**Ratio Proportion**

## Chapter 12

## Exercise 12.2

**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