## RD Sharma Solutions for Class 6 Chapter 9 Ratio, Proportion and Unitary Method Free Online

Exercise 9.1 page: 9.5

**1. Express each of the following in the language of ratios:**

**(i) In a class, the number of girls in the merit list of the board examination is two times that of boys.**

**(ii) The number of students passing mathematics test is 2/3 of the number that appeared.**

**Solution:**

(i) Ratio of the number of girls to that of boys in the merit list is 2: 1.

(ii) Ratio of the number of students passing a mathematics test to that of total students appearing in the test is 2: 3.

**2. Express the following ratios in language of daily life:**

**(i) The ratio of the number of bad pencils to that of good pencils produced in a factory is 1: 9.**

**(ii) In India, the ratio of the number of villages to that of cities is about 2000: 1.**

**Solution:**

(i) The number of bad pencils produced in a factory is 1/9 of the number of good pencils produced in the factory.

(ii) The number of villages is 2000 times that of cities in India.

**3. Express each of the following ratios in its simplest form:**

**(i) 60: 72**

**(ii) 324: 144**

**(iii) 85: 391**

**(iv) 186: 403**

**Solution:**

(i) 60: 72

It can be written as 60/72

We know that the HCF of 60 and 72 is 12

By dividing the term by 12 we get

(60/72) × (12/12) = 5/6

So we get 60: 72 = 5: 6

(ii) 324: 144

It can be written as 324/144

We know that the HCF of 324 and 144 is 36

By dividing the term by 36 we get

(324/144) × (36/36) = 9/4

So we get 324: 144 = 9: 4

(iii) 85: 391

It can be written as 85/391

We know that the HCF of 85 and 391 is 17

By dividing the term by 17 we get

(85/391) × (17/17) = 5/23

So we get 85: 391 = 5: 23

(iv) 186: 403

It can be written as 186/403

We know that the HCF of 186 and 403 is 31

By dividing the term by 31 we get

(186/403) × (31/31) = 6/13

So we get 186: 403 = 6: 13

**4. Find the ratio of the following in the simplest form:**

**(i) 75 paise to Rs 3**

**(ii) 35 minutes to 45 minutes**

**(iii) 8 kg to 400 gm**

**(iv) 48 minutes to 1 hour**

**(v) 2 metres to 35 cm**

**(vi) 35 minutes to 45 seconds**

**(vii) 2 dozen to 3 scores**

**(viii) 3 weeks to 3 days**

**(ix) 48 min to 2 hours 40 min**

**(x) 3 m 5 cm to 35 cm**

**Solution:**

(i) 75 paise to Rs 3

It can be written as

75 paise to Rs 3 = 75 paise: Rs 3

We know that 1 Rs = 100 paise

So we get

75 paise to Rs 3 = 75 paise: 300 paise

Dividing the two terms by HCF 75

75 paise to Rs 3 = 1: 4

(ii) 35 minutes to 45 minutes

It can be written as

35 minutes to 45 minutes = 35 minutes: 45 minutes

Dividing the two terms by HCF 5

35 minutes to 45 minutes = 7: 9

(iii) 8 kg to 400 gm

It can be written as

8 kg to 400 gm = 8 kg: 400 gm

We know that 1 kg = 1000 gm

So we get

8 kg to 400 gm = 8000 gm: 400 gm

Dividing the two terms by HCF 400

8 kg to 400 gm = 20: 1

(iv) 48 minutes to 1 hour

It can be written as

48 minutes to 1 hour = 48 minutes: 1 hour

We know that 1 hour = 60 minutes

So we get

48 minutes to 1 hour = 48 minutes: 60 minutes

Dividing the two terms by HCF 12

48 minutes to 1 hour = 4: 5

(v) 2 metres to 35 cm

It can be written as

2 metres to 35 cm = 2 metres: 35 cm

We know that 1 m = 100 cm

So we get

2 metres to 35 cm = 200 cm: 35 cm

Dividing the two terms by HCF 5

2 metres to 35 cm = 40: 7

(vi) 35 minutes to 45 seconds

It can be written as

35 minutes to 45 seconds = 35 minutes: 45 seconds

We know that 1 minute = 60 seconds

So we get

35 minutes to 45 seconds = 2100 seconds: 45 seconds

Dividing the two terms by HCF 15

35 minutes to 45 seconds = 140: 3

(vii) 2 dozen to 3 scores

It can be written as

2 dozen to 3 scores = 2 dozen: 3 scores

We know that 1 dozen = 12 score = 20

So we get

2 dozen to 3 scores = 24: 60

Dividing the two terms by HCF 12

2 dozen to 3 scores = 2: 5

(viii) 3 weeks to 3 days

It can be written as

3 weeks to 3 days = 3 weeks: 3 days

We know that 1 week = 7 days

So we get

3 weeks to 3 days = 21 days: 3 days

Dividing the two terms by HCF 3

3 weeks to 3 days = 7: 1

(ix) 48 min to 2 hours 40 min

It can be written as

48 min to 2 hours 40 min = 48 min: 2 hours 40 min

