## Selina Concise Mathematics class 7 ICSE Solutions – Simple Linear Equations (Including Word Problems)

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**POINTS TO REMEMBER**

**Equation:**An equation is a statement which states that two expressions are equal.- To solve an equation means to find the value of the variable (unknown quantity) used in it.

**Note :**An equation remains unchanged if

**(i)**the same number is added to each side of the equation. .

**(ii)**the same number is subtracted from each side of the equation.

**(iii)**the same number is multiplied to each side of the equation.

**(iv)**Each side of the equation is divided by the same non-zero number.

**(v)**In transposing any term of an equation from one side to another, then its sign is reversed is

**(a)**from positive to negative and from negative to positive

**(b)**from multiplication to division and from division to multiplication. **In equation :**

It is a statement of inequality between two expressions involving a single variable with the highest power one.**Replacement set**

For a given inequation, the set from which the values of its variable are taken is called the replacement set or domain of the variable.**Solution set**

It is the subset of the replacement set, consisting of those values of the variable which satisfy the given inequation**Properties of inequations**

Adding, subtracting, multiplying or dividing by the same positive number to each side of an inequation does not change the inequality but multiplying or dividing by a negative number to each side of an inequation, it changes the inequality.

**EXERCISE 12 (A)**

**Solve the following equations :**

**Question 1.**

**x + 5 = 10**

**Solution:**

x + 5 = 10

⇒ x=10 -5 = 5

**Question 2.**

**2 + y=7**

**Solution:**

2 + y = 7

⇒ = 7- 2 = 5

**Question 3.**

**a – 2 = 6**

**Solution:**

a -2 =6

⇒a = 6 + 2 = 8

**Question 4.**

**x – 5 = 8**

**Solution:**

x-5 =8

⇒ x = 8 +5 = 13

**Question 5.**

**5 – d= 12**

**Solution:**

5-d = 12

⇒ -d = 12-5 =7

⇒ d = – 7

**Question 6.**

**3p = 12**

**Solution:**

3p = 12

⇒ P = = 4 Ans.

**Question 7.**

**14 = 7m**

**Solution:**

14 = 7m

⇒ m = = 2

**Question 8.**

**2x = 0**

**Solution:**

2x = 0 ⇒ x = = 0

**Question 9.**

** = 2**

**Solution:**

= 2

⇒x = 2 ×9 = 18

∴ x = 18

**Question 10.**

** = -4**

**Solution:**

= -4

⇒ = -4

⇒ y = (-4) × (-12)

