## Selina Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion (Including Word Problems)

**Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 12 Proportion (Including Word Problems)**

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### Proportion Exercise 12A – Selina Concise Mathematics Class 6 ICSE Solutions

**Question 1.**

In each of the following, check whether or not the given ratios form a proportion :

(i) 8 : 16 and 12 : 15

(ii) 16 : 28 and 24 : 42

(iii) 12 ÷ 3 and 8 ÷ 2

(iv) 25 : 40 and 20 : 32

(v) \(\frac { 15 }{ 18 } and \frac { 10 }{ 12 }\)

(vi) \(\frac { 7 }{ 8 }\) and 14 : 16

**Solution:**

**Question 2.**

Find the value of x in .each of the following proportions :

(i) x : 4 = 6 : 8

(ii) 14 : x = 7 : 9

(iii) 4 : 6 = x : 18

(iv) 8 : 10 = x : 25

(v) 5 : 15 = 4 : x

(vi) 16 : 24 = 6 : x

**Solution:**

**Question 3.**

Find the value of x so that the given four numbers are in proportion :

(i) x, 6, 10 and 15

(ii) x, 4, 15 and 30

(iii) 2, x, 10 and 25

(iv) 4, x, 6 and 18

(v) 9, 12, x and 8

(vi) 4, 10, 36 and x

(vii) 7, 21, x and 45

(viii) 6, 8, 12 and x.

**Solution:**

**Question 4.**

The first, second and the fourth terms of a proportion are 6, 18 and 75, respectively. Find its third term.

**Solution:**

Let the third term = x

6 : 18 : : x : 75

= 18 x x = 6 x 75

x = \(\frac { 6\times 75 }{ 18 } =\frac { 75 }{ 3 }\) = 25

The third term of proportion is 25

**Question 5.**

Find the second term of the proportion whose first, third and fourth terms are 9, 8 and 24 respectively.

**Solution:**

Let the second term = x

9 : x : : 8 : 24

=> x x 8 = 24 x 9

x = \(\frac { 24\times 9 }{ 8 }\) = 3 x 9 = 27

The second term of proportion = 27

**Question 6.**

Find the fourth term of the proportion whose first, second and third terms are 18, 27, and 32 respectively.

**Solution:**

Let the fourth term = x

18 : 27 : : 32 : x

=> 18 x x = 27 x 32

=> x = \(\frac { 27\times 32 }{ 18 }\) = 3 x 16 = 48

Fourth term = 48

**Question 7.**

The ratio of the length and the width of a school ground is 5 : 2. Find the length, if the width is 40 metres.

**Solution:**

Let the length = x m,

width = 40 m

The ratio of length to width = x : 40

as per given statement 5 : 2 = x : 40

=> 2 x x = 40 x 5

x = \(\frac { 40\times 5 }{ 2 }\) = 20 x 5 = 100 m

**Question 8.**

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

**Solution:**

Let, the sale of eggs on Sunday = x

Sale in week = Rs 360

According to question, 2 : 9 = x : 360

=> 9 x x = 360 x 2

x = \(\frac { 360\times 2 }{ 9 }\) = Rs 80

Sale on Sunday = Rs 80

**Question 9.**

The ratio of copper and zinc in an alloy is 9 : 8. If the weight of zinc, in the alloy, is 9.6 kg ; find the weight of copper in the alloy.

**Solution:**

Let the weight of copper = x kg

Weight of zinc = 9.6 kg.

According to question,

9 : 8 = x : 9.6

=> 8 x x = 9 x 9.6

=> x = \(\frac { 9\times 9.6 }{ 8 }\) = 9 x 1.2 = 10.8 kg.

Weight of cooper in alloy = 10.8

**Question 10.**

The ratio of the number of girls to the number of boys in a school is 2 : 5. If the number of boys is 225 ; find:

(i) the number of girls in the school.

(ii) the number of students in the school.

**Solution:**

Let, the number of girls in school = x

Number of boys in school = 225

According to question 2 : 5 = x : 225

=> 5 x x = 2 x 225

x = \(\frac { 2\times 225 }{ 5 }\) = 2 x 45 = 90

Number of girls in school = 90

Total number of student in the school = (number of boys + number of girls) = (225 + 90) = 315

**Question 11.**

In a class, one out of every 5 students pass. If there are 225 students in all the sections of a class, find how many pass ?

**Solution:**

Total number of students in all sections = 225

Given, One of every five students pass

Total students pass = 225 x \(\frac { 1 }{ 5 }\) = 45 studetns

**Question 12.**

Make set of all possible proportions from the numbers 15, 18, 35 and 42.

**Solution:**

The possible proportions that can be made from the numbers 15, 18, 35 and 42 are

(i) 15 : 35 :: 18 : 42

(ii) 42 : 18 :: 35 : 15

(iii) 42 : 35 :: 18 : 15

(iv) 15 : 18 :: 35 : 42

### Proportion Exercise 12B – Selina Concise Mathematics Class 6 ICSE Solutions

**Question 1.**

If x, y and z are in continued proportion, then which of the following is true :

(i) x : y = x : z

(ii) x : x = z : y

(iii) x : y = y : z

(iv) y : x = y : z

**Solution:**

(iii) x : y = y : z

**Question 2.**

Which of the following numbers are in continued proportion :

(i) 3, 6 and 15

(ii) 15, 45 and 48

(iii) 6, 12 and 24

(iv) 12, 18 and 27

**Solution:**

(iii) and (iv)

**Question 3.**

Find the mean proportion between

(i) 3 and 27

(ii) 0.06 and 0.96

**Solution:**

**Question 4.**

Find the third proportional to :

(i) 36, 18

(ii) 5.25, 7

(iii) ₹ 1.60, ₹ 0.40

**Solution:**

=> x = 0.1

**Question 5.**

The ratio between 7 and 5 is same as the ratio between ₹ x and ₹ 20.50 ; find the value of x.

