The DAV Class 6 Maths Book Solutions Pdf and **DAV Class 6 Maths Chapter 4 Worksheet 1 **Solutions of Ratio, Proportion and Unitary Method offer comprehensive answers to textbook questions.

## DAV Class 6 Maths Ch 4 WS 1 Solutions

Question 1.

Express the following as ratios:

(a) \(\frac{3}{5}\)

Solution:

3 : 5

(b) \(\frac{13}{17}\)

Solution:

13 : 17

(c) \(\frac{49}{36}\)

Solution:

49 : 36

(d) \(\frac{1000}{537}\)

Solution:

1000 : 537

(e) \(\frac{91}{92}\)

Solution:

91: 92

(f) \(\frac{1}{49}\)

Solution:

1 : 49

(g) 15

Solution:

15 : 1

(h) \(\frac{42}{13}\)

Solution:

42 : 13

Question 2.

Find the ratio of the shaded region to that of the whole figure.

(a)

Solution:

The whole figure is equally divided into 7 parts and the number of shaded parts = 4.

Hence, the required ratio = 4:7.

(b)

Solution:

The whole figure is equally divided into 8 parts and the number of shaded parts = 3.

Hence, the required ratio = 3 : 8.

Question 3.

Express the following ratios in the simplest form.

(a) 36 m to 16 m

Solution:

36 m to 16 m

=

= \(\frac{9}{4}\)

Hence, the simplest form of 36 m to 16 m = 9 : 4.

(b) ₹ 125 to ₹ 35

Solution:

₹ 125 to ₹ 35

=

= \(\frac{25}{7}\)

Hence, the required simplest form = 25 : 7.

(c) 324 : 144

Solution:

324 : 144

=

= \(\frac{9}{4}\)

Hence, the required simplest form = 9 : 4.

(d) 65 books to 91 books

Solution:

65 books to 91 books

=

= \(\frac{5}{7}\)

Hence, the required simplest form = 5 : 7.

(e) 125 : 1125

Solution:

125 : 1125

=

= \(\frac{1}{9}\)

Hence, the required simplest form = 1 : 9.

(f) 45 hours to 36 hours

Solution:

45 hours to 36 hours

=

= \(\frac{5}{4}\)

Hence, the required ratio = 5 : 4.

Question 4.

Express the following as ratio in the simplest form.

(a) 10 cm to 10 m

Solution:

10 m = 10 × 100 = 1000 cm

∴ 10 cm to 1000 cm

=

= \(\frac{1}{100}\)

Hence, the required ratio = 1 : 100.

(b) 45 minutes to 4 hours

Solution:

4 hours = 4 × 60 = 240 minutes

= \(\frac{1}{2}\)

∴ 45 minutes to 240 minutes

=

= \(\frac{3}{16}\)

Hence, the required ratio = 3 : 16.

(c) 35 days to 3 weeks

Solution:

35 days to 3 weeks

3 weeks = 3 × 7 = 21 days

∴ 35 days to 21 days = 35 : 21

=

= \(\frac{5}{3}\)

Hence, the required ratio = 5 : 3.

(d) 2 dozen to 1 score

Solution:

2 dozen to 1 score

2 dozen = 2 × 12 = 24 items

1 score = 20 items

∴ ratio = 24 : 20

=

= \(\frac{6}{5}\)

Hence, the required ratio = 6 : 5.

(e) ₹ 3.50 to 75 paise

Solution:

₹ 3.50 to 75 Paise

₹ 3.50 = 3.50 × 100 = 350 Paise

∴ ratio is 350 : 75

=

= \(\frac{14}{3}\)

Hence, the required ratio = 14 : 3.

(f) 4 kg to 250 gram

Solution:

4 kg to 250 gm

4 kg = 4 × 1000 = 4000 gm

∴ ratio = 4000 : 250

=

= \(\frac{16}{1}\)

∴ required ratio = 16 : 1.

Question 5.

Which of the following pairs of ratio is greater?

