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Chapter 12: Ratio and Proportion

    Introduction

    Ratio

    Proportion

    Unitary Method

    Exercise 12.1

    Exercise 12.2

    Exercise 12.3

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Chapter 12: Ratio and Proportion > Exercise 12.2

Exercise 12.2

1. Determine if the following are in proportion.

(a - c)

(a) 15, 45, 40, 120

Ratio = 1545 = (fraction form) = (ratio form)

Ratio = 40120 = (fraction form) = (ratio form)

Hence 15:45 40:120

Therefore 15, 45, 40, 120 are .

(b) 33, 121, 9,96

Ratio = 33121 = (fraction form) = (ratio form)

Ratio = 996 = (fraction form) = (ratio form)

Hence 33:121 9 : 96

Therefore 15, 45, 40, 120 are .

(c) 24, 28, 36, 48

Ratio = 2428 = (fraction form) = (ratio form)

Ratio = 3648 = (fraction form) = (ratio form)

Hence 24:28 36:48

Therefore 24, 28, 36, 48 are .

(d - f)

(d) 32, 48, 70, 210

Ratio = 3248 = (fraction form) = (ratio form)

Ratio = 70210 = (fraction form) = (ratio form)

Hence 32:48 70:210

Therefore 32, 48, 70, 210 are .

(e) 4, 6, 8, 12

Ratio = 46 = (fraction form) = (ratio form)

Ratio = 812 = (fraction form) = (ratio form)

Hence 4:6 8:12

Therefore 4, 6, 8, 12 are .

(f)33, 44, 75, 100

Ratio = 3344 = (fraction form) = (ratio form)

Ratio = 75100 = (fraction form) = (ratio form)

Hence 33:44 75:100

Therefore 33, 44, 75, 100 are .

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

(a - c)

(a) 16 : 24 :: 20 : 30

Product of the extreme terms = 16 × 30 =

Product of the middle terms = 24 × 20 =

∴ The given statement is

(b) 21: 6 :: 35 : 10

Product of the extreme terms = 21 × 10 =

Product of the middle terms = 6 × 35 =

∴ The given statement is

(c) 12 : 18 :: 28 : 12

Product of the extreme terms = 12 × 12 =

Product of the middle terms = 18 × 28 =

∴ The given statement is

(d - f)

(d) 8 : 9 :: 24 : 27

Product of the extreme terms = 8 × 27 =

The product of the middle terms = 9 × 24 =

∴ The given statement is

(e) 5.2 : 3.9 :: 3 : 4

Product of the extreme terms = 5.2 × 4 =

Product of the middle terms = 3.9 × 3 =

∴ The given statement is

(f) 0.9 : 0.36 :: 10 : 4

Product of the extreme terms = 0.9 × 4 =

Product of the middle terms = 0.36 × 10 =

∴ The given statement is

3. Are the following statements true?

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

40 : 200 = 40200 = [40÷40200÷40]

15 : 75 = 1575 = [15÷1575÷15]

Statement is .

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

7.5 : 15 = 7.515 = 75÷75105÷75

5 : 10 = 510 = 5÷510÷5

Statement is .

(c) 99 kg : 45 kg = ₹ 44 : ₹ 20

99 : 45 = 9945 = 99÷945÷9

44 : 20 = 4420 = 44÷420÷4

Statement is .

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

32 : 64 = 3264 = 32÷3264÷32

6 : 12 = 612 = 6÷612÷6

Statement is .

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

45 : 60 = 4560 = 45÷1560÷15

12 : 15 = 1215 = 12÷315÷3

Statement is .

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

(a) 25 cm : 1 m and ₹ 40 : ₹ 160

Covert 1m to cm : 1m = cm

So, 25 : 100 = 25100 =

For, 40 : 160 = 40160 =

Since, both ratios simplify to 14 they are .

Middle terms : and , Extreme terms : and .

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

So, 39 : 65 = 3965 =

For, 6 : 10 = 610 =

Since, both ratios simplify to 14 they are .

Middle terms : and , Extreme terms : and .

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

So, 2 : 80 = 280 =

For, 25 : 625 = 25625 =

Since, both ratios simplify to 14 they are .

(d) 200 mL : 2.5 litre and ₹ 4 : ₹ 50

Convert 2.5 liters to ml : 2.5 liters = ml

So, 200 : 2500 = 2002500 =

For, 4 : 50 = 450 =

Since, both ratios simplify to 14 they are .

Middle terms : and , Extreme terms : and .