Simple Linear Equations ICSE Class-7th Concise Selina

Simple Linear Equations ICSE Class-7th Concise Selina mathematics Solutions Chapter-12. We provide step by step Solutions of Exercise / lesson-12 Simple Linear Equations for ICSE Class-7 Concise Selina Mathematics. Our Solutions contain all type Questions with Exe-12 A , Exe-12 B Exe-12 C and Exe-12 D  to develop skill and confidence. Visit official Website CISCE for detail information about ICSE Board Class-7.

Simple Linear Equations ICSE Class-7th Concise Selina mathematics Solutions Chapter-12


–: Select Topics :–

Exe-12 A,

Exe-12 B,

Exe-12 C,

Exe-12 D,


 Exercise – 12 A Simple Linear Equations ICSE Class-7th 

Solve the following equations :

Question 1.

x + 5 = 10
Answer

x + 5 = 10

⇒ x = 10 – 5 = 5

Question 2.

2 + y = 7
Answer

2 + y = 7

⇒ y = 7 – 2 = 5

Question 3.

a – 2 = 6
Answer

a – 2 = 6

⇒ a = 6 + 2 = 8

Question 4.

x – 5 = 8
Answer

x – 5 = 8

⇒ x = 8 + 5 = 13

Question 5.

5 – d= 12
Answer

5 – d= 12

⇒ – d = 12 – 5 = 7

⇒ d = – 7

Question 6.

3p = 12
Answer

3p = 12

⇒ P = 12/3 = 4

Question 7.

14 = 7m
Answer

14 = 7m

⇒ m = 14/7=2

Question 8.

2x = 0
Answer

2x = 0

⇒ x = 0/2

=0

Question 9.

\frac { x }{ 9 } = 2
Answer

\frac { x }{ 9 } = 2

⇒ x = 2 × 9 = 18

∴ x = 18

Question 10.

\frac { y }{ -12 } = -4
Answer

\frac { y }{ -12 } = -4

y = (- 4) × (- 12)

∴ y = 48

Question 11.

8x-2 =38
Answer

8x – 2 = 38

8x = 38 + 2 = 40

⇒ x = 40/8

=5

∴ x = 5

Question 12.

2x + 5 = 5
Answer

2x + 5 = 5

⇒ 2x = 5 – 5 = 0

x = 0/2= 0

∴ x = 0

Question 13.

5x – 1 = 74
Answer

5x – 1 = 74

⇒ 5x = 74 + 1 = 75

⇒ x = 75/5

=5

Question 14.

14 = 27-x
Answer

14 = 27 – x

⇒ x = 27- 14

⇒ x = 13

∴ x = 13

Question 15.

10 + 6a = 40
Answer

10 + 6a = 40

10 + 6a = 40

⇒ 6a = 40 -10 = 30

⇒ a =30/6 = 5

∴ a= 5

Question 16.

Selina Concise Mathematics class 7 ICSE Solutions - Simple Linear Equations (Including Word Problems) -a16

Answer

Selina Concise Mathematics class 7 ICSE Solutions - Simple Linear Equations (Including Word Problems) -a16

Exercise -12 ICSE Class-7th Concise Selina mathematics img 1

Question 17.

Selina Concise Mathematics class 7 ICSE Solutions - Simple Linear Equations (Including Word Problems) -a17

Answer

Selina Concise Mathematics class 7 ICSE Solutions - Simple Linear Equations (Including Word Problems) -a17

⇒a/15=2

a=2×15=30

∴ a = 30

Question 18.

12 = c – 2
Answer

12 = c – 2

⇒ 12 + 2 = c

⇒ 14 = c

∴ c = 14

Question 19.

4 = x- 2.5
Answer

4 = x – 2.5

⇒4 + 2.5 = x

⇒ 6.5 = x

∴ x = 6.5

Question 20.

Selina Concise Mathematics class 7 ICSE Solutions - Simple Linear Equations (Including Word Problems) -a20

Answer

Exercise -12 ICSE Class-7th Concise Selina mathematics img 2

Question 21.

Selina Concise Mathematics class 7 ICSE Solutions - Simple Linear Equations (Including Word Problems) -a21

Answer

Selina Concise Mathematics class 7 ICSE Solutions - Simple Linear Equations (Including Word Problems) -a21

Exercise -12 ICSE Class-7th Concise Selina mathematics img 3

Question 22.

p + 0.02 = 0.08

Answer

p + 0.02 = 0.08

⇒ p = 0.08 – 0.02 = 0.06

∴ p = 0 06

Question 23.

