# RS Aggarwal Solutions for Class 6 Chapter 10 Ratio, Proportion and Unitary Method Exercise 10A

The ratio of two non zero numbers a and b is the fraction a/b and we write it as â€˜a:bâ€™ read as â€˜a is to bâ€™. The first exercise of chapter 10 has problems which are solved based on ratio of numbers and the steps followed according to CBSE guidelines. RS Aggarwal Solutions are a major study material for the students in order to gain a better hold on the concepts. The students can use RS Aggarwal Solutions for Class 6 Chapter 10 Ratio, Proportion and Unitary Method Exercise 10A to improve their speed of solving which are important from exam point of view.

## Download PDF of RS Aggarwal Solutions for Class 6 Chapter 10 Ratio, Proportion and Unitary Method Exercise 10A

### Access answers to Maths RS Aggarwal Solutions for Class 6 Chapter 10 Ratio, Proportion and Unitary Method Exercise 10A

1. Find each of the following ratios in the simplest form:

(i) 24 to 56

(ii) 84 paise to Rupees 3

(iii) 4 Kg to 750 g

(iv) 1.8 Kg to 6 Kg

(v) 48 Minutes to 1 hour

(vi) 2.4 Km to 900 m

Solution

(i) To convert given ratio a: b to its simplest form, we divide each term by the HCF of a and b

24: 56 = 24 / 56

= 24 Ã· 8 / 56 Ã· 8

= 3 / 7

Since the HCF of 3 and 7 is 1

âˆ´ The simplest form of 24: 56 is 3: 7

(ii) To convert given ratio a: b to its simplest form, we divide each term by the HCF of a and b

84 paise to Rupees 3 = 0.84 to 3

= 0.84: 3

= 0.84 / 3

= 0.84 Ã· 3 / 3 Ã· 3

= 0.28 / 1

= 28 / 100

= 28 Ã· 4 /100 Ã· 4

= 7 / 25

Since the HCF of 7 and 25 is 1

âˆ´ The simplest form of 0.84: 3 is 7: 25

(iii) To convert given ratio a: b to its simplest form, we divide each term by the HCF of a and b

4 kg to 750 g =4000 g to 750 g

= 4000: 750

= 4000 Ã· 250 / 750 Ã· 250

= 16 / 3

Since the HCF of 16 and 3 is 1

âˆ´ The simplest form of 4000: 750 is 16: 3

(iv) To convert given ratio a: b to its simplest form, we divide each term by the HCF of a and b

1.8 kg to 6 kg = 1.8: 6

= 1.8 / 6

= 18 / 60

= 18 Ã· 6 / 60 Ã· 6

= 3 / 10

Since the HCF of 3 and 10 is 1

âˆ´ The simplest form of 1.8: 6 is 3: 10

(v) To convert given ratio a: b to its simplest form, we divide each term by the HCF of a and b

48 minutes to 1 hour = 48 min : 60 min

= 48: 60

= 48 Ã· 12 / 60 Ã· 12

= 4 / 5

Since the HCF of 4 and 5 is 1

âˆ´ The simplest form of 48: 60 is 4: 5

(vi) To convert given ratio a: b to its simplest form, we divide each term by the HCF of a and b