We know that 1 hour = 60 minutes

So we get

48 min to 2 hours 40 min = 48 min: 160 min

Dividing the two terms by HCF 16

48 min to 2 hours 40 min = 3: 10

(x) 3 m 5 cm to 35 cm

It can be written as

3 m 5 cm to 35 cm = 3 m 5 cm: 35 cm

We know that 1 m = 100 cm

So we get

3 m 5 cm to 35 cm = 305 cm: 35 cm

Dividing the two terms by HCF 5

3 m 5 cm to 35 cm = 61: 7

**5. Find the ratio of**

**(i) 3.2 metres to 56 metres**

**(ii) 10 metres to 25 cm**

**(iii) 25 paise to Rs 60**

**(iv) 10 litres to 0.25 litre**

**Solution:**

(i) 3.2 metres to 56 metres

It can be written as

3.2 metres to 56 metres = 3.2 metres: 56 metres

Dividing the two terms by HCF 1.6

3.2 metres to 56 metres = 2: 35

(ii) 10 metres to 25 cm

It can be written as

10 metres to 25 cm = 10 m: 25 cm

We know that 1 m = 100 cm

10 metres to 25 cm = 1000 cm: 25 cm

Dividing the two terms by HCF 25

10 metres to 25 cm = 40: 1

(iii) 25 paise to Rs 60

It can be written as

25 paise to Rs 60 = 25 paise: Rs 60

We know that 1 Rs = 100 paise

25 paise to Rs 60 = 25 paise: 6000 paise

Dividing the two terms by HCF 25

25 paise to Rs 60 = 1: 240

(iv) 10 litres to 0.25 litre

It can be written as

10 litres to 0.25 litre = 10 litres: 0.25 litre

Dividing the two terms by HCF 0.25

10 litres to 0.25 litre = 40: 1

**6. The number of boys and girls in a school are 1168 and 1095 respectively. Express the ratio of the number of boys to that of the girls in the simplest form.**

**Solution:**

No. of boys = 1168

No. of girls = 1095

So the ratio of the number of boys to that of the girls = 1168: 1095

Dividing the two terms by HCF 73

Ratio of number of boys to that of the girls = 16: 15

Hence, the ratio of the number of boys to that of girls in simplest form is 16: 15.

**7. Avinash works as a lecturer and earns Rs 12000 per month. His wife who is a doctor earns Rs 15000 per month. Find the following ratios:**

**(i) Avinash’s income to the income of his wife.**

**(ii) Avinash’s income to their total income.**

**Solution:**

Avinash salary earned per month = Rs 12000

Avinash wife salary per month = Rs 15000

(i) Avinash’s income to the income of his wife = 12000/15000 = 4: 5

(ii) Avinash’s income to their total income = 12000/ (12000 + 15000) = 4: 9

**8. Of the 72 persons working in an office, 28 are men and the remaining are women. Find the ratio of the number of:**

**(i) men to that of women,**

**(ii) men to the total number of persons**

**(iii) persons to that of women.**

**Solution:**

No. of persons working in an office = 72

No. of men = 28

So the number of women = 72 – 28 = 44

(i) men to that of women = 28: 44

Multiplying and dividing the equation by HCF 4

Men to that of women = (28/44) × (4/4) = 7: 11

(ii) men to the total number of persons = 28: 72

Multiplying and dividing the equation by HCF 4

Men to the total number of persons = (28/72) × (4/4) = 7: 18

(iii) persons to that of women = 72: 44

Multiplying and dividing the equation by HCF 4

Persons to that of women = (72/44) × (4/4) = 18: 11

**9. The length of a steel tape for measurements of buildings is 10 m and its width is 2.4 cm. What is the ratio of its length to width?**

**Solution:**

It is given that

Length of a steel tape = 10 m

Width of steel tape = 2.4 cm

So the ratio of its length to width = 10 m/ 2.4 cm

We know that 1 m = 100 cm

Ratio of its length to width = 1000 cm/ 2.4 cm

Dividing the two terms by HCF 0.8 cm

Ratio of its length to width = 1250: 3

Hence, the ratio of its length to width is 1250: 3.

**10. An office opens at 9 am and closes at 5 pm with a lunch interval of 30 minutes. What is the ratio of lunch interval to the total period in office?**

**Solution:**

Duration of office = 9 am to 5 pm = 8 hours

Lunch interval = 30 minutes

So the ratio of lunch interval to the period in office = 30 minutes/8 hours

We know that 1 hour = 60 minutes

Ratio of lunch interval to the period in office = 30/ (8 × 60) = 30/480

Dividing the two terms by HCF 30

Ratio of lunch interval to the period in office = (30/480) × (30/30) = 1: 16

Hence, the ratio of lunch interval to the total period in office is 1: 16.

