**Proportion ICSE Class-6th Concise** Mathematics Selina Solutions Chapter-12 . We provide step by step Solutions of Exercise / lesson-12 **Proportion**** **for **ICSE Class-6 Concise** Selina Mathematics. Our Solutions contain all type Questions of Exe-12 A, Exe-12 B and Exe-12 C to develop skill and confidence. Visit official Website CISCE for detail information about ICSE Board Class-6 .

**Proportion ICSE Class-6th Concise** Mathematics Selina Solutions Chapter-12

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### Exercise – 12 A **Proportion ICSE Class-6th Concise** Mathematics

**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) ^{15}⁄_{18} and ^{10}⁄_{12}

(vi) ^{7}⁄_{8} and ^{14}⁄_{16}

**Answer-1**

if a ratio is in proportion then **Product of mean = product of extream
**

**(i) 8 : 16 and 12 : 15**

Product of mean = product of extream

Product of mean =16 x 12= 192

product of extream = 8 x 15 =120

since Product of mean ≠ product of extream

Therefore it is not in proportion

**(ii) 16 : 28 and 24 : 42**

Product of mean = product of extream

Product of mean =28 x 24= 672

product of extream = 16 x 42 =672

since Product of mean = product of extream

Therefore it is in proportion

**(iii) 12 ÷ 3 and 8 ÷ 2**

since 12/3 =4

and 8/ 2 = 4

Therefore it is in proportion

**(iv) 25 : 40 and 20 : 32**

since 25/40 = 5/8

and 20/32 = 5/8

Therefore it is in proportion

**(v) ^{15}⁄_{18} and ^{10}⁄_{12}**

since 15/18 = 5/6

and 10/12 = 5/6

Therefore it is in proportion

**(vi) ^{7}⁄_{8} and ^{14}⁄_{16}**

since 7/8 = 7/8

and 14/16 = 7/8

Therefore it is in proportion

**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

**Answer-2**

**(i) x : 4 = 6 : 8**

Product of mean = product of extream

Product of mean =4 x 6= 24

product of extream = x x 8 = 8x

8x = 24

x = 24/8

x =3

**(ii) 14 : x = 7 : 9**

Product of mean = product of extream

Product of mean =7 x X = 7x

product of extream = 14 x 9 = 126

7x = 126

x = 126 / 7

x =18

(iii) 4 : 6 = x : 18

Product of mean = 6x

Product of extream =18 x 4= 72

6x = 72

x = 72/6

x =12

**(iv) 8 : 10 = x : 25**

10 x = 25 x 8

x = 200/10

x =20

**(v) 5 : 15 = 4 : x**

5 x = 15 x 4

x = 60/5

x =12

**(vi) 16 : 24 = 6 : x**

16 x = 24 x 6

x = 144/16

x =9

**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.

**Answer-3**

**(i) x, 6, 10 and 15**

15x = 6 x 10

x =^{60}⁄_{15}

x =4

**(ii) x, 4, 15 and 30**

30x = 15×4

x = ^{15×4}⁄_{30}

x =2

**(iii) 2, x, 10 and 25**

10x = 25 x 2

x = ^{50}⁄_{10}

x =5

**(iv) 4, x, 6 and 18**

6x = 18 x 4

x = ^{72}⁄_{6}

x = 12

**(v) 9, 12, x and 8**

12x = 9 x 8

x = ^{72}⁄_{12}

x = 6

**(vi) 4, 10, 36 and x**

4 x = 10 x 36

x = ^{360}⁄_{4}

x =90

**(vii) 7, 21, x and 45**

21 x = 7 x 45

x = ^{315}⁄_{21}

x =15

**(viii) 6, 8, 12 and x.**

6 x = 12 x 8

x = ^{96}⁄_{6}

x =16

**Question- 4.**

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

**Answer-4**

Let the third term = x

6 : 18 : : x : 75

= 18 x x = 6 x 75

x = ^{6×75}⁄_{18}

=** ^{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.

**Answer-5**

Let the second term = x

9 : x : : 8 : 24

=> x x 8 = 24 x 9

x = (24×9)/8 = 3 x 9 = 27

The second term of proportion = 27

**Question-6**

**Answer-6**

Let the fourth term = x

18 : 27 : : 32 : x

=> 18 x x = 27 x 32

=> x = (27×32)/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.

**Answer-7**

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 = (40×5)/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.

**Answer-8**

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 = (360×2)/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.

