The DAV Class 6 Maths Book Solutions Pdf and **DAV Class 6 Maths Chapter 4 Worksheet 2 **Solutions of Ratio, Proportion and Unitary Method offer comprehensive answers to textbook questions.

## DAV Class 6 Maths Ch 4 WS 2 Solutions

Question 1.

Are the following numbers in proportion?

(a) 9, 12, 18, 24

Solution:

9, 12, 18, 24

Product of extremes = 9 × 24 = 216

Product of means = 12 × 18 = 216

Hence, 9 : 12 : : 18 : 24.

(b) 3, 4, 8, 16

Solution:

3, 4, 8, 16

Product of extremes = 3 × 16 = 48

Product of means = 4 × 8 = 32

Product of extremes is not equal to the product of means

∴ 3, 4, 8, 16 are not in proportion.

(c) 22, 33, 16, 24

Solution:

22, 33, 16, 24

Product of extremes = 22 × 24 = 528

Product of means = 33 × 16 = 528

Hence, 22 : 33 : : 16 : 24.

(d) 63, 55, 32, 72

Solution:

63, 55, 32, 72

Product of extremes = 63 × 72 = 4536

Product of means = 55 × 32 = 1760

Product of extremes is not equal to product of means

∴ 63, 55, 32, 72 are not in proportion.

(e) 4, 9, 32, 72

Solution:

4, 9, 32, 72

Product of extremes = 4 × 72 = 288

Product of means = 9 × 32 = 288

Hence, 4 : 9 : : 32 : 72.

(f) 15, 75, 45, 120

Solution:

15, 75, 45, 120

Product of extremes = 15 × 120 = 1800

Product of means = 75 × 45 = 3375

Product of extremes is not equal to product of means

∴ 15, 25, 45, 120 are not in proportion.

Question 2.

Fill in the following boxes so that the four numbers are in proportion.

(a) 32, ___, 6, 12

Solution:

32, ___, 6, 12

If the given numbers are in proportion

∴ 32 : ___ : : 6 : 12

___ × 6 = 32 × 12

___ = \(\frac{32 \times 12}{6}\)

___ = 64

Hence, 64 should be filled in the blank box.

(b) 21, 27, 14, ___

Solution:

21, 27, 14, ___

If the given numbers are in proportion

∴ 21 : 27 : : 14 : ___

___ × 21 = 27 × 14

___ =

Hence, the required number = 18.

(c) 15, ___, 27, 36

Solution:

15, ___, 27, 36

If the give numbers are in proportion

∴ 15 : ___ : : 27 : 36

___ × 27 = 15 × 36

___ =

Hence, the required number = 20.

(d) 33, 132, ___, 16

Solution:

33, 132, ___, 16

If the given numbers are in proportion

∴ 33 : 132 : : ___ : 16

___ × 132 = 33 × 16

___ =

= 4

Hence, the required number = 4.

Question 3.

Are the following in continued proportion?

(a) 27, 36, 42

Solution:

27, 36, 42

If they are in continued proportion

∴ 27 : 36 : : 36 : 24

Product of extremes = 27 × 24 = 648

Product of means = 36 × 36 = 1296

∴ 648 ≠ 1296

Hence, they are not in continued proportion.

(b) 3, 9, 27

Solution:

3, 9, 27

If they are in continued proportion

∴ 3 : 9 : : 9 : 27

Product of extremes = 3 × 27 = 81

Product of means = 9 × 9 = 81

Hence, they are in continued proportion.

(c) 48, 36, 27

Solution:

48, 36, 27

If they are in continued proportion

∴ 48 : 36 : : 36 : 27

Product of extremes = 48 × 27 = 1296

Product of means = 36 × 36 = 1296

Hence, they are in continued proportion.

(d) 36, 90, 75

Solution:

36, 90, 75

They are in continued proportion

If 36 : 90 : : 90 : 75

Product of extremes = 36 × 75 = 2700

Product of means = 90 × 90 = 8100

∴ 2700 ≠ 8100

Hence, they are not in continued proportion.

Question 4.

Fill in the boxes so that the three numbers are in continued proportion:

(a) 6, 18, ___

Solution:

6, 18, ___

As they are in continued proportion

∴ 6 : 18 : : 18 : ___

6 × ___ = 18 × 18

___ =

= 54

Hence, the required number = 54.

(b) 25, 20, ___

Solution:

25, 20, ___

As they are in continued proportion

∴ 25 : 20 : : 20 : ___

25 × ___ = 20 × 20

___ =

= 16

Hence, the required number = 16.

(c) ___, 32, 64

Solution:

___, 32, 64

As they are in continued proportion

∴ ___ : 32 : : 32 : 64

___ × 64 = 32 × 32

___ =

= 16

Hence, the required number = 16.

(d) ___, 60, 45

Solution:

___, 60, 45

As they are in continued proportion

∴ ___ : 60 : : 60 : 45

___ × 45 = 60 × 60

___ =

= 80

Hence, the required number = 80.

Question 5.

Determine if the following ratios are in proportion:

(a) 48 kg : 6 kg and 25 g : 200 g

Solution:

48 kg : 6 kg and 25 g : 200 g

They are in proportion if 48 : 6 : : 25 : 200

Product of extremes = 48 × 200 = 9600

Product of means = 6 × 25 = 150

9600 ≠ 150

Hence, they are not in proportion.

(b) 8 m : 21 m and ₹ 24 : ₹ 63

Solution:

8 m : 21 m and ₹ 24 : ₹ 63

They are in proportion if 8 : 21 : : 24 : 63

Product of extremes = 8 × 63 = 504

Product of means = 21 × 24 = 504

Hence, they are in proportion.

(c) 45 girls : 60 girls and 48 boys : 64 boys

Solution:

45 girls : 60 girls and 48 boys : 64 boys

They are in proportion

if 45 : 60 : : 48 : 64

Product of extremes = 45 × 64 = 2880

Product of means = 60 × 48 = 2880

Hence, they are in proportion.

(d) 5.2 l : 3.9 l = 3 ml : 4 ml

Solution:

They are in proportion

if 5.2 : 3.9 : : 3 : 4

Product of extremes = 5.2 × 4 = 20.8

Product of means = 3.9 × 3 = 11.7

20.8 ≠ 11.7

Hence, they are not in proportion.

Question 6.

Fill in the following blanks:

(a) Equality of two ratios is called _________.

Solution:

Proportion

(b) A proportion has _________ terms.

Solution:

4

(c) The first and fourth terms of a proportion are called _________.

Solution:

extremes

(d) The _________ and _________ terms of a proportion are called means.

Solution:

second, third

(e) For 4 numbers to be in proportion, the product of _________ should be equal to the product of _________.

Solution:

extremes, means