**11. A bullock-cart travels 24 km in 3 hours and a train travels 120 km in 2 hours. Find the ratio of their speeds.**

**Solution:**

Distance travelled by bullock-cart = 24 km in 3 hours

Distance travelled by train = 120 km in 2 hours

It can be written as

Distance travelled by bullock-cart = 24 km/ 3 = 8 km

Distance travelled by train = 120 km/2 = 60 km

So the ratio of their speeds = 8/60

Dividing the two terms by HCF 4

Ratio of their speeds = (8/60) × (4/4) = 2/15

Hence, the ratio of their speeds is 2: 15.

**12. Margarette works in a factory and earns Rs 955 per month. She saves Rs 185 per month from her earnings. Find the ratio of:**

**(i) her savings to her income**

**(ii) her income to her expenditure**

**(iii) her savings to her expenditure.**

**Solution:**

Margarette monthly income = Rs 955

Margarette monthly savings = Rs 185

Margarette expenditure = 955 – 185 = Rs 770

(i) her savings to her income = 185/955

Dividing the two terms by HCF 5

Her savings to her income = (185/955) × (5/5) = 37: 191

(ii) her income to her expenditure = 955/770 = 191: 154

(iii) her savings to her expenditure = 185/770 = 37: 154

Exercise 9.2 page: 9.9

**1. Which ratio is larger in the following pairs?**

**(i) 3: 4 or 9: 16**

**(ii) 15: 16 or 24: 25**

**(iii) 4: 7 or 5: 8**

**(iv) 9: 20 or 8: 13**

**(v) 1: 2 or 13: 27**

**Solution:**

(i) 3: 4 or 9: 16

It can be written as

3: 4 = 3/4 and 9: 16 = 9/16

LCM of 4 and 16 is 16

Multiplying by 4 to make the denominator 16

3/4 = (3/4) × (4/4) = 12/16 and 9/16

We know that 12 > 9

So we get 12/16 > 9/16

We can write it as

3/4 > 9/16

Hence, 3: 4 > 9: 16.

(ii) 15: 16 or 24: 25

It can be written as

15: 16 = 15/16 and 24: 25 = 24/25

LCM of 16 and 25 is 400

Multiplying by relevant numbers to make denominator as 400

15/16 = (15/16) × (25/25) = 375/400 and 24/25 = (24/25) × (16/16) = 384/400

We know that 384 > 375

So we get 384/400 > 375/400

We can write it as 24/25 > 15/16

Hence, 24: 25 > 15: 16.

(iii) 4: 7 or 5: 8

It can be written as

4: 7 = 4/7 and 5: 8 = 5/8

LCM of 7 and 8 is 56

Multiplying by relevant numbers to make denominator as 56

4/7 = (4/7) × (8/8) = 32/56 and 5/8 = (5/8) × (7/7) = 35/56

We know that 35 > 32

So we get 35/56 > 32/56

We can write it as 5/8 > 4/7

Hence, 5: 8 > 4: 7.

(iv) 9: 20 or 8: 13

It can be written as

9: 20 = 9/20 and 8: 13 = 8/13

LCM of 20 and 13 is 260

Multiplying by relevant numbers to make denominator as 260

9/20 = (9/20) × (13/13) = 117/260 and 8/13 = (8/13) × (20/13) = 160/260

We know that 160 > 117

So we get 160/260 > 117/260

We can write it as 8/13 > 9/20

Hence, 8: 13 > 9: 20.

(v) 1: 2 or 13: 27

It can be written as

1: 2 = 1/2 and 13: 27 = 13/27

LCM of 2 and 27 is 54

Multiplying by relevant numbers to make denominator as 54

1/2 = (1/2) × (27/27) = 27/54 and 13/27 = (13/27) × (2/2) = 26/54

We know that 27 > 26

So we get 27/54 > 26/54

We can write it as 1/2 > 13/27

Hence, 1: 2 > 13: 27.

**2. Give two equivalent ratios of 6: 8.**

**Solution:**

The given ratio = 6: 8

It can be written as = 6/8

Dividing the fraction by 2 we get

6/8 = (6/8) ÷ (2/2) = 3/4

Hence, 3: 4 is an equivalent ratio of 6: 8

Multiply the fraction by 2 we get

6/8 = (6/8) × (2/2) = 12/16

Hence, 12: 16 is an equivalent ratio of 6: 8

So, 3: 4 and 12: 16 are the equivalent ratios of 6: 8.

**3. Fill in the following blanks:**

**12/20 = ☐/5 = 9/☐**

**Solution:**

It is given that

12/20 = ☐/5 = 9/☐

We know that LCM of 20 and 5 is 20

It can be written as 20/4 = 5

Dividing the fraction by 4

12/20 = (12/20) × (4/4) = 3/5

So the first number is 3 and the ratio is 3/5.