(a) 5 : 8 or 4 : 5

Solution:

5 : 8 or 4 : 5

∴ \(\frac{5}{8}\) or \(\frac{4}{5}\)

= \(\frac{5 \times 5}{8 \times 5}\) or \(\frac{4 \times 8}{5 \times 8}\)

= \(\frac{25}{40}\) or \(\frac{32}{40}\)

Here, 32 > 25

∴ \(\frac{32}{40}>\frac{25}{40}\)

Hence, 4 : 5 is greater than 5 : 8.

(b) 9 : 11 or 11 : 9

Solution:

9 : 11 or 11 : 9

\(\frac{9}{11}\) or \(\frac{11}{9}\)

= \(\frac{9 \times 9}{11 \times 9}\) or \(\frac{11 \times 11}{9 \times 11}\)

= \(\frac{81}{99}\) or \(\frac{121}{99}\)

Here, 81 < 121

∴ \(\frac{11}{9}>\frac{9}{11}\)

Hence, 11 : 9 is greater than 9 : 11.

(c) 23 : 24 or 15 : 16

Solution:

23 : 24 or 15 : 16

\(\frac{23}{24}\) or \(\frac{15}{16}\)

= \(\frac{23 \times 16}{24 \times 16}\) or \(\frac{15 \times 24}{16 \times 24}\)

= \(\frac{368}{384}\) or \(\frac{360}{384}\)

Here, 368 > 360

∴ \(\frac{23}{24}>\frac{15}{16}\)

Hence, 23 : 24 is greater than 15 : 16.

(d) 3 : 10 or 15 : 40

Solution:

3 : 10 or 15 : 40

= \(\frac{3}{10}\) or \(\frac{15}{40}\)

= \(\frac{3 \times 40}{10 \times 40}\) or \(\frac{15 \times 10}{40 \times 10}\)

= \(\frac{120}{400}\) or \(\frac{150}{400}\)

Here, 120 < 150

∴ \(\frac{15}{40}>\frac{3}{10}\)

Hence, 15 : 40 is greater than 3 : 10.

Question 6.

There are 50 students in a class. If 24 of them are boys, find the ratio of boys to the girls.

Solution:

Total number of students = 50

Number of boys = 24

∴ Number of girls = 50∴24 = 26

Ratio of boys to girls = 24 : 26 = 12 : 13

Hence, the required ratio = 12 : 13.

Question 7.

Sahil ran a distance of 1.5 km and his younger sister could run only 500 m. Express the distance as ratio.

Solution:

Distance run by Sahil = 1.5 km

= 1.5 × 1000 m = 1500 m

Distance run by his sister = 500 m

∴ ratio = 1500 m : 500 m = 3 : 1

Hence, the required ratio = 3 : 1.

Question 8.

Out of 32 m long cloth, 24 metres were used for making 8 frocks. Find the ratio of:

(a) Total cloth and cloth used.

(b) Remaining cloth and cloth used.

Solution:

Total length of cloth = 32 m

Length of cloth used = 24 m

Length of remaining cloth = 32 m∴24 m = 8 m

(a) Ratio of total length to the length used = 32 : 24

= 4 : 3

(b) Ratio of remaining cloth to the used cloth = 8 : 24

= 1 : 3

Question 9.

Mr. Arun earns ₹ 9500 per month and his wife earns ₹ 8000. Find the ratio of:

(a) Mr. Arun’s income to his wife’s income

(b) Wife’s income to total income

Solution:

Mr. Arun’s monthly income = ₹ 9500

His wife’s monthly income = ₹ 8000

Total income = ₹ 9500 + ₹ 8000 = ₹ 17500

(а) Ratio of Mr. Arun’s income to his wife’s income

∴ ratio = 9500 : 8000

= 95 : 80

= 19 : 16

(b) Ratio of wife’s income to total income = 8000 : 17500

= 80 : 175

= 16 : 35

Question 10.

In a dictation test of 20 words, Rohan spelled 18 words correctly. Find the ratio of:

(a) Total words to wrongly spelled words.

(b) Correctly spelled words to wrongly spelled words.

