 = 4/5

2 × 5 = 3 × 4 ⇒ 10 = 12 not in proportion

(iii) 18, 10, 9, 5
18 : 10 : : 9 : 5

⇒ 18/10 = 9/5
∴ 18 × 5 = 10 × 9 ⇒ 90 = 90
∴ 18 : 10 :: 9 : 5 are in proportion
(iv) 18, 9, 10, 5
18 : 9 :: 10 : 5

⇒ 18/9 = 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

Answer:

(i) 39kg : 36 kg = 26 men : 24 men
we have; 39: 36 = 39/36 = 13/12
And, 26:24 = 26/24 = 13/12
∴ 39 : 36 = 26 : 24
So, the given statement is true

(ii) 45km : 60 km = 12 hours : 15 hours
We have, 45 : 60 = 45/60 = 3/4

And, 12 : 15 = 12/15 = 4/5

∴ 45 : 60 ≠ 12 : 15
So, the given statement is false

(iii) 40 people : 200 people = ₹1000 : ₹5000
We have, 40:200 = 40/200 = 1/5

And, 1000 : 5000 = 1000/5000 = 1/5
∴ 40 : 200 = 1000 : 5000
So, the given statement is true

(iv) 7.5 litres : 1.5 litres = 15 children : 30 children
We have, 7.5 : 15 = 7.7/15 = 2.5/5

25/(5 x 10) = 25/50 = 1/2

And, 15: 30 = 15/30 = 1/2
∴ 7. 5 : 1.5 = 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

Answer:

(i) 25 cm : 1 m and ₹40 : ₹ 160

∵ 1 m = 100 cm
∴ 25 cm : 1m = 25cm : 100 cm

= 25/100 = 1/4 = 1 : 4

₹40 : ₹160 =

= 40/160 = 1/4 = 1 : 4

Since, the two ratio are equal, therefore, the given ration form a proportion. Middle terms are 1m and ₹40. Extreme terms are 25 cm and ₹160

(ii) 39 litres : 65 litres and 6 bottles : 10 bottles

39 litre : 65 litre

39/65 = 3/5 = 3 : 5

6 bottle : 10 bottle = 6/10

= 3/5 = 3 : 5

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.

(iii) 2 kg : 80 kg and 30 sec : 5 minutes

2kg : 80 kg

= 2/80 = 1/40 = 1 : 40

30 sec : 5 min. = 30 sec : 5 × 60 sec

30/300 = 1/10 = 1 : 10

Since the two ratios are not equal, therefore, the given ratios do not form a proportion.

(iv) 200 g : 2.5 kg and ₹4 : ₹50

2.5 kg = 2.5 × 1000 g = 2500 g
∴ 200 g : 2.5kg = 200 g : 2500 g

= 200/2500 = 2/25 = 2 : 25

₹ 4 : ₹50 = 4/50 = 2/25 = 2 : 25

Since, the two ratios are equal, therefore the given ratios form a proportion. Middle term are 2.5 kg and ₹4. Extreme terms are 200g and ₹50

—  : End of ML Aggarwal Ratio and Proportion Exe-8.2 Class 6 ICSE Maths Solutions :–

Return to   ML Aggarwal Maths Solutions for ICSE Class -6

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