In the same way,

Consider 2/3 + 3/5 = 9/☐

We know that 9/3 = 3

Multiply the fraction by 3

3/5 = (3/5) × (3/3) = 9/15

So the second number is 15 and the ratio is 9/15.

Exercise 9.3 page: 9.14

**1. Which of the following statements are true?**

**(i) 16: 24 = 20: 30**

**(ii) 21: 6 = 35: 10**

**(iii) 12: 18 = 28: 12**

**(iv) 51: 58 = 85: 102**

**(v) 40 men: 200 men = Rs 5: Rs 25**

**(vi) 99 kg: 45 kg = Rs 44: Rs 20**

**Solution:**

(i) 16: 24 = 20: 30

It can be written as

16/24 = 20/30

Dividing 16/24 by 4/4 and 20/30 by 5/5

(16/24) ÷ (4/4) = (20/30) ÷ (5/5)

On further calculation

4/6 = 4/6

We get

2/3 = 2/3

Hence, 16: 24 = 20: 30 is true.

(ii) 21: 6 = 35: 10

It can be written as

21/6 = 35/10

Dividing 21/6 by 3/3 and 35/10 by 5/5

(21/6) ÷ (3/3) = (35/10) ÷ (5/5)

On further calculation

7/2 = 7/2

Hence, 21: 6 = 35: 10 is true.

(iii) 12: 18 = 28: 12

It can be written as

12/18 = 28/12

On further calculation

6/9 ≠ 14/6

Hence, 12: 18 = 28: 12 is false.

(iv) 51: 58 = 85: 102

It can be written as

51/58 = 85/102

On further calculation

51/58 ≠ 5/6

Hence, 51: 58 = 85: 102 is false.

(v) 40 men: 200 men = Rs 5: Rs 25

It can be written as

40/200 = 5/25

We get 40/200 = 1/2 and 5/25 = 1/5

Hence, 40 men: 200 men = Rs 5: Rs 25 is true.

(vi) 99 kg: 45 kg = Rs 44: Rs 20

It can be written as

99/45 = 44/20

Dividing the fraction by 9

(99/45) ÷ (9/9) = (44/20) ÷ (9/9)

On further calculation

11/5 = 11/5

Hence, 99 kg: 45 kg = Rs 44: Rs 20 is true.

**2. Find which of the following are in proportion:**

**(i) 8, 16, 6, 12**

**(ii) 6, 2, 4, 3**

**(iii) 150, 250, 200, 300**

**Solution:**

(i) 8, 16, 6, 12

We know that

8: 16 = 8/16 = 1/2

6: 12 = 6/12 = 1/2

So we get 8/16 = 6/12

Therefore, 8, 16, 6, 12 are in proportion.

(ii) 6, 2, 4, 3

We know that

6: 2 = 6/2 = 3/1

4: 3 = 4/3

So we get 3/1 ≠ 4/3

Therefore, 6, 2, 4, 3 are not in proportion.

(iii) 150, 250, 200, 300

We know that

150: 250 = 150/250 = 3/5

200: 300 = 200/300 = 4/6 = 2/3

So we get 3/5 ≠ 2/3

Therefore, 150, 250, 200, 300 are not in proportion.