Selina Concise Mathematics class 7 ICSE Solutions - Simple Linear Equations (Including Word Problems) -a23

Answer:

Selina Concise Mathematics class 7 ICSE Solutions - Simple Linear Equations (Including Word Problems) -a23

Exercise -12 ICSE Class-7th Concise Selina mathematics img 4

Question 24.

– 3x = 15

Answer

– 3x = 15

⇒x=(15/-3)

=-5

∴ x = -5

Question 25.

1.3 b = 39

Answer

1.3b = 39

⇒b= (39/1.3)

= (39×10)/13

=30

∴ b = 30

Question 26.

Selina Concise Mathematics class 7 ICSE Solutions - Simple Linear Equations (Including Word Problems) -a26
Answer

Selina Concise Mathematics class 7 ICSE Solutions - Simple Linear Equations (Including Word Problems) -a26

⇒ 5n = 20 × 8 = 160

⇒ n = 160/5

=32

∴ n = 32

Question 27.

Selina Concise Mathematics class 7 ICSE Solutions - Simple Linear Equations (Including Word Problems) -a27
Answer

Selina Concise Mathematics class 7 ICSE Solutions - Simple Linear Equations (Including Word Problems) -a27

⇒ 3m = 21 × 16 = 336

⇒ m = 336/3

=112

∴ m = 112

Question 28.

2a – 3 =5
Answer

2a – 3 =5

⇒2a = 5 +3

⇒ 2a = 8

⇒ a =8/2

= 4

∴ a = 4

Question 29.

3p – 1 = 8
Answer

3p – 1 = 8

⇒3p = 8 + 1 = 9

⇒ p = 9/3

= 3

∴p = 3

Question 30.

9y -7 = 20
Answer

9y -7 = 20

⇒ 9y = 20 + 7 = 27

⇒ y = 27/9

=3

∴ y = 3

Question 31.

2b – 14 = 8
Answer

2b – 14 = 8

⇒ 2b = 8 + 14 = 22

⇒ b = 22/2

=11

∴ b =  11

Question 32.

Selina Concise Mathematics class 7 ICSE Solutions - Simple Linear Equations (Including Word Problems) -a32
Answer

Selina Concise Mathematics class 7 ICSE Solutions - Simple Linear Equations (Including Word Problems) -a32

⇒ (7/10)x = 41 – 6 = 35

⇒ 7x = 35 × 10 = 350

⇒ x = 350/7

=50

∴ x = 50

Question 33.

Selina Concise Mathematics class 7 ICSE Solutions - Simple Linear Equations (Including Word Problems) -a33
Answer

(5/12)m – 12 = 48

⇒ (5/12)m

= 48 + 12 = 60

⇒ 5m = 60 × 12

= 720

⇒ m = 720/5

=144

∴ m = 144


 Exercise -12 B ICSE Class-7th Concise Selina mathematics 

Question 1.

8y – 4y = 20
Answer

8y – 4y = 20

⇒ 4y = 20

⇒ y = 20/4

=5

∴ y = 5

Question 2.

9b – 4b + 3b = 16
Answer

9b – 4b + 3b = 16

⇒ (9 – 4 + 3)b = 16

⇒ 8b = 16

⇒ b = 16/8

=2

∴ b = 2

Question 3.

5y + 8 = 8y – 18
Answer

5y + 8 = 8y – 18

⇒ 5y – 8y = – 18 – 8

⇒ – 3y = – 26

⇒ y = (-26/-3)

=26/3

∴ y = 8 (2/3)

Question 4.

6 = 7 + 2p -5
Answer

6 = 7 + 2p -5

⇒ – 2p = 7 – 5 – 6

⇒ – 2p = – 4

⇒ p = (-4/-2)

=2

∴ p = 2

Question 5.

8 – 7x = 13x + 8
Answer

8 – 7x = 13x + 8

⇒ – 7x – 13x = 8 – 8

⇒ – 20x = 0

⇒ x = 0/-20

=0

∴ x = 0

Question 6.

4x – 5x + 2x  = 28 + 3x
Answer

4x – 5x + 2x = 28 + 3x

⇒ 4x – 5x + 2x – 3x = 28

⇒ 6x – 8x = 28

⇒ x = (28/-2)

=-14

∴ x = – 14

Question 7.

