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  for detail information about ICSE Board Class-6 .

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

–: Select Topics :–

Exe-12 A,

Exe-12 B,

Exe-12 C,

### 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) 1518 and  1012

(vi)  78 and  1416

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) 1518 and  1012

since 15/18   = 5/6

and 10/12   = 5/6

Therefore it is  in proportion

(vi)  78 and  1416

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

(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.

(i) x, 6, 10 and 15

15x = 6 x 10

x =6015

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

30x = 15×4

x = 15×430
x =2

(iii) 2, x, 10 and 25

10x = 25 x 2

x = 5010
x =5

(iv) 4, x, 6 and 18

6x = 18 x 4

x = 726

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

12x = 9 x 8

x = 7212
x = 6

(vi) 4, 10, 36 and x

4 x = 10 x 36

x = 3604
x =90

(vii) 7, 21, x and 45

21 x = 7 x 45

x  = 31521

x =15

(viii) 6, 8, 12 and x.

6 x = 12 x 8

x  = 966

x =16

#### Question- 4.

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

Let the third term = x
6 : 18 : : x : 75
= 18 x x = 6 x 75
x =  6×7518

=753 = 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.

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

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

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.

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.

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.

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.

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 ?

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.

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

(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

the options (iii) and (iv) only

#### Question -3.

Find the mean proportion between
(i) 3 and 27
(ii) 0.06 and 0.96

#### Question- 4.

Find the third proportional to :
(i) 36, 18
(ii) 5.25, 7
(iii) ₹ 1.60, ₹ 0.40

(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= 913
(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 =110

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.

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

(i)

x : y = 9 : 10
(ii)

(iii)

#### Question -7.

If ,2y+5x3y-5x find:
(i) x : y
(ii) x, if y = 70
(iii) y, if x = 33

### 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 ?

(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

(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
45135 = 90x
=> 45 x  =90 x 135

x = 90×13545

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.

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

74 2800x

7x=  2800 x 4

x = 2800×47

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.

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 x17.5

5x = 8 x 17.5

x = 8×17.55

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.

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 = 8×156

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.

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 ?

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 ?

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

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 = 1750350 = 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.

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= 22.5×57
=> x  = 16.07

#### Question-11.

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

4, x and 9 are in continued proportion
=> 4 : x = x : 9
=> x2 = 9 x 4
=> x = √36
x = 6

#### Question -12.

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

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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