2.4 Km to 900 m = 2400 m : 900 m

= 2400 / 900

= 24 / 9

= 24 Ã· 3 / 9 Ã· 3

= 8 / 3

Since the HCF of 3 and 8 is 1

âˆ´ The simplest form of 2400: 900 is 8: 3

2. Express each of the following ratios in the simplest from:

(i) 36 : 90

(ii) 324 : 144

(iii) 85 : 561

(iv) 480 : 384

(v) 186 : 403

(vi) 777 : 1147

Solution

(i) HCF of 36 and 90 is 18

âˆ´ 36: 90 = 36 / 90

= 36 Ã· 18 / 90 Ã· 18

= 2 / 5

= 2: 5

Hence, the simplest form of 36: 90 is 2: 5

(ii) HCF of 324 and 144 is 36

âˆ´ 324: 144 = 324 / 144

= 324 Ã· 36 / 144 Ã· 36

= 9 / 4

Hence, the simplest form of 324: 144 is 9: 4

(iii) HCF of 85 and 561 is 17

âˆ´ 85: 561 = 85 / 561

= 85 Ã· 17/ 561 Ã·17

= 5 / 33

Hence, the simplest form of 85: 561 is 5: 33

(iv) HCF of 480 and 384 is 96

âˆ´ 480: 384 = 480 / 384

= 480 Ã· 96 / 384 Ã· 96

= 5 / 4

Hence, the simplest form of 480: 384 is 5: 4

(v) HCF of 186 and 403 is 31

âˆ´ 186: 403 = 186 / 403

= 186 Ã· 31 / 403 Ã· 31

= 6 / 13

Hence, the simplest form of 186: 403 is 6: 13

(vi) HCF of 777 and 1147 is 37

âˆ´ 777: 1147 = 777 / 1147

= 777 Ã· 37 / 1147 Ã· 37

= 21 / 31

Hence, the simplest form of 777: 1147 is 21: 31

3. Write each of the following ratios in the simplest from:

(i) Rupees 6.30 : Rupees 16.80

(ii) 3 weeks : 30 days

(iii) 3 m 5 cm : 35 cm

(iv) 48 min : 2 hrs 40 min

(v) 1 L 35 mL : 270 mL

(vi) 4 kg : 2 kg 500 g

Solution

(i) Rupees 6.30: Rupees 16.80

= 6. 30 / 16. 80

= 63 / 168

Since HCF of 63 and 168 is 21

= 63 Ã· 21 / 168 Ã· 21

= 3 / 8

âˆ´ Simplest form of Rupees 6.30: Rupees 168 is 3: 8

(ii) 3 weeks : 30 days = 21 days: 30 days

= 21: 30

= 21 / 30

Since HCF of 21 and 30 is 3

= 21 Ã· 3 / 30 Ã· 3

= 7 / 10

âˆ´ Simplest form of 21: 30 is 7:10

(iii) 3 m 5 cm : 35 cm = 300 cm 5 cm : 35 cm [ 1m = 100 cm]

= 305 cm: 35 cm

= 305: 35

= 305 / 35

Since, HCF of 305 and 35 is 5

= 305 Ã· 5 / 35 Ã· 5

= 61 / 7

âˆ´ Simplest form of 305: 30 is 61: 7

(iv) 48 min : 2 hrs 40 min = 48 min : 120 min 40 min [ 1 hour = 60 minutes]

= 48 min : 160 min

= 48: 160

= 48 / 160

Since, HCF of 48 and 160 is 4

= 48 Ã· 16 / 160 Ã· 16

= 3 / 10

âˆ´ Simplest form of of 48:140 is 3: 10

(v) 1 L 35 ml: 270 ml = 1035 ml: 270 ml [1 L = 1000 ml]

= 1035: 270

= 1035 / 270

Since, HCF of 1035 and 270 is 45

= 1035 Ã· 45 / 270 Ã· 45

= 23 / 6

âˆ´ Simplest form of 1035: 270 is 23: 6

(vi) 4 kg: 2 kg 500g = 4000g: 2500 g [1 kg = 1000 g]

= 4000 / 2500

= 40 / 25

Since, HCF of 40 and 25 is 5

= 40 Ã· 5 / 25 Ã· 5

= 8 / 5

âˆ´ Simplest form of 4000:2500 is 8: 5

4. Mr Sahai and his wife are both school teachers and earn rupees 16,800 and 10,500 per month respectively. Find the ratio of

(i) Mr Sahaiâ€™s income to his wifeâ€™s income;

(ii) Mrs Sahaiâ€™s income to her husbandâ€™s income;

(iii) Mr Sahaiâ€™s to the total income of the two.