**3. Find x in the following proportions:**

**(i) x: 6 = 55: 11**

**(ii) 18: x = 27: 3**

**(iii) 7: 14 = 15: x**

**(iv) 16: 18 = x: 96**

**Solution:**

(i) x: 6 = 55: 11

It can be written as

x/6 = 55/11

We get

x/6 = 5/1

On further calculation

x = 5 (6) = 30

(ii) 18: x = 27: 3

It can be written as

18/x = 27/3

We get

18/x = 9/1

On further calculation

x = 18/9 = 2

(iii) 7: 14 = 15: x

It can be written as

7/14 = 15/x

We get

1/2 = 15/x

On further calculation

x = 15 (2) = 30

(iv) 16: 18 = x: 96

It can be written as

16/18 = x/96

We get

8/9 = x/96

On further calculation

x = 8/9 (96) = 256/3

**4. Set up all proportions from the numbers 9, 150, 105, 1750.**

**Solution:**

The proportions from the numbers are

9: 150 = 3: 50

9: 105 = 3: 35

9: 1750

150: 9 = 50: 3

150: 105 = 10: 7

150: 1750 = 3: 35

105: 9 = 35: 3

105: 150 = 7: 10

105: 1750 = 3: 50

1750: 9

1750: 150 = 35: 3

1750: 105 = 50: 3

Hence, the proportions that are formed are

9: 150 :: 105: 1750

150: 9 :: 1750: 105

1750: 150 :: 105: 9

9: 105 :: 150: 1750

**5. Find the other three proportions involving terms of each of the following:**

**(i) 45: 30 = 24: 16**

**(ii) 12: 18 = 14: 21**

**Solution:**

(i) 45: 30 = 24: 16 can be written as 3: 2 in simplest form

So the other three proportions involving terms are

45: 24 = 3: 16 can be written as 15: 8 in simplest form

30: 45 = 16: 24 can be written as 2: 3 in simplest form

16: 3 = 24: 45 can be written as 8: 15 in simplest form

(ii) 12: 18 = 14: 21 can be written as 2: 3 in simplest form

So the other three proportions involving terms are

12: 14 = 18: 21 can be written as 6: 7 in simplest form

21: 18 = 14: 12 can be written as 7: 6 in simplest form

18: 12 = 21: 14 can be written as 3: 2 in simplest form

**6. If 4, x, 9 are in continued proportion, find the value of x.**

**Solution:**

We know that 4, x, 9 are in continued proportion

It can be written as

4: x :: x: 9

We get

4/x = x/9

On further calculation

x2 = 9 (4) = 36

So we get

x = 6

**7. If in a proportion, the first, second and fourth terms are 32, 112 and 217 respectively, find the third term.**

**Solution:**

It is given that in a proportion the first, second and fourth terms are 32, 112 and 217

Consider x as the third term

We can write it as

32: 112 :: x: 217

On further calculation

32/112 = x/217

So we get

x = 32/112 (217) = 62

**8. Show that the following numbers are in continued proportion:**

**(i) 36, 90, 225**

**(ii) 48, 60, 75**

**(iii) 16, 84, 441**

**Solution:**

(i) 36, 90, 225

Consider the fraction 36/90

By dividing the fraction by 18

We get

36/90 = 2/5

Consider the fraction 90/225

By dividing the fraction by 45

We get

90/225 = 2/5

Hence, 36: 90 :: 90: 225.

(ii) 48, 60, 75

Consider the fraction 48/60

By dividing the fraction by 12

We get

48/60 = 4/5

Consider the fraction 60/75

By dividing the fraction by 15

We get

60/75 = 4/5

Hence, 48: 60 :: 60: 75.

(iii) 16, 84, 441

Consider the fraction 16/84

By dividing the fraction by 4

We get

16/84 = 4/21

Consider the fraction 84/441

By dividing the fraction by 21

We get

84/441 = 4/21

Hence, 16: 84 :: 84: 441.

**9. The ratio of the length of a school ground to its width is 5: 2. Find its length if the width is 40 metres.**

**Solution:**

It is given that

Ratio of length of a school ground to its width = 5: 2

Width of the school ground = 40 m

So the length of the school ground = 5/2 (40) = 100 m

Hence, the length of the school ground is 100 m.

**10. The ratio of the sale of eggs on a Sunday to that of the whole week of a grocery shop was 2: 9. If the total sale of eggs in the same week was Rs 360, find the sale of eggs on Sunday.**

**Solution:**

It is given that

Ratio of the sale of eggs on a Sunday to that of the whole week of a grocery shop = 2: 9

We know that the sale of eggs in a week is Rs 9 and on Sunday is Rs 2

If eggs of Rs 1 is sold in a week, the cost of egg on Sunday = Rs 2/9

If the total sale of eggs in the same week was Rs 360, the sale of eggs on Sunday = 2/9 (360) = Rs 80

Hence, the sale of eggs on Sunday is Rs 80.

**11. The ratio of copper and zinc in an alloy is 9: 7. If the weight of zinc in the alloy is 9.8 kg, find the weight of copper in the alloy.**

**Solution:**

It is given that

Ratio of copper and zinc in an alloy = 9: 7

We know that

If the weight of zinc is 7 kg then the weight of copper is 9 kg

If the weight of zinc is 1 kg then the weight of copper = 9/7 kg

So if the weight of zinc is 9.8 kg then the weight of copper = 9/7 (9.8) = 12.6 kg

Hence, the weight of copper in the alloy is 12.6 kg.

**12. The ratio of the income to the expenditure of a family is 7: 6. Find the savings if the income is Rs 1400.**

**Solution:**

It is given that

Ratio of the income to the expenditure of a family = 7: 6

We know that saving = total income – expenditure

So we get

Ratio of saving to the income = [7 – 6]: 7 = 1: 7

It is given that income = Rs 1400

So the saving of the family = 1/7 (1400) = Rs 200

Hence, the saving of the family is Rs 200.

**13. The ratio of story books in a library to other books is 1: 7. The total number of story books is 800. Find the total number of books in the library.**

**Solution:**

It is given that

Ratio of story books in a library to other books = 1: 7

We know that 1 is a story book our of 1 + 7 = 8 books

So if there is 1 story book then the total number of books = 8

If there is 800 story books then the total number of books = 8 (800) = 6400

Hence, the total number of books in the library is 6400.

Exercise 9.4 PAGE: 9.18

**1. The price of 3 metres of cloth is Rs 79.50. Find the price of 15 metres of such cloth.**

**Solution:**

It is given that

Price of 3 m of cloth = Rs 79.50

We get

Price of 1 m of cloth = 79.50/3 = Rs 26.5

So the price of 15 m of cloth = 26.5 (15) = Rs 397.50

Hence, the price of 15 m of such cloth is Rs 397.50.