**Answer-9**

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 = (9×9.6)/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.

**Answer-10**

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 = (2×225)/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 ?

**Answer-11**

Total number of students in all sections = 225

Given, One of every five students pass

Total students pass = 225 x (1/5) = 45 students

**Question- 12.**

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

**Answer-12**

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

### Exercise – 12 B **Proportion Solved Questions for ICSE Class-6th ** Concise Mathematics

**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

**Answer-1**

(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

**Answer-2**

the options (iii) and (iv) only

**Question -3.**

Find the mean proportion between

(i) 3 and 27

(ii) 0.06 and 0.96

**Answer-3**

**Question- 4.**

Find the third proportional to :

(i) 36, 18

(ii) 5.25, 7

(iii) ₹ 1.60, ₹ 0.40

**Answer-4**

**(i) 36, 18**

Let third proportional be x

36 x 18 = 18 x x

36x = 18 x 18

x = (18×18) / 36

x =9

**(ii) 5.25, 7**

Let third proportional be x

5.25 x 7 = 7 x x

5.25x = 7 x 7

x = (7 x 7) / 5.25

x =28/3

x= 9^{1}⁄_{3}

**(iii) ₹ 1.60, ₹ 0.40**

Let third proportional be x

1.60 x 0.40 = 0.40 x x

1.60x = 0.40 x 0.40

x = (0.40 x 0.40) / 1.60

x =^{1}⁄_{10}

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.

**Answer-5**

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

7 : 5 = x : 20.25

5x = 20.25 x 7

x = (20.25 x 7) / 5

x= 82.7

**Question- 6.**

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

(i) x : y

(ii) x, if y = 10

(iii) y, if x = 27

**Answer-6**

(i)

x : y = 9 : 10

(ii)

(iii)

**Question -7.**

If ,^{2y+5x}⁄_{3y-5x} find:

(i) x : y

(ii) x, if y = 70

(iii) y, if x = 33

**Answer-7**

### **Proportion Exercise-12 C for ICSE Class-6th Concise** Mathematics Selina Solutions

**Question- 1.**

Are the following numbers in proportion:

(i) 32, 40, 48 and 60 ?

(ii) 12,15,18 and 20 ?

**Answer-1**

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

if 32 : 40 = 48 : 60

if 32 x 60 = 40 x 48

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

**Answer-2**

**(i) 14, 42, x and 75**

14, 42, x and 75 are in proportion

14 / 42=𝑥 / 75

=> 14 x 75 =x x 42

x = (14 x 75) / 42

x = 270

**(ii) 45, 135, 90 and x**

45, 135, 90 and x are in proportion

^{45}⁄_{135} = ^{90}⁄_{x}

=> 45 x =90 x 135

x = ^{90×135}⁄_{45}

x = 270

**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.

**Answer-3**

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

^{7}⁄4 = ^{2800}⁄_{x}

7x= 2800 x 4

x = ^{2800×4}⁄_{7}

x= 1600

**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.

**Answer-4**

Let length of sheet = x cm

Ratio in length and breadth = 8 : 5

and width = 17.5 cm

8 : 5 = x : 17.5

^{8}⁄5 = ^{x}⁄_{17.5}

5x = 8 x 17.5

x = ^{8×17.5}⁄_{5}

x= 28

**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.

**Answer-5**

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

6x = 15 x 8

x = ^{8×15}⁄_{6}

x = 15

**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.

**Answer-6**

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 ?

**Answer**

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 do not form a proportion

**Question- 8.**

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

**Answer-8**

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

2 : 80 :: 25 : 625

1 : 40 :: 1 : 25

No, they do not 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

**Answer-9**

10 kg of sugar costs = ₹ 350

and x kg of sugar cost = ₹ 175

10 kg : x kg :: 350 : 175

=> 10 x 175 = 350 x x

=> 350x= 1750

=> x = ^{1750}⁄_{350} = 5

Hence, ₹ 175 is the cost of **5** kg sugar

**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.

**Answer-10**

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

7 : 5 :: 22.5 : x

=> 7x = 22.5 x 5

=> x= ^{22.5×5}⁄_{7}

=> x = 16.07

**Question-11.**

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

**Answer-11**

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.

**Answer-12**

25, 35 and x are in continued proportion

=> 25 : 35 = 35 : x

=> 25 x x = 35 x 35

=> x = (35×35)/25

=> x = 49

— End of **Proportion ICSE Class-6th** Solutions :–

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