Proportion ICSE Class-6th Concise Maths Selina Solutions Ch-12

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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 –: Select Topics :–

Exe-12 A,

 Exe-12 B,

 Exe-12 C,

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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

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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= 9¹⁄₃
(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

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 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
=> x² = 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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