The document RD Sharma Solutions -Page No.9.14, Ratio Proportion And Unitary Method, Class 6, Maths Class 6 Notes | EduRev is a part of the Class 6 Course RD Sharma Solutions for Class 6 Mathematics.

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**PAGE NO 9.14:**

**Question 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**

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

16/24 = 2/3 (Dividing numerator and denominator by 8)

20/30 = 2/3 (Dividing numerator and denominator by 10)

âˆ´ 16/24 = 20/30

Thus, the statement is true.

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

21/6 = 7/2 (Dividing numerator and denominator by 3)

35/10 = 7/2 (Dividing numerator and denomenator by 5)

âˆ´ 21/6 = 35/10

Thus, the statement is true.

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

12/18 = 2/3 (Dividing numerator and denominator by 6)

28/12 = 7/3 (Dividing numerator and denominator by 4)

âˆ´ 16/24 = 20/30 are not equal.

Thus, the statement is not true.

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

51/58

And 85/102 = 5/6 (Dividing numerator and denominator by 17)

âˆ´ 51/58 is not equal to 85/102.

Thus, the statement is not true.

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

40/200 = 1/5 (Dividing numerator and denominator by 40)

5/25 = 1/5 (Dividing numerator and denominator by 5)

âˆ´ 40/200 = 5/25

Thus, the statement is true.

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

99/45 = 11/5 (Dividing numerator and denominator by 9)

44/20 = 11/5 (Dividing numerator and denominator by 4)

âˆ´ 99/45 = 11/5

Thus, the statement is true.

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

(ii) 6, 2, 4, 3

(iii) 150, 250, 200, 300

**ANSWER:** (i) Consider 8/16 = 1/2

And 6/12 = 1/2

âˆµ 8 : 16 = 6 : 12

âˆ´ 8, 16, 6, 12 are in proportion.

(ii) Consider 6/2 = 3/1

And 4/3

âˆµ 6 : 2 â‰ â‰ 4 : 3

âˆ´ 6, 2, 4, 3 are not in proportion.

(iii) Consider 150/250 = 3/5 (Dividing numerator and denominator by 50)

And 200/300 = 2/3 (Dividing numerator and denominator by 100)

âˆµ 150 : 250 â‰ â‰ 200 : 300

âˆ´ 150, 250, 200, 300 are not in proportion.

**Question 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**

**ANSWER:**

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

(iii) 7 : 14 = 15 : *x*1624=23 (Dividing numerator and denominator by 8)2030= 23 (Dividing numerator and denominator by 1

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

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

**ANSWER:**

All proportions are:

9 : 150 = 3 : 50

9 : 105 = 3 : 35

9 : 1750

150 : 105 = 10 : 7

150 : 1750 = 3 : 35

105 : 1750 = 3 : 50

Thus, all proportions that can be formed are:

3 : 50, 3 : 35, 10 : 7, 9 : 1750, 1750 : 9, 7 : 10, 35 : 3 and 50 : 3

**Question 5:**

**Find the other three proportions involving terms of each of the following:(i) 45 : 30 = 24 : 16(ii) 12 : 18 = 14 : 21**

**ANSWER:** (i) 45 : 30 = 24 : 16 (3 : 2 is its simplest form)

Other three proportions are:

45 : 24 = 30 : 16 (15 : 8 is its simplest form)

30 : 45 = 16 : 24 (2 : 3 is its simplest form)

16 : 30 = 24 : 45 (8 : 15 is its simplest form)

(ii) 12 : 18 = 14 : 21 (2 : 3 is its simplest form)

Other three proportions are:

12 : 14 = 18 : 21 (6 : 7 is its simplest form)

21 : 18 = 14 : 12 (7 : 6 is its simplest form)

18 : 12 = 21 : 14 (3 : 2 is its simplest form)

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

**ANSWER: **It is given that 4, x, 9 are in continued proportion; therefore, we have:

4 : x : : x : 9

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

**ANSWER:** In a proportion, the first, second and fourth terms are 32, 112 and 217, respectively.

Let the third term is be x.

Then, we have:

32 : 112 : : x : 217

**Question 8: Show that the following numbers are in continued proportion:(i) 36, 90, 225(ii) 48, 60, 75(iii) 16, 84, 441**

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

**Consider 36/90 = 2/5 **(Dividing numerator and denominator by 18)

90/225 = 2/5 ** **(Dividing numerator and denominator by 45)

â‡’ 36 : 90 : : 90 : 225

(ii) 48, 60, 75

Consider 48/60 = 4/5 (Dividing numerator and denominator by 12)

60/75 = 4/5 (Dividing numerator and denominator by 15)

â‡’ 48 : 60 : : 60 : 75

(iii) 16, 84, 441

Consider 16/84 = 4/21 (Dividing numerator and denominator by 4)

84/441 = 4/21 (Dividing numerator and denominator by 4)

â‡’ 16 : 84 : : 84 : 441

**Question 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.**

**ANSWER: **Ratio of the length to the width of a school ground = 5 : 2

âˆµ Width = 40 m

**Question 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.**

**ANSWER: **Ratio of the sale of eggs on Sunday to that of the whole week = 2 : 9

When total eggs of Rs. 9 is sold in a week, the sale of eggs on Sunday = Rs. 2

When total eggs of Rs. 1 sold in a week, th sale of eggs on Sunday = 2/9

When total eggs of Rs. 360 sold in a week, the sale of eggs on Sunday

**Question 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.**

**ANSWER:** The ratio of copper and zinc in an alloy is 9 : 7.

When the weight of zinc is 7 kg, the weight of copper = 9 kg

When the weight of zinc is 1 kg, the weight of copper = 9/7 kg

When the weight of zinc is 9.8 kg, the weight of copper =

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

**ANSWER: **The ratio of the income to the expenditure of a family is 7 : 6.

âˆ´ Ratio of saving to the income = (7 âˆ’ 6) : 7 = 1 : 7 (Saving = Total income âˆ’- Expenditure)

âˆµ Income of the family = Rs. 1400

âˆ´ Saving = 1400 Ã— 17 = Rs. 200

**Question 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.**

**ANSWER:**

The ratio of story books in a library to other books is 1 : 7.

Out of (1 + 7) = 8 books, 1 book is a story book

Therefore,

When number of story books is 1, the total number of books = 8

When number of story books is 800, the total number of books = 8 Ã— 800

= 6400