9 + m = 6m + 8 – m
Answer

9 + m = 6m + 8 – m

⇒ m – 6m + m = 8 – 9

⇒ 2m – 6m = -1

⇒ – 4m = -1

∴ m = (-1/-4)

=1/4

Question 8.

24 = y + 2y + 3 + 4y
Answer

24 = y + 2y + 3 + 4y

⇒ 24 – 3 = y + 2y + 4y

⇒ 21 = 7y

⇒ 7y = 21

⇒ y = 21/7

=3

∴ y = 3

Question 9.

19x -+ 13 -12x + 3 = 23
Answer

19x + 13 -12x + 3 = 23

⇒ 19x – 12x = 23 – 13 – 3

⇒ 7x = 23 – 16 = 7

⇒ x = 7/7

=1

∴ x = 1

Question 10.

6b + 40 = – 100 – b
Answer

6b + 40 = – 100 – b

⇒ 6b + b = – 100 – 40

⇒ 7b = – 140

⇒ b = (-140/7)

=-20

∴ b = – 20

Question 11.

6 – 5m – 1 + 3m = 0
Answer

6 – 5m – 1 + 3m = 0

⇒ – 5m + 3m = -6 + 1

⇒ – 2m = – 5

⇒ m = (-5/-2)=5/2

∴ m = 5/2

=2 (1/2)

Question 12.

0.4x – 1.2  = 0.3x + 0.6
Answer

0.4x – 1.2 = 0.3x + 0.6

⇒ 0.4x – 0.3x = 0.6 + 1.2

⇒ 0.1x = 1.8

⇒ (1/10)x

=18/10

⇒ x = (18/10)×(10/1)=18

∴ x = 18

Question 13.

6(x+4) = 36
Answer

6(x+4) = 36

⇒ 6x + 24 = 36

⇒ 6x = 36 – 24 = 12

⇒ x = 12/6

=2

∴ x = 2

Question 14.

9 ( a+ 5) + 2 = 11
Answer

9 (a+ 5) + 2 = 11

⇒ 9a + 45 + 2 = 11

⇒ 9a = 11 – 45 – 2

⇒ 9a = 11 – 47 = – 36

⇒ a = (-36/9)=-4

∴ a = – 4

Question 15.

4 ( x- 2 ) = 12
Answer

4 (x – 2) = 12

⇒ 4x – 8 = 12

⇒ 4x = 12 + 8 = 20

⇒ x = (20/4)

=5

∴ x = 5

Question 16.

-3 (a- 6 ) = 24
Answer:

-3 (a – 6) = 24

⇒ – 3a + 18 = 24

⇒ -3a = 24 -18 = 6

⇒ a = (6/-3)

=-2

∴ a = -2

Question 17.

7 ( x-2) = 2 (2x -4)
Answer:

7 (x – 2) = 2 (2x – 4)

⇒ 7x – 14 = 4x – 8

⇒ 7x – 4x = – 8 + 14

⇒ 3x = 6

⇒ x = 6/3

=2

∴ x = 2

Question 18.

(x-4) (2x +3 ) = 2x²
Answer:

(x – 4) (2x + 3 ) = 2x²

⇒ x (2x + 3) – 4 (2x + 3) = 2x²

⇒ 2x² + 3x – 8x – 12 = 2x²

⇒ 2x² + 3x – 8x – 2x² = 12

⇒ – 5x = 12

⇒ x = (12/-5)

=-12/5

∴ x = -2 (2/5)

Question 19.

21 – 3 ( b-7 ) = b+ 20
Answer:

21 – 3 (b – 7) = b+ 20

⇒ 21 – 3b + 21 = b + 20

⇒ – 3b + 42 = b + 20

⇒ – 3b – b = 20 – 42

⇒ – 4b = – 22

⇒ b = (-22/-4)

=11/2

∴ b = 11/2

=5 (1/2)

Question 20.

x (x +5 ) = x² +x + 32
Answer:

x (x + 5) = x² +x + 32

⇒ x² + 5x = x² + x + 32

⇒ x² + 5x – x² – x = 32

⇒ 4x = 32

⇒ x = 32/4

=8

∴ x = 8


Simple Linear Equations Exe- 12 C Selina ICSE Maths  Class-7

Question 1.