Solution

Mr Sahaiâ€™s earning = 16,800

And, Mrs Sahaiâ€™s earning = 10,500

(i) 16,800 : 10,500 = 168: 105

= 168 / 105

Since, HCF of 168 and 105 is 21

= 168 Ã· 21 / 105 Ã· 21

= 8 / 5

= 8: 5

(ii) 10,500: 16,800 = 105: 168

= 105 / 168

Since, HCF of 105 and 168 is 21

= 105 Ã· 21 / 168 Ã· 21

= 5 / 8

= 5: 8

(iii) Total income of the two = 16,800 + 10,500

= 27,300

16,800: 27,300 = 168: 273

= 168 / 273

Since, HCF of 168 and 273 is 21

= 168 Ã· 21 / 273 Ã· 21

= 8 / 13

= 8: 13

5. Rohit earns Rupees 15,300 and saves Rupees 1,224 per month. Find the ratio of

(i) his income and savings;

(ii) his income and expenditure;

(iii) his expenditure and savings.

Solution

Rohitâ€™s income = 15,300

Rohitâ€™s saving = 1,224

(i) 15,300: 1,224 = 15,300 / 1,224

HCF of 15,300 and 1,224 is 612

= 15,300 Ã· 612 / 1,224 Ã· 612

= 25 / 2

Income: saving = 25: 2

Monthly expenditure = (15300 â€“ 1224)

= 14076

(ii) 15,300: 14076 = 15,300 / 14076

HCF of 15,300 and 14076 is 612

= 15,300 Ã· 612 / 14076 Ã· 612

= 25 / 23

= 25: 23

Income: Expenditure = 25: 23

(iii) 14,076: 1,224 = 14,076 / 1,224

HCF of 14,076 and 1,224 is 612

= 14,076 Ã· 612 / 1,224 Ã· 612

= 23 / 2

Expenditure: Saving = 23: 2

6. The ratio of the number of male and female in a textile mill is 5:3. If there are 115 male workers, what is the number of female workers in the mill?

Solution

Given,

Number of male: Number of female = 5: 3

Let x be the number

Number of male = 5x

Number of female = 3x

Given number of male = 115

5x = 115

x = 115 / 5

x = 23

Number of female workers = 3x

= 3 Ã— 23

= 69

âˆ´ there are 69 female workers in the mill

7. The boys and girls in a school are in the ratio 9: 5. If the total strength of the school is 448, find the number of girls.

Solution

Given

Number of boys: number of girls = 9: 5

Let number of boys be 9x

Number of girls be 5x

Total strength = 448

According to the question we have,

9x + 5x = 448

14x = 448

x = 448 / 14

= 32

Number of boys = 9x = 9 Ã— 32

= 288

Number of girls = 5x = 5 Ã— 32

= 160

âˆ´ Number of girls are 160

8. Divide Rupees 1,575 between Kamal and Madhu in the ratio 7: 2.

Solution

Given

Sum of ratios = 7 + 2 = 9

Kamalâ€™s share = 7 / 9 Ã— 1,575 = 11025 / 9

= Rupees 1,225

Madhuâ€™s share = 2 / 9 Ã— 1,575 = 3150 / 9

= Rupees 350

9. Divide Rupees 3,450 among A, B and C in the ratio 3: 5: 7.

Solution

Given A: B: C = 3: 5: 7

Sum of the ratios = 3 + 5 + 7

= 15

Share of A = 3 / 15 Ã— 3,450

= 10,350 / 15

= Rupees 690

Share of B = 5 / 15 Ã— 3,450

= 17,250 / 15

= Rupees 1,150

Share of C = 7 / 15 Ã— 3,450

= 24,150 / 15

= Rupees 1,610

10. Two numbers are in the ratio 11: 12 and their sum is 460. Find the numbers.

Solution

Given

Two numbers are in the ratio = 11: 12

Let x be the number

According to the question = 11x + 12x = 460

23x = 460

x = 460 / 23

x = 20

11x = 11 Ã— 20 = 220

12x = 12 Ã— 20 = 240

Hence, 220 and 240 are the numbers in the ratio 11: 12 and their sum is 460