∴ y= 48

**Question 11.**

**8x-2 =38**

**Solution:**

8x-2 =38

8x = 38 + 2 = 40

⇒ x = = 5

∴ x = 5

**Question 12.**

**2x + 5 = 5**

**Solution:**

2x + 5 = 5

⇒ 2x = 5 – 5 = 0

x = = 0

∴x = 0

**Question 13.**

**5x – 1 = 74**

**Solution:**

5x- 1 = 74

⇒ 5x = 74 + 1 = 75

⇒ x = = 15

**Question 14.**

**14 = 27-x**

**Solution:**

14 = 27 -x

⇒ x = 27- 14

⇒ x = 13

∴ x= 13

**Question 15.**

**10 + 6a = 40**

**Solution:**

10 + 6a = 40

⇒ 6a = 40 -10 = 30

⇒ a = = 5

∴ a= 5

**Question 16.**

**Solution:**

**Question 17.**

**Solution:**

**Question 18.**

**12 = c – 2**

**Solution:**

12 = c – 2

⇒ 12 + 2 =c

⇒ 14 = c

∴c = 14

**Question 19.**

**4 = x- 2.5**

**Solution:**

4 = x – 2.5

⇒4 + 2.5=x

⇒ 6.5 =x

∴ x = 6.5

**Question 20.**

**Solution:**

**Question 21.**

**Solution:**

**Question 22.**

**p + 0.02 = 0.08**

**Solution:**

p + 0.02 = 0.08

⇒ p = 0.08 – 0.02 = 0.06

∴ p = 0 06

**Question 23.**

**Solution:**

**Question 24.**

**Solution:**

**Question 25.**

**Solution:**

**Question 26.**

**Solution:**

**Question 27.**

**Solution:**

**Question 28.**

**2a – 3 =5**

**Solution:**

2a – 3 = 5

⇒2a = 5 +3

⇒ 2a = 8

⇒ a = = 4

∴a = 4

**Question 29.**

**3p – 1 = 8**

**Solution:**

3p – 1 = 8

⇒3p = 8 + 1 = 9

⇒ p = = 3

∴p = 3

**Question 30.
**

**9y -7 = 20**

**Solution:**

**Question 31.
**

**2b – 14 = 8**

**Solution:**

**Question 32.**

**Solution:**

**Question 33.**

**Solution:**

**EXERCISE 12 (B)**

**Question 1.
**

**8y – 4y = 20**

**Solution:**

**Question 2.
**

**9b – 4b + 3b = 16**

**Solution:**

**Question 3.
**

**5y + 8 = 8y – 18**

**Solution:**

**Question 4.
**

**6 = 7 + 2p -5**

**Solution:**

**Question 5.
**

**8 – 7x = 13x + 8**

**Solution:**

**Question 6.
**

**4x – 5x + 2x = 28 + 3x**

**Solution:**

**Question 7.
**

**9 + m = 6m + 8 – m**

**Solution:**

**Question 8.
**

**24 = y + 2y + 3 + 4y**

**Solution:**

**Question 9.
**

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

**Solution:**

**Question 10.
**

**6b + 40 = – 100 – b**

**Solution:**

**Question 11.
**

**6 – 5m – 1 + 3m = 0**

**Solution:**

**Question 12.
**

**0.4x – 1.2 = 0.3x + 0.6**

**Solution:**

**Question 13.
**

**6(x+4) = 36**

**Solution:**

**Question 14.
**

**9 ( a+ 5) + 2 = 11**

**Solution:**

**Question 15.
**

**4 ( x- 2 ) = 12**

**Solution:**

**Question 16.
**

**-3 (a- 6 ) = 24**

**Solution:**

**Question 17.
**

**7 ( x-2) = 2 (2x -4)**

**Solution:**

**Question 18.
**

**(x-4) (2x +3 ) = 2x²**

**Solution:**

**Question 19.
**

**21 – 3 ( b-7 ) = b+ 20**

**Solution:**

**Question 20.
**

**x (x +5 ) = x² +x + 32**

**Solution:**

**EXERCISE 12 (C)**

**Solve**

**Question 1.**

**Solution:**

**Question 2.**

**Solution:**

**Question 3.**

**Solution:**

**Question 4.**

**Solution:**

**Question 5.**

**Solution:**

**Question 6.**

**Solution:**

**Question 7.**

**Solution:**

**Question 8.**

**Solution:**

**Question 9.**

**Solution:**

**Question 10.**

**Solution:**

**Question 11.**

**Solution:**

**Question 12.
**

**0.6a +0.2a = 0.4 a +8**

**Solution:**

**Question 13.
**

**p + 104p= 48**

**Solution:**

**Question 14.
**

**10% of x = 20**

**Solution:**

**Question 15.
**

**y + 20% of y = 18**

**Solution:**

**Question 16.
**

**x – 13% of x = 35**

**Solution:**

**Question 17.**

**Solution:**

**Question 18.**

**Solution:**

**Question 19.**

**Solution:**

**Question 20.**

**Solution:**

**Question 21.**

**Solution:**

**Question 22.**

**Solution:**

**Question 23.
**

**15 – 2 (5-3x ) = 4 ( x-3 ) + 13**

**Solution:**

**Question 24.**

**Solution:**

**Question 25.
**

**21 – 3 (x – 7) = x + 20**

**Solution:**

**Question 26.**

**Solution:**

**Question 27.**

**Solution:**

**Question 28.**

**Solution:**

**Question 29.**

**Solution:**

**Question 30.
**

**2x + 20% of x = 12.1**

**Solution:**

**EXERCISE 12 (D)**

**Question 1.**

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

**Solution:**

Let the number = x

According to the condition

x = 5 ⇒ x = 5 x 5

⇒ x = 25

∴ Number = 25

**Question 2.**

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

**Solution:**

Let the number = x

According to the condition

6x = 72

⇒ x =

⇒x= 12

∴ Number = 12

**Question 3.**

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

**Solution:**

Let 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.**

**Solution:**

Let the number = x

According to the condition

2x + 4 = 80

⇒2x = 80 – 4

⇒ 2x = 76

⇒ x = = 38

Number = 38

**Question 5.**

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

**Solution:**

**Question 6.**

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

**Solution:**

**Question 7.**

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

**Solution:**

Let the number = x

According to the condition

x – 35 = 53 – x

⇒ x + x = 53 + 35

88

⇒2x = 88

⇒ x = = 44

∴Number = 44

**Question 8.**

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

**Solution:**

Let 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= = 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.**

**Solution:**

Let 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 = = 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.**

**Solution:**

Let 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 = = 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.**

**Solution:**

Let 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 = =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.**

**Solution:**

Let the total amount be x

According to the condition

2x = 86

⇒x =

⇒ 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.**

**Solution:**

Let 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.**

**Solution:**

Let the number = x

According to the condition,

3x – 5 = 16

⇒ 3x = 16 + 5

⇒ 3x = 21

⇒ x =

⇒ 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.**

**Solution:**

Let the first conscutive 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.**

**Solution:**

Let 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 = = 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.**

**Solution:**

**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 Find the fraction.**

**Solution:**

**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.**

**Solution:**

Let 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.**

**Solution:**

Let 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 =

⇒ x = 80

∴ The number of ₹5 notes = x = 80

and the number of ₹10 notes = 90 – x

= 90 – 80= 10

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