**2. The cost of 17 chairs is Rs 9605. Find the number of chairs that can be purchased in Rs 56500.**

**Solution:**

No. of chairs purchased for Rs 9605 = 17

We get

No. of chairs purchased for Rs 1 = 17/9605

So the number of chairs purchased for Rs 56500 = 17/9605 (56500) = 100

Hence, 100 chairs can be purchased in Rs 56500.

**3. Three ferryloads are needed to carry 150 people across a river. How many people will be carried on 4 ferryloads?**

**Solution:**

We know that

No. of people required to carry 3 ferryloads = 150

We get

No. of people required to carry 1 ferryload = 150/3 = 50

So the number of people required to carry 4 ferryloads = 4 (50) = 200

Hence, 200 people are required to carry 4 ferryloads.

**4. If 9 kg of rice costs Rs 120.60, what will 50 kg of such a quality of rice cost?**

**Solution:**

It is given that

Cost of 9 kg rice = Rs 120.60

We know that

Cost of 1 kg rice = 120.60/9 = Rs 13.4

So the cost of 50 kg rice = 13.4 (50) = Rs 670

Hence, 50 kg of such a quality of rice costs Rs 670.

**5. A train runs 200 kilometres in 5 hours. How many kilometres does it run in 7 hours?**

**Solution:**

Distance travelled by train in 5 hours = 200 km

We know that

Distance travelled by train in 1 hour = 200/5 = 40 km

So the distance travelled by train in 7 hours = 40 (7) = 280 km

Hence, the train runs 280 km in 7 hours.

**6. 10 boys can dig a pitch in 12 hours. How long will 8 boys take to do it?**

**Solution:**

It is given that

1 boys can dig a pitch in 12 hours

We know that the time taken by one boy = 10 (12) = 120 hours

So the time taken by 8 boys to dig the pitch = 120/8 = 15 hours

Hence, 8 boys will take 15 hours to dig the pitch.

**7. A man can work 8 hours daily and finishes a work in 12 days. If he works 6 hours daily, in how many days will the same work be finished?**

**Solution:**

It is given that

A man can work 8 hours daily and finishes a work in 12 days

We know that the time taken by the man to finish work = 8 (12) = 96 hours

If he works 6 hours daily, the days required to finish the work = 96/6 = 16 days

Hence, the man requires 16 days to finish the same work.

**8. Fifteen post cards cost Rs 2.25. What will be the cost of 36 post cards? How many postcards can be buy in Rs 45?**

**Solution:**

It is given that

Cost of fifteen post cards = Rs 2.25

We know that

Cost of one post card = Rs 2.25/15

So the cost of 36 post cards = 2.25/15 (36) = Rs 5.40

We get

No. of postcards that can be purchased in Rs 1 = 15/2.25

So the number of postcards that we can buy in Rs 45 = 15/2.25 (45) = 300

Hence, the cost of 36 post cards is Rs 5.40 and 300 post cards can be bought in Rs 45.

**9. A rail journey of 75 km costs Rs 215. How much will a journey of 120 km cost?**

**Solution:**

It is given that

Cost of rail journey of 75 km = Rs 215

We know that

Cost of rail journey of 1 km = Rs 215/75

So the cost of rail journey of 120 km = 215/75 (120) = Rs 344

Hence, the cost of rail journey of 120 km is Rs 344.

**10. If the sales tax on a purchase worth Rs 60 is Rs 4.20. What will be the sales tax on the purchase worth Rs 150?**

**Solution:**

It is given that

Sales tax on a purchase worth Rs 60 = Rs 4.20

We know that

Sales tax on a purchase worth Rs 1 = Rs 4.20/60

So the sales tax on the purchase worth Rs 150 = 4.20/60 (150) = Rs 10.50

Hence, the sales tax on the purchase worth Rs 150 is Rs 10.50.

**11. The cost of 17 chairs is Rs 19210. Find the number of such chairs that can be purchased in Rs 113000?**

**Solution:**

It is given that

No. of chairs purchase in Rs 19210 = 17

We know that

No. of chairs purchased in Rs 1 = 17/19210

So the number of chairs that can be purchased in Rs 113000 = 17/19210 (113000) = 100

Hence, 100 chairs can be purchased in Rs 113000.

**12. A car travels 165 km in 3 hours**

**(i) How long will it take to travel 440 km?**

**(ii) How far will it travel in 7 hours?**

**Solution:**

Distance travelled by car = 165 km in 3 hours

So the speed of car = Distance/ time = 165/3 = 55 km per hour

(i) Time taken to travel 440 km = 440/55 = 8 hours

(ii) Distance covered in 7 hours = 55 (7) = 385 km

**13. 2 dozens of oranges cost Rs 60. Find the cost of 120 similar oranges?**

**Solution:**

It is given that

Cost of 2 dozens of oranges = Rs 60

We know that

Cost of 1 orange = Rs 60/24

So the cost of 120 similar oranges = 60/24 (120) = Rs 300

Hence, the cost of 120 similar oranges is Rs 300.