Selina Concise Mathematics class 7 ICSE Solutions - Simple Linear Equations (Including Word Problems) -c1

Answer:

(x/2)+x=9

(x/2)+(x/1)=9

(x + 2x)/2=9

⇒ x + 2x = 2 × 9

⇒ 3x = 18

⇒  x = 18/3

=6

∴ x = 6

Question 2.

Selina Concise Mathematics class 7 ICSE Solutions - Simple Linear Equations (Including Word Problems) -c2
Answer:

Exercise -12 ICSE Class-7th Concise Selina mathematics img 5

∴ x = 15

Question 3.

Selina Concise Mathematics class 7 ICSE Solutions - Simple Linear Equations (Including Word Problems) -c3
Answer:

Exercise -12 ICSE Class-7th Concise Selina mathematics img 6

⇒  3x + 16x = 38 × 4

∴ 3x + 16x = 152

⇒ 19x = 152

⇒ x = 152/19

=8

∴ x = 8

Question 4.

Selina Concise Mathematics class 7 ICSE Solutions - Simple Linear Equations (Including Word Problems) -c4
Answer:

Selina Concise Mathematics class 7 ICSE Solutions - Simple Linear Equations (Including Word Problems) -c4

⇒ (5x + 2x)/10=14

⇒  5x + 2x = 14 × 10

⇒ 5x + 2x = 140

⇒ 7x = 140

⇒ x = 140/7

=20

∴ x = 20

Question 5.

Selina Concise Mathematics class 7 ICSE Solutions - Simple Linear Equations (Including Word Problems) -c5
Answer:

Selina Concise Mathematics class 7 ICSE Solutions - Simple Linear Equations (Including Word Problems) -c5

⇒ (4x – 3x)/12

=2

⇒  4x – 3x = 2 × 12

⇒ x = 24

Question 6.

Selina Concise Mathematics class 7 ICSE Solutions - Simple Linear Equations (Including Word Problems) -c6
Answer:

Selina Concise Mathematics class 7 ICSE Solutions - Simple Linear Equations (Including Word Problems) -c6

⇒ (y/1)+(y/2)

=(7/4)-(y/4)

⇒  (4y + 2y = 7 – y)/4

⇒ 4y + 2y = 7 – y

⇒  4y + 2y ⇒ 7y = 7

⇒ y = 7/7

=1

∴ y = 1

Question 7.

Exercise -12 ICSE Class-7th Concise Selina mathematics img 7
Answer:

Selina Concise Mathematics class 7 ICSE Solutions - Simple Linear Equations (Including Word Problems) -c7..

Question 8.

Selina Concise Mathematics class 7 ICSE Solutions - Simple Linear Equations (Including Word Problems) -c8
Answer:

Exercise -12 ICSE Class-7th Concise Selina mathematics img 8

⇒ 2m + 3m – 4m = 10

⇒ 5m – 4m = 10

⇒ m = 10

Question 9.

Selina Concise Mathematics class 7 ICSE Solutions - Simple Linear Equations (Including Word Problems) -c9
Answer:

Selina Concise Mathematics class 7 ICSE Solutions - Simple Linear Equations (Including Word Problems) -c9

⇒ (8x + 6x – 9x)/12=1

⇒ 8x + 6x – 9x = 12 × 1

⇒ 8x + 6x – 9x = 12

⇒ 14x – 9x = 12

⇒ 5x = 12

⇒ x = (12/5)

=2 (2/5)

Question 10.

Selina Concise Mathematics class 7 ICSE Solutions - Simple Linear Equations (Including Word Problems) -c10
Answer:

Selina Concise Mathematics class 7 ICSE Solutions - Simple Linear Equations (Including Word Problems) -c10

⇒ (9a + 2a)12=66

⇒  (9a+2a)=66×12

⇒ 9a + 2a = 792

⇒ 11a = 792

⇒ a = 792/11

=72

⇒ a = 72

Question 11.

Selina Concise Mathematics class 7 ICSE Solutions - Simple Linear Equations (Including Word Problems) -c11

Answer:

Selina Concise Mathematics class 7 ICSE Solutions - Simple Linear Equations (Including Word Problems) -c11

 

 

⇒ (10p – 3p)/15=35

⇒ 10p – 3p = 35 × 15

⇒ 10p – 3p = 525

⇒ 7p = 525

⇒ p = 525/7

=75

⇒ p = 75

Question 12.

