## EX 12.2 QUESTION 1.

Determine if the following are in proportion.

(a) 15, 45, 40, 120

(b) 33, 121, 9, 96

(c) 24, 28, 36, 48

(d) 32, 48, 70, 210

(e) 4, 6, 8, 12

(f) 33, 44, 75, 100

Solution:

(a) 15, 45, 40, 120

15 / 45 = 1 / 3 = 1 : 3

40 / 120 = 1 / 3 = 1 : 3

Since 15: 45 = 40:120

∴ 15, 45, 40, 120 are in a proportion

(b) 33, 121, 9, 96

33 / 121 = 3 / 11 = 3 : 11

9 / 96 = 3 / 32 = 3 : 32

Since 33:121 ≠ 9: 96

∴ 33, 121, 9, 96 are not in a proportion

(c) 24, 28, 36, 48

24 / 28 = 6 / 7 = 6 : 7

36 / 48 = 3 / 4 = 3 : 4

Since, 24: 28 ≠ 36:48

∴ 24, 28, 36, 48 are not in a proportion

(d) 32, 48, 70, 210

32 / 48 = 2 / 3 = 2 : 3

70 / 210 = 1 / 3 = 1 : 3

Since, 32: 48 ≠ 70: 210

∴ 32, 48, 70, 210 are not in a proportion

(e) 4, 6, 8, 12

4 / 6 = 2 / 3 = 2 : 3

8 / 12 = 2 / 3 =  2 : 3

Since, 4: 6 = 8: 12

∴ 4, 6, 8, 12are in a proportion

(f) 33, 44, 75, 100

33/ 44 = 3/ 4 = 3 : 4

75 / 100 = 3 / 4 = 3 : 4

Since, 33:44 = 75: 100

∴ 33, 44, 75, 100 are in a proportion

## EX 12.2 QUESTION 2.

Write True (T) or False ( F ) against each of the following statements :

(a) 16 : 24 :: 20 : 30

(b) 21: 6 :: 35 : 10

(c) 12 : 18 :: 28 : 12

(d) 8 : 9 :: 24 : 27

(e) 5.2 : 3.9 :: 3 : 4

(f) 0.9 : 0.36 :: 10 : 4

Solution:

16: 24 :: 20: 30

16 / 24 = 2 / 3

20 / 30 = 2 / 3

Hence, 16: 24 = 20: 30

Therefore True

(b) 21: 6:: 35: 10

21 / 6 = 7 / 2

35 / 10 = 7 / 2

Hence, 21: 6 = 35: 10

Therefore True

(c) 12: 18 :: 28: 12

12 / 18 = 2 / 3

28 / 12 = 7 / 3

Hence, 12: 18 ≠ 28:12

Therefore False

(d) 8: 9:: 24: 27

We know that = 24 / 27 = (3 × 8) / (3 × 9)

= 8 / 9

Hence, 8: 9 = 24: 27

Therefore True

(e) 5.2: 3.9:: 3: 4

As 5.2 / 3.9 = 3 / 4

Hence, 5.2: 3.9 ≠ 3: 4

Therefore False

(f) 0.9: 0.36:: 10: 4

0.9 / 0.36 = 90 / 36

= 10 / 4

Hence, 0.9: 0.36 = 10: 4

Therefore True

## EX 12.2 QUESTION 3.

Are the following statements true?

(a) 40 persons : 200 persons = ₹ 15 : ₹ 75

(b) 7.5 litres : 15 litres = 5 kg : 10 kg

(c) 99 kg : 45 kg = ₹ 44 : ₹ 20

(d) 32 m : 64 m = 6 sec : 12 sec

(e) 45 km : 60 km = 12 hours : 15 hours

Solutions:

(a) 40 persons : 200 persons = ₹ 15 : ₹ 75

40 / 200 = 1 / 5

15 / 75 = 1 / 5

Hence, True

(b) 7.5 litres : 15 litres = 5 kg : 10 kg

7.5 / 15 = 1 / 2

5 / 10 = 1 / 2

Hence, True

(c) 99 kg : 45 kg = ₹ 44 : ₹ 20

99 / 45 = 11 / 5

44 / 20 = 11 / 5

Hence, True

(d) 32 m : 64 m = 6 sec : 12 sec

32 / 64 = 1 / 2

6 / 12 = 1 / 2

Hence, True

(e) 45 km : 60 km = 12 hours : 15 hours

45 / 60 = 3 / 4

12 / 15 = 4 / 5

Hence, False

## EX 12.2 QUESTION 4.

Determine if the following ratios form a proportion. Also, write the middle terms and extreme terms where the ratios form a proportion.

(a) 25 cm : 1 m and ₹ 40 : ₹ 160

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

(c) 2 kg : 80 kg and 25 g : 625 g

(d) 200 mL : 2.5 litre and ₹ 4 : ₹ 50

Solutions:

(a) 25 cm : 1 m and ₹ 40 : ₹ 160

25 cm = 25 cm / 100 cm            [ 1 m = 100 cm]

= 1 / 4

40 / 160 = 1 / 4

Yes, these are in a proportion

Middle terms = 1 m, ₹ 40 and Extreme terms = 25 cm, ₹ 160

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

39 / 65 = 3 /5

6 / 10 = 3 / 5

Yes, these are in a proportion

Middle terms a= 65 litres, 6 bottles and Extreme terms = 39 litres, 10 bottles

(c) 2 kg : 80 kg and 25 g : 625 g

2 / 80 = 1 / 40

25 / 625 = 1 / 25

No, these are not in a proportion

(d) 200 mL : 2.5 litre and ₹ 4 : ₹ 50

2.5 litre = 2500 ml                               [1 litre = 1000 ml]

200 / 2500 = 2 / 5

4 / 50 = 2 / 25

Yes, these are in a proportion

Middle terms = 2.5 litres, ₹ 4 and Extreme terms = 200 ml, ₹ 50

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