**14. A family of 4 members consumes 6 kg of sugar in a month. What will be the monthly consumption of sugar, if the number of family members becomes 6?**

**Solution:**

It is given that

Amount of sugar used by a 4 members family = 6 kg

We know that

Amount of sugar used by 1 member = 6/4 kg

So the sugar consumed by 6 members of a family = 6/4 (6) = 9kg

Hence, 9 kg is the monthly consumption of sugar, if the number of family members becomes 6.

**15. The weight of 45 folding chairs is 18 kg. How many such chairs can be loaded on a truck having a capacity of carrying 4000 kg load?**

**Solution:**

It is given that

No. of folding chairs weighing 18 kg = 45

We know that

No. of folding chairs weighing 1 kg = 45/18

So the number of folding chairs weighing 4000 kg = 45/18 (4000) = 10000

Hence, 10000 chairs can be loaded on a truck having a capacity of carrying 4000 kg load.

Objective Type Questions page: 9.19

**Mark the correct alternative in each of the following:**

**1. A ratio equivalent of 2 : 3 is**

(a) 4 : 3

(b) 2 : 6

(c) 6 : 9

(d) 10 : 9

(a) 4 : 3

(b) 2 : 6

(c) 6 : 9

(d) 10 : 9

**Solution:**

The option (c) is correct answer.

We know that 6: 9 when divided by 3 we get 2: 3.

**2. The angles of a triangle are in the ratio 1 : 2 : 3. The measure of the largest angle is**

(a) 30°

(b) 60°

(c) 90°

(d) 120°

(a) 30°

(b) 60°

(c) 90°

(d) 120°

**Solution:**

The option (c) is correct answer.

We know that the sum of all the angles = 180°

So the largest angle = 3/ (1 + 2 + 3) × 180

We get

Largest angle = 3/6 × 180 = 90°

**3. The sides of a triangle are in the ratio 2 : 3 : 5. If its perimeter is 100 cm, the length of its smallest side is**

(a) 2 cm

(b) 20 cm

(c) 3 cm

(d) 5 cm

(a) 2 cm

(b) 20 cm

(c) 3 cm

(d) 5 cm

**Solution:**

The option (b) is correct answer.

We know that the length of smallest side = 100 × 2/ (2 + 3 + 5) = 20 cm

**4. Two numbers are in the ratio 7 : 9. If the sum of the numbers is 112, then the larger number is**

(a) 63

(b) 42

(c) 49

(d) 72

(a) 63

(b) 42

(c) 49

(d) 72

**Solution:**

The option (a) is correct answer.

Consider x as the largest number

So we get

9/ (7 + 9) = x/ 112

By cross multiplication

x = 9/16 × 112 = 63

**5. Two ratio 384 : 480 in its simplest form is**

(a) 3 : 5

(b) 5 : 4

(c) 4 : 5

(d) 2 : 5

(a) 3 : 5

(b) 5 : 4

(c) 4 : 5

(d) 2 : 5

**Solution:**

The option (c) is correct answer.

384: 480 can be written as

384/480 = 4/5 when divided by 96

**6. If A**

(a) Rs 240

(b) Rs 600

(c) Rs 380

(d) Rs 360

*,*B*,*C, divide Rs 1200 in the ratio 2 : 3 : 5, then B’s share is(a) Rs 240

(b) Rs 600

(c) Rs 380

(d) Rs 360

**Solution:**

The option (d) is correct answer.

So B’s share = 1200 × 3/ (2 + 3 + 5)

On further calculation

B’s share = 1200 × 3/10 = Rs 360

**7. If a bus travels 126 km in 3 hours and a train travels 315 km in 5 hours, then the ratio of their speeds is**

(a) 2 : 5

(b) 2 : 3

(c) 5 : 2

(d) 25 : 6

(a) 2 : 5

(b) 2 : 3

(c) 5 : 2

(d) 25 : 6

**Solution:**

The option (b) is correct answer.

We know that speed = distance/time

So the speed of bus = 126/3 = 42 km/h

Speed of train = 315/5 = 63 km/h

So the ratio of their speeds = 42: 63 = 2: 3

**8. The ratio of male and female employees in a multinational company is 5 : 3. If there are 115 male employees in the company, then the number off female employees is**

(a) 96

(b) 52

(c) 69

(d) 66

(a) 96

(b) 52

(c) 69

(d) 66

**Solution:**

The option (c) is correct answer.

Consider x as the number of female employees

So we get

5/3 = 115/x

By cross multiplication

x = 115/5 × 3 = 69

**9. Length and width of a field are in the ratio 5 : 3. If the width of the field is 42 m, then its length is**

(a) 50 m

(b) 70 m

(c) 80 m

(d) 100 m

(a) 50 m

(b) 70 m

(c) 80 m

(d) 100 m

**Solution:**

The option (b) is correct answer.