0.6a +0.2a = 0.4 a +8
Answer:

0.6a +0.2a = 0.4 a + 8

⇒ (6/10)a+(2/10)a

=(4/10)a+(8/1)

⇒(6a + 2a)/10

=4a + 80

⇒ 6a + 2a = 4a + 80

⇒ 6a + 2a – 4a = 80

⇒ 4a = 80

⇒ a = 80/4

=20

∴ a = 20

Question 13.

p + 104p= 48
Answer:

p + 1.4p = 48

⇒ p+(14/10)p=48

⇒ (10p + 14p)/10=48

⇒ 10 P + 14P = 48 × 10

⇒ 10p + 14p = 480

⇒ 24p = 480

⇒ p = 480/24

=20

∴ p = 20

Question 14.

10% of x = 20
Answer:

10% of x = 20

⇒ (10/100)×x=20

⇒ (x/10)=20

⇒ x = 20 × 10 = 200

∴ x = 200

Question 15.

y + 20% of y = 18
Answer:

y + 20% of y = 18

⇒ y + (20/100)×y=18

⇒ (100y+20y)/100=18

⇒ 100y + 20y = 18 × 100

⇒ 100y+ 20y = 1800

⇒ 120y = 1800

⇒ y = 1800/120

=15

∴ y = 15

Question 16.

x – 13% of x = 35
Answer:

x – 30% of x = 35

⇒ x (-30/100)×x=35

⇒ (100x-30x)/100=35

⇒ 100x – 30y = 35 × 100

⇒ 100x – 30x = 3500

⇒ 70x = 3500

⇒ x = 3500/70

=50

∴ x = 50

Question 17.

Selina Concise Mathematics class 7 ICSE Solutions - Simple Linear Equations (Including Word Problems) -c17
Answer:

Selina Concise Mathematics class 7 ICSE Solutions - Simple Linear Equations (Including Word Problems) -c17

⇒ (3x+12x+2x)/6=7

⇒ 3x + 12 + 2x = 7 × 6

⇒ 3x + 12 + 2x = 42

⇒ 5x = 42 – 12 = 30

⇒ x = 30/5=6

∴ x = 6

Question 18.

Selina Concise Mathematics class 7 ICSE Solutions - Simple Linear Equations (Including Word Problems) -c18
Answer:

Selina Concise Mathematics class 7 ICSE Solutions - Simple Linear Equations (Including Word Problems) -c18

⇒ (4y+8+3y+15)/12=6

⇒ 4y + 8 + 3y + 15 = 6 × 12

⇒ 7y + 23 = 72

⇒ 7y = 72 – 23 = 49

⇒ y = 49/7=7

∴ y = 7

Question 19.

Selina Concise Mathematics class 7 ICSE Solutions - Simple Linear Equations (Including Word Problems) -c19
Answer:

Selina Concise Mathematics class 7 ICSE Solutions - Simple Linear Equations (Including Word Problems) -c19

⇒ (12a-8-7a+14)/28=2

⇒ 12a – 8 – 7a + 14 = 2 × 28

⇒ 12a – 8 – 7a + 14 = 56

⇒ 12a – 7a + 14 – 8 = 56

⇒ 5a + 6 = 56

⇒ 5a = 56 – 6 = 50

⇒ a = 50/5=10

∴ a = 10

Question 20.

Selina Concise Mathematics class 7 ICSE Solutions - Simple Linear Equations (Including Word Problems) -c20
Answer:

Selina Concise Mathematics class 7 ICSE Solutions - Simple Linear Equations (Including Word Problems) -c20

⇒ (3(x+5)-2(x-2))/6=4

⇒ 3x + 15 – 2x + 4 = 4 × 6

⇒ 3x + 15 – 2x + 4 = 24

⇒ 3x – 2x = 24 – 15 – 4

⇒ x = 24 – 19 = 5

∴ x = 5

Question 21.

Selina Concise Mathematics class 7 ICSE Solutions - Simple Linear Equations (Including Word Problems) -c21

Answer:

Selina Concise Mathematics class 7 ICSE Solutions - Simple Linear Equations (Including Word Problems) -c21

⇒ (6(x-1)-4(x-2)-3(x-3))/12=0

⇒ 6(x – 1) – 4(x – 2) – 3(x – 3) = 0

∴ 6x – 6 – 4x + 8 – 3x + 9 = 0

∴ 6x – 4x – 3x – 6 + 8 + 9 = 0

∴ 6x – 7x = 6 – 8 – 9

⇒ – x = 6 – 17 = – 11

∴ x = 11

Question 22.