Solution:

Total number of words = 20

Number of words spelled correctly = 18

∴ Number of wrongly spelled words = 20∴18 = 2

(a) Total words to wrongly spelled words

∴ 20 : 2 = 10 : 1

(b) Correctly spelled words to wrongly spelled words

∴ 18 : 2 = 9 : 1

Question 11.

Mrs. Sareen earns ₹ 2,50,000 every year and pays ₹ 24,000 as income tax. Find the ratio of:

(a) Income tax to income

(b) Income to income tax

Solution:

Total income = ₹ 2,50,000

Income tax = ₹ 24000

Ratio of income tax to income = 24,000 : 2,50,000

= 24 : 250

= 12 : 125

Ratio of income to income tax = 2,50,000 : 24,000

= 250 : 24

= 125 : 12.

Question 12.

Fill in the following blanks:

(a) Comparing two quantities by division is called _____.

Solution:

Ratio

(b) A ratio is always expressed in its _____ form.

Solution:

lowest

(c) The first term of a ratio 11 : 24 is _____ and the second term is _____.

Solution:

11, 24

(d) The ratio of the letter M in the word MATHEMATICS to the total letters in the word is _____.

Solution:

2 : 11

(e) The ratio of even numbers to odd numbers in a set of natural numbers from 1 to 25 is _____.

Solution:

12 : 13

### DAV Class 6 Maths Chapter 4 Worksheet 1 Notes

**Ratio:**

Ratio is a comparison between two quantities. It is represented by ‘:‘

Example:

Ramesh is 10 years old and Mohan is 15 years old

∴ Ratio between their ages = \(\frac{10}{15}\)

= \(\frac{2}{3}\) (lowest form) = 2 : 3

Ratio is always calculated between the quantities of the same unit. Therefore, ratio has no unit.

Ratio 2 : 3 may be read as ‘2 is to 3’.

Ratio is always represented in its simplest form.

Example:

Ratio 14 : 35 = 2 : 5 (simplest form).

**Proportion:**

Any two ratios represented is their lowest form are called proportional to each other.

Example:

Ratios 2 : 3, 4 : 6, 6 : 9 and 8 : 12 are all proportional to each other.

Symbol of proportion is : :

Ratio 6 : 9 is same as the ratio 18 : 27

So we can represent it as Product of extremes = Product of means

6 × 27 = 9 × 18

162 = 162.

Example 1:

Convert the given ratios in their simplest form:

(a) 20 : 32

Solution:

20 : 32 =

Hence, the simplest form of 20 : 32 = 5 : 8.

(b) 56 : 100

Solution:

56 : 100 =

Hence, the simplest form of 56 : 100 = 14 : 25.

(c) 8 : 512

Solution:

8 : 512 =

Hence, the simplest form of 8 : 512 = 1 : 64.

(d) 16 : 20

Solution:

16 : 20 =

Hence, the simplest form of 16 : 20 = 4 : 5.

Example 2:

Find the ratio of:

(a) 20 cm to 2 m

Solution:

We know that

2 m = 2 × 100 = 200 cm

∴ 20 : 200 =

Hence, the required ratio = 1 : 10.

(b) 50 grams to 2 kg

Solution:

We know that

2 kg = 2 × 1000 = 2000 g

∴ 50 : 2000 =

Hence, the required ratio = 1 : 40.

(c) ₹ 2.50 to 2575 paise

Solution:

We know that

₹ 2.50 = 2.50 × 100 = 250 Paise

∴ 250 : 2575 =

Hence, the required ratio = 10 : 103.

Example 3:

Check whether the following terms are in proportion.

(a) 8, 12, 10, 15

Solution:

Here, extremes are = 8 and 15

and means are = 12 and 10

Product of extremes is = 8 × 15 =120

Product of means is = 12 × 10 = 120

Product of extremes = Product of means

Hence, the given terms are in proportion and we can write 8 : 12 :: 10 : 15.

(b) 6, 8, 12, 16

Solution:

Here, extremes are = 6 and 16

and means are = 8 and 12

Product of extremes = 6 × 16 = 96

Product of means = 8 × 12 = 96

Product of extremes = Product of means

Hence, the given terms are in proportion and we can write 6 : 8 : : 12 : 16.