It is given that length and width of a field = 5: 3

Consider x m as the length

Width of the filed = 42 m

So the length can be written as

5/3 = x/42

By cross multiplication

x = 5/3 × 42 = 70 m

**10. If 57 : x = 51 : 85, then the value of x is**

(a) 95

(b) 76

(c) 114

(d) None of these

(a) 95

(b) 76

(c) 114

(d) None of these

**Solution:**

The option (a) is correct answer.

It can be written as

57/x = 51/85

By cross multiplication

57 × 85/51 = x

So we get

x = 95

**11. The ratio of boys and girls in a school is 12 : 5. If there are 840 girls in the school, then the number of boys is**

(a) 1190

(b) 2380

(c) 2856

(d) 2142

(a) 1190

(b) 2380

(c) 2856

(d) 2142

**Solution:**

The option are not correct.

Consider x as the number of boys

Ratio of boys and girls = 12: 5

It can be written as

12/5 = x/840

By cross multiplication

x = 12/5 × 840 = 2016

**12. If 4, a**

(a) 24

(b) 12

(c) 3

(d) 24

*,*a*,*36 are in proportion, then a =(a) 24

(b) 12

(c) 3

(d) 24

**Solution:**

The option (b) is correct answer.

It is given that 4, a, a, 36 are in proportion

We can write it as 4 : a :: a : 36

So we get

4/a = a/36

By cross multiplication

4 × 36 = a × a

We get

a2 = 144

So a = 12

**13. If 5 : 4 : : 30 : x, then the value of x is**

(a) 24

(b) 12

(c) 3/2

(d) 6

(a) 24

(b) 12

(c) 3/2

(d) 6

**Solution:**

The option (a) is correct answer.

It can be written as

5/4 = 30/x

By cross multiplication

x = 30 × 4/5 = 24

**14. If a**

(a) ab = cd

(b) ac = bd

(c) ad = bc

(d) None of these

*,*b*,*c*,*d are in proportion, then(a) ab = cd

(b) ac = bd

(c) ad = bc

(d) None of these

**Solution:**

The option (c) is correct answer.

It is given that a, b, c, d are in proportion

We can write it as a : b = c : d

So we get

a/b = c/d

By cross multiplication

ad = bc

**15. If a, b, c, are in proportion, then**

(a) a2 = bc

(b) b2 = ac

(c) c2 = ab

(a) a2 = bc

(b) b2 = ac

(c) c2 = ab

*(d) None of these*

**Solution:**

The option (b) is correct answer.

It is given that a, b, c are in proportion

We can write it as

a : b :: b : c

So we get

a/b = b/c

By cross multiplication

b2 = ac

**16. If the cost of 5 bars of a soap is Rs. 30, then the cost of one dozen bars is**

(a) Rs 60

(b) Rs 120

(c) Rs 72

(d) Rs 140

(a) Rs 60

(b) Rs 120

(c) Rs 72

(d) Rs 140

**Solution:**

The option (c) is correct answer.

Consider Rs x as the cost of one dozen bars

It can be written as

30/5 = x/12

So we get

x = 30/5 × 12 = Rs 72

**17. 12 men can finish a piece of work in 25 days. The number of days in which the same piece of work can be done by 20 men, is**

(a) 10 days

(b) 12 days

(c) 15 days

(d) 14 days

(a) 10 days

(b) 12 days

(c) 15 days

(d) 14 days

**Solution:**

The option (c) is correct answer.

Consider x days required by 20 men to do the same work

20/12 = 25/x

So we get

x = 12 × 20/25 = 15 days

**18. If the cost of 25 packets of 12 pencils each is Rs 750, then the cost of 30 packets of 8 pencils each is**

**Solution:**

The option (a) is correct answer.

We know that

Cost of 300 pencils = Rs 750

So consider Rs x as the cost of 240 pencils

It can be written as

750: 300 :: x: 240

So we get

Cost of 240 pencils = 750/300 × 240 = Rs 600

**19. If a, b, c are in proportion, then**

(a) a : b : : b : c

(b) a : b : : c : a

(c) a : b : : c : b

(d) a : c : : b : c

(a) a : b : : b : c

(b) a : b : : c : a

(c) a : b : : c : b

(d) a : c : : b : c

**Solution:**

The option (a) is correct answer.

We know that a, b, c are in proportion

So we get a: b :: b: c

It can be written as ac = b2

**20. The first, second and fourth terms of a proportion are 16, 24 and 54 respectively. The third term is**

(a) 32

(b) 48

(c) 28

(d) 36

(a) 32

(b) 48

(c) 28

(d) 36

**Solution:**

The option (d) is correct answer.

Consider x as the third term

We can write it as

16: 24 = x: 54

So we get

16/24 = x/54

By cross multiplication

x = 16/24 × 54

We get

x = 36