Selina Concise Mathematics class 7 ICSE Solutions - Simple Linear Equations (Including Word Problems) -c22
Answer

Selina Concise Mathematics class 7 ICSE Solutions - Simple Linear Equations (Including Word Problems) -c22

⇒ (35(x+1)+21(x+4)=15(x-4))/105

…(LCM of 3,5,7 = 105)

⇒ 35(x + 1) + 21 (x + 4) = 15(x – 4)

⇒ 35x + 35 + 21x + 84 = 15x – 60

⇒ 35x + 21x – 15x = -60 – 35 – 84

⇒ 56x – 15x = – (60 + 35 + 84)

⇒ 41x = – 179

∴ x = (-179/41)

=-4 (15/21)

Question 23.

15 – 2 (5-3x ) = 4 ( x-3 ) + 13
Answer

15 – 2 (5 – 3x) = 4 (x – 3) + 13

⇒ 15 – 10 + 6x = 4x  – 12 + 13

⇒ 6x – 4x = – 12 + 13 – 15 + 10

⇒ 2x = 23 – 27 = – 4

⇒ x =(-4/2)=-2

Hence x = -2

Question 24.

Selina Concise Mathematics class 7 ICSE Solutions - Simple Linear Equations (Including Word Problems) -c24
Answer

Selina Concise Mathematics class 7 ICSE Solutions - Simple Linear Equations (Including Word Problems) -c24

⇒ (2x+1)/(3x-2)=5/4

By cross multiplication

(3x – 2)× 5 = 4 (2x + 1)

⇒ 15x – 10 = 8x + 4

⇒ 15x – 8x = 4 + 10

⇒ 7x = 14

⇒ x = 14/7

=2

∴ x = 2

Question 25.

21 – 3 (x – 7) = x + 20
Answer

21 – 3 (x – 7) = x + 20

⇒ 21 – 3x + 21 = x + 20

⇒ 42 – 3x = x + 20

⇒ 42 – 20 = x + 3x

⇒ 4x = 22

⇒ x = 22/4

=11/2=5 (1/2)

∴ x = 5 (1/2)

Question 26.

Selina Concise Mathematics class 7 ICSE Solutions - Simple Linear Equations (Including Word Problems) -c26
Answer

Selina Concise Mathematics class 7 ICSE Solutions - Simple Linear Equations (Including Word Problems) -c26

⇒ (12x-8-7x+14)/28=2

⇒ (5x+6)/28=2

⇒ 5x + 6 = 28 × 2

⇒ 5x + 6 = 56

⇒ 5x = 56 – 6 = 50

⇒ x = 50/5

=10

∴ x = 10

Question 27.

Selina Concise Mathematics class 7 ICSE Solutions - Simple Linear Equations (Including Word Problems) -c27
Answer

Selina Concise Mathematics class 7 ICSE Solutions - Simple Linear Equations (Including Word Problems) -c27

⇒ (2x-3)/3-(x-5)/1=x/3

⇒ (2x-3-3x+15=x)/3

⇒ – x + 12 = x

⇒ 12 = x + x

⇒ 2x = 12

∴ x = 122=6

Question 28.

Exercise -12 ICSE Class-7th Concise Selina mathematics img 9

Answer

Exercise -12 ICSE Class-7th Concise Selina mathematics img 9

⇒ (5x-20=5x+15+7x+283)/5

⇒ 5x – 5x – 7x = 15 + 28 + 20

⇒ – 7x = 63

⇒ x = 63-7=-9

∴ x = – 9

Question 29.

Selina Concise Mathematics class 7 ICSE Solutions - Simple Linear Equations (Including Word Problems) -c29
Answer

Selina Concise Mathematics class 7 ICSE Solutions - Simple Linear Equations (Including Word Problems) -c29

⇒ (6x-6-10x=30-15x+30)/30

⇒ – 4x – 6 = 60 – 15x

⇒ 15x – 4x = 60 + 6

⇒ 11x = 66

⇒ x = 66/11=6

∴ x = 6

Question 30.

2x + 20% of x = 12.1
Answer

2x + 20% of x = 12.1

Exercise -12 ICSE Class-7th Concise Selina mathematics img 10


Simple Linear Equations Exercise 12 D – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.

