ML Aggarwal CBSE Solutions Class 6 Math 9th Chapter Ratio and Proportion Exercise 9.2
Exercise 9.2
(1) Check whether the given two ratios form a proportion or not:
(i) 4 : 6 and 12 : 18
Solution: 4 : 6 = 4/6 = 2/3
12 : 18 = 12/18 = 2/3
As, 2/3 = 2/3, the given ratios are in proportion.
(ii) 15:45 and 40:120
Solution: 15/45 = 1/3
40/120 = 1/3
As, 1/3 = 1/3, the given ratios are in proportion.
(iii) 14:4 and 18:6
Solution: 14/4 = 7/2
18/6 = 3/1
As, 7/2 ≠ 3/1, the given ratio do not form a proportion.
(iv) 12:18 and 28: 12
Solution: 12 / 18 = 2/3
28:12 = 28/12 = 7/3
As, 2/3 ≠ 7/3, the given ratio do not form a proportion.
(2) Write true (T) or false (F) against each of the following statements:
(i) 16 : 24 = 20 : 30
=> 2 : 3 = 2 : 3
They are equal since, True.
(ii) 16 : 24 = 30 : 20
=> 2 : 3 = 3 : 2
They are not equal since, False.
(iii) 21 : 6 :: 35 : 10
=> 21/6 = 35/10
=> 21 x 10 = 35 x 6
=> 210 = 210
They are equal, since true.
(iv) 5.2 : 3.9 :: 3 : 4
=> 5/2 = ¾
=> 5.2 x 4 = 3.9 x 3
=> 20.8 = 11.7
They are not equal since, false.
(3) Find which of the following are in proportion:
(i) 12, 16, 6, 8
Solution: 12, 16, 6, 8 are in proportion if the product of extremes is equal to the product of means.
Here, product of extremes = 12 x 8 = 96,
Product of means = 16 x 6 = 96
Hence, 12, 16, 6, 8 are in proportion.
(ii) 2, 3, 4, 5
Solution: 2, 3, 4, 5 are in proportion if the product of extremes is equal to the product of means.
Here, product of extremes = 2 x 5 = 10
Product of means = 3 x 4 = 12,
Hence, 2, 3, 4, 5 are not in proportion.
(iii) 18, 10, 9, 5
Solution: 18, 10, 9, 5 are in proportion if the product of extremes is equal to the product of means.
Here, product of extremes = 18 x 5 = 90
Product of means = 10 x 9 = 90
Hence, 18, 10, 9, 5 are in proportion.
(iv) 18, 9, 10, 5
Solution: 18, 9, 10, 5 are in proportion if the product of extremes is equal to the product of means.
Here, product of extremes = 18 x 5 = 90
Product of means = 9 x 10 = 90
Hence, 18, 9, 10, 5 are in proportion.
(4) Are the following statement true?
(i) 39 kg : 36 kg :: 26 men : 24 men
=> Product of extremes = 39 kg x 24 men = 936
Product of means = 36 kg x 26 men = 936
Hence, True
(ii) 45 km : 60 km = 12 hours : 15 hours
= 45/60 = 12/15
=> ¾ = 4/5
Hence, False
(iii) 40 people : 200 people = Rs 1000 : Rs. 5000
=> 40/200 = 1000/5000
=> 1/5 = 1/5
Hence, True
(iv) 7.5 litres : 15 litres = 15 children : 30 children
=> 7.5/15 = 15/30
=> ½ = ½
Hence, True.
(5) Determines if the following ratios are in proportion. Also write the middle terms and extreme terms when the ratio form a proportion.
(i) 25 cm : 1 m and Rs. 40 : Rs. 160
Solution: 1 m = 100 cm
Ratio of 25 cm to 1 m = 25/100 = ¼
Ratio of Rs. 40 to Rs. 160 = 40/160 = ¼
As ¼ = ¼ , the given ratio are in proportion.
Extreme terms = 25 cm x 160
Middle terms = 1 m x Rs. 40
(ii) 39 litre : 65 litre and 6 bottles : 10 bottles
Solution: Ratio of 39 litre to 65 litre= 39/65 = 3/5
Ratio of 6 bottles to 10 bottles = 6/10 = 3/5
As 3/5 = 3/5, the give ratio are in proportion.
Extreme terms = 39 litre, 10 bottles
Middle terms = 65 litre, 6 bottles.
(iii) 2 kg : 80 kg and 30 sec : 5 minutes
Solution: Ratio of 2 kg to 80 kg = 2/80 = 1/40
5 minutes = 5 x 60 = 300 seconds
Ratio of 30 sec to 5 minutes = 30/300 = 1/10
As 1/40 ≠ 1/10, are not in proportion.
(iv) 200 g : 2.5 kg and Rs. 4 : Rs. 50
Solution: 2.5 kg = 2500 g
Ratio of 200 g to 2.5 kg = 200/2500 = 2/25
Ratio of Rs. 4 to Rs. 50 = 4/50 = 2/25
Hence, 2/25 = 2/25, the given ratio are in proportion.
Extreme terms = 200 g, Rs. 50
Middle terms = 2.5 kg, Rs. 4