**Solution:**

Since, It is given that the ratio between 7 and 5 is same as the ratio between ₹ x and ₹ 20.50

**Question 6.**

If (4x + 3y) : (3x + 5y) = 6 : 7, find :

(i) x : y

(ii) x, if y = 10

(iii) y, if x = 27

**Solution:**

**Question 7.**

If \(\frac { 2y+5x }{ 3y-5x } =2\frac { 1 }{ 2 }\), find:

(i) x : y

(ii) x, if y = 70

(iii) y, if x = 33

**Solution:**

### Proportion Exercise 12C – Selina Concise Mathematics Class 6 ICSE Solutions

**Question 1.**

Are the following numbers in proportion:

(i) 32, 40, 48 and 60 ?

(ii) 12,15,18 and 20 ?

**Solution:**

(i) 32, 40, 48 and 60 are in proportion

if 32 : 40 = 48 : 60

if 32 x 60 = 40 x 48

\(\left\{ \frac { a }{ b } =\frac { c }{ d } \Longrightarrow \quad ad=bc \right\}\)

if 1920 = 1920

Which is true.

32, 40, 48 and 60 are in proportion

(ii) 12, 15, 18 and 20 are in proportion

if 12 : 15 = 18 : 20

if 12 x 20 = 15 x 18 {ad = bc}

if 240 = 270

which is not true.

12, 15, 18 and 20 are not in proportion.

**Question 2.**

Find the value of x in each of the following such that the given numbers are in proportion.

(i) 14, 42, x and 75

(ii) 45, 135, 90 and x

**Solution:**

14, 42, x and 75 are in proportion

\(\frac { 14 }{ 42 } =\frac { x }{ 75 }\)

=> 14 x 75 =x x 42

**Question 3.**

The costs of two articles are in the ratio 7 : 4. If the cost of the first article is Rs. 2,800 ; find the cost of the second article.

**Solution:**

Ratio in the cost of two articles = 7 : 4

Cost of first article = Rs. 2800

Let cost of the second article = x

7 : 4 = 2800 : x

**Question 4.**

The ratio of the length and the width of a rectangular sheet of paper is 8 : 5. If the width of the sheet is 17.5 cm; find the length.

**Solution:**

Let length of sheet = x cm

Ratio in length and breadth = 8 : 5

and width = 17.5 cm

8 : 5 = x : 17.5

Length of sheet = 28 cm

**Question 5.**

The ages of A and B are in the ratio 6 : 5. If A’s age is 18 years, find the age of B.

**Solution:**

Ratio in the ages of A and B = 6 : 5

A’s age = 18 years

Let B’s age = x years

6 : 5 = 18 : x

**Question 6.**

A sum of Rs. 10, 500 is divided among A, B and C in the ratio 5 : 6 : 4. Find the share of each.

**Solution:**

Total amount = Rs. 10, 500

Ratio in A, B, and C = 5 : 6 : 4

Sum of ratio = 5 + 6 + 4 = 15

**Question 7.**

Do the ratios 15 cm to 2 m and 10 sec to 3 minutes form a proportion ?

**Solution:**

15 cm : 2 m : : 10 sec : 3 min

15 cm : 2 x 100 cm :: 10 sec : 30 x 60 sec

15 : 200 :: 10 : 1800

3 : 40 :: 1 : 180

No, they donot form a proportion

**Question 8.**

Do the ratios 2 kg : 80 kg and 25 g : 625 g form a proportion ?

**Solution:**

2 kg : 80 kg : : 25 g : 625 g

2 : 80 :: 25 : 625

1 : 40 :: 1 : 25

No, they donot form a proportion.

**Question 9.**

10 kg sugar cost ₹ 350. If x kg sugar of the same kind costs ₹ 175, find the value of x

**Solution:**

10 kg of sugar costs = ₹ 350

and x kg of sugar cost = ₹ 175

A.T.Q.

10 kg : x kg :: 350 : 175

=> 10 x 175 = 350 x x

=> 350x= 1750

=> x = \(\frac { 1750 }{ 350 }\) = 5

Hence, 5 kg of sugar costs ₹ 175

**Question 10.**

The length of two ropes are in the ratio 7 : 5. Find the length of:

(i) shorter rope, if the longer one is 22.5 ni

(ii) longer rope, if the shorter is 9.8 m.

**Solution:**

Length of the ropes are in the ratio = 7 : 5

(i) Let the length of shorter rope = x

Length of longer rope = 22.5 m

A.T.Q.

**Question 11.**

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

**Solution:**

4, x and 9 are in continued proportion

=> 4 : x = x : 9

=> x^{2} = 9 x 4

=> x = √36

x = 6

**Question 12.**

If 25, 35 and x are in continued proportion, find the value of x.

**Solution:**

25, 35 and x are in continued proportion

=> 25 : 35 = 35 : x

=> 25 x x = 35 x 35

=> x = \(\frac { 35\times 35 }{ 25 }\)

=> x = 49

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