One-fifth of a number is 5, find the number.
Answer

The number = x

According to the condition

(1/5)x=5

⇒ x = 5 x 5

⇒ x = 25

∴ Number = 25

Question 2.

Six times a number is 72, find the number.
Answer

The number = x

According to the condition

6x = 72

⇒ x = 72/6

⇒ x= 12

∴ Number = 12

Question 3.

If 15 is added to a number, the result is 69, find the number.
Answer

The number = x

According to the condition

x + 15 = 69

⇒ x = 69 – 15 x = 54

∴Number = 54

Question 4.

The sum of twice a number and 4 is 80, find the number.
Answer

The number = x

According to the condition

2x + 4 = 80

⇒ 2x = 80 – 4

⇒ 2x = 76

⇒ x = 76/2

=38

Number = 38

Question 5.

The difference between a number and one- fourth of itself is 24, find the number.
Answer

Let the number = x

According to the condition

x-(1/4)x=24

⇒(4x – x)/x=24

⇒3x/4=24

⇒x=24×(4/3)

⇒x=8×4

⇒ x = 32

∴ Number = 32

Question 6.

Find a number whose one-third part exceeds its one-fifth part by 20.
Answer

Let the number = x

According to the condition

(1/3)x-(1/5)x=20

⇒(5x – 3x)/15=20  …(LCM of 3, and 5 = 15)

⇒2x/15=20

⇒x=(20×15)/2

⇒x=150

∴ Number = 150

Question 7.

A number is as much greater than 35 as is less than 53. Find the number.
Answer

The number = x

According to the condition

x – 35 = 53 – x

⇒ x + x = 53 + 35

⇒ 2x = 88

⇒ x = 88/2

=44

∴ Number = 44

Question 8.

The sum of two numbers is 18. If one is twice the other, find the numbers.
Answer

The first number = x

and the second number = y

According to the condition

x + y= 18 …(i)

and x = 27 ….(ii)

Substitute the eq. (ii) in eq. (i), we get

2y + y= 18

x= 2y = 18

⇒ 3y= 18

⇒ y = 18/3

=6

Now, substitute the value of y in eq. (ii), we get

x = 2 x 6= 12

∴ The two numbers are 12, 6

Question 9.

A number is 15 more than the other. The sum of of the two numbers is 195. Find the numbers.
Answer

The First number = x

and the Second number = y

According to the condition

x = y+ 15 …(i)

x + 7=195 …(ii)

Substitute the eq. (i) in eq. (ii), we get

y + 15 + 7 = 195

⇒ 2y = 195 – 15

⇒ y = 180/2

=90

Now, substitute the value of y in eq. (i), we get

x = 90+ 15 = 105

∴ The two numbers are 105 and 90

Question 10.

The sum of three consecutive even numbers is 54. Find the numbers.
Answer

The first even number = x

second even number = x + 2

and third even number = x + 4

According to the condition,

x + x + 2 + x + 4 = 54

⇒ 3x + 6 = 54

⇒ 3x = 54 – 6

⇒ x = 483=16

∴ First even number = 16

Second even number = 16 + 2 = 18

and third even number = 16 + 4 = 20

Question 11.

The sum of three consecutive odd numbers is 63. Find the numbers.
Answer

The first odd number = x

second odd number = x + 2

and third odd number = x + 4

According to the condition,

x+ x + 2 + x+4 = 63

3x + 6 = 63 ⇒ 3x = 63 – 6

⇒3x = 57 ⇒ x =57/3

=19

∴ First odd number = 19

Second odd number = 19 + 2 = 21

third odd number = 19 + 4 = 23

Question 12.

A man has ₹ x from which he spends ₹6. If twice of the money left with him is ₹86, find x.
Answer

The total amount be x

According to the condition

2x = 86

⇒ x = 86/2

⇒ x = 43

Amount spent by him = 6

∴ Total money he have = ₹43 + ₹6 = ₹49

Question 13.

A man is four times as old as his son. After 20 years, he will be twice as old as his son at that time. Find their present ages.
Answer

The present age of the son = x years

Present age of the father = 4x years

After 20 years,

Son’s age will be (x + 20) years

and Father’s age will be (4x + 20) years

According to the condition,

4x + 20 = 2 (x + 20)

4x + 20 = 2x + 40

4x – 2x = 40 – 20

2x = 20

⇒ x = 10

∴ Present age of the son = 10 years and Present age of the father = 4×10 years = 40 years

Question 14.

