**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