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 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
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