If 5 is subtracted from three times a number, the result is 16. Find the number.
Answer

The number = x

According to the condition,

3x – 5 = 16

⇒ 3x = 16 + 5

⇒ 3x = 21

⇒ x = 213

⇒ x = 7

∴The number = 7

Question 15.

Find three consecutive natural numbers such that the sum of the first and the second is 15 more than the third.
Answer

The first consecutive number = x,

Second consecutive number = x + 1

and Third consecutive number = x + 2

According to the condition,

x + x + 1 = 15 + x + 2

⇒ 2x + 1 = 17 +x

⇒ 2x -x = 17 – 1

⇒ x= 16

∴ The first consecutive number = 16

Second consecutive number =16+1 = 17

Third consecutive number =16 + 2=18

Question 16.

The difference between two numbers is 7. Six times the smaller plus the larger is 77. Find the numbers.
Answer

The smallest number = x

and the largest number = y

According to the condition,

y – x = 7 …(i)

and 6x + y = 77 ….(ii)

From eq. (i)

y = 7 + x …(iii)

Substitute the eq. (iii) in eq. (ii)

6x + 7 + x = 77

⇒ 7x = 77 – 7

⇒ x = 70/7

=10

Now, substitute the value of x in eq. (iii)

y = 7+ 10= 17

∴ The smallest number 10 and the largest number is 17.

Question 17.

The length of a rectangular plot exceeds its breadth by 5 metre. If the perimeter of the plot is 142 metres, find the length and the breadth of the plot.
Answer

The length of a rectangular plot = x

and the breadth of a rectangular plot = y

According to the condition,

x = y + 5   …(i)

and 2(x + y) = 142

⇒ x + y = 142/2

=71

⇒ x + y = 71      …(ii)

Now, substitute the value of eq. (i) in eq (ii)

y + 5 + y = 71

⇒ 2y = 71 – 5

⇒ y = 66/2=33

Now, put the value of y in eq. (i)

x = 33 + 5 = 38

∴ The length of rectangular plot is 38 m and breadth is 33 m.

Question 18.

The numerator of a fraction is four less than its denominator. If 1 is added to both, is numerator and denominator, the fraction becomes \frac { 1 }{ 2 } Find the fraction.
Answer

The numerator of a fraction = x

and the denominator of a fraction = y

According to the condition,

x = y – 4      …..(i)

and (x + 1)/(y + 1)=12

⇒ 2(x + 1) = y + 1

⇒ 2x + 2 = y + 1

⇒ 2x – y = -1     …(ii)

Substitute the eq.(i) in eq.(ii)

2(y – 4) – y = -1

2y – 8 – y = – 1

y = – 1 + 8

y = 7

Now, put the value of y in eq.(i), we get

x = 7 – 4 = 3

∴ The numerator of a fraction is 3

and denominator is 7 and the fraction is 3/7

Question 19.

A man is thrice as old as his son. After 12 years, he will be twice as old as his son at that time. Find their present ages.
Answer

The present age of the son = x years

and the present age of the father = 3x years

After 12 years,

Son’s age will be (x + 12) years

and father’s age will be (3x + 12) years

According to the condition,

3x + 12 = 2 (x + 12)

3x + 12 = 2x+ 24

3x – 2x = 24 – 12

x = 12

∴Present age of the son = 12 years

and Present age of the father = 3×12 years

= 36 years

Question 20.

A sum of ₹ 500 is in the form of notes of denominations of ₹ 5 and₹ 10. If the total number of notes is 90, find the number of notes of each type.
Answer

The number of ₹ 5 notes = x

∴ The number of ₹10 notes = 90 – x

Value of ₹10 notes = x ×₹ 5 = ₹ 3x

and value of ₹10 notes = (90 – x) x ₹ 10 =₹(900 – 10x)

∴Total value of all the notes = ₹ 500

∴5x+ (900- 10x) = 500

⇒ 5x + 900 – 10x = 500

⇒ -5x = 500 – 900

⇒ x = 400/5

⇒ x = 80

∴ The number of ₹5 notes = x = 80

and the number of ₹10 notes = 90 – x

= 90 – 80 = 10

 

— End of Simple Linear Equations Solutions :–

Return to – Concise Selina Maths Solutions for ICSE Class -7 


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