Selina Concise Class 6 Math Chapter 20 Simple (Linear) Equations Exercise 20D Solution
EXERCISE 20D
(1) Let the number be x.
∴ x + 17 = 54
⇒ x = 54 – 17
⇒ x = 37
The required number = 37.
(2) Let the number be x.
∴ x – 8 = 26
⇒ x = 26 + 8
⇒ x = 34
The required number = 34.
(5) Let the number be x.
∴ (x + 12)
⇒ 5x + 60 = 95
⇒ 5x = 95 – 60
⇒ 5x = 35
⇒ x = 7
The required number = 7.
(7) Let the age of the son is = x years.
His father’s age is (27 + x) years.
∴ x + x + 27 = 47
⇒ 2x = 47 – 27
⇒ 2x = 20
⇒ x = 10
Therefore, the age of the boy is 10 years and his father’s age is (10 + 27) = 37 years.
(8) Let the age of Gopal be x years.
His father’s age is = (x + 26) years.
∴ x + x + 26 = 56
⇒ 2x = 56 – 26
⇒ 2x = 30
⇒ x = 15
Therefore the age of Gopal is 15 years and his father age is (15 + 26) = 41 years.
(9) Let the two consecutive natural numbers be x and (x + 1).
∴ x + x + 1 = 31
⇒ 2x = 31 – 1 = 30
⇒ x = 15
Therefore, the numbers are 15 and (15 + 1) = 16
(10) Let the numbers be x and (x + 1) and (x + 2).
∴ x + x + 1 + x + 2 = 66
⇒ 3x + 3 = 66
⇒ 3x = 66 – 3 = 63
⇒ x = 21
Therefore, the numbers are 21 and (21 + 1) = 22 and (21 + 2) = 23.
(11) Let the number be x.
∴ x – 7 = 12
⇒ x = 12 + 7 = 19
The required number = 19.
(13) Let the number be x.
∴ (x + 7)
⇒ 5x + 35 = 45
⇒ 5x = 45 – 35
⇒ 5x = 10
⇒ x = 2
The required number = 2
(14) Let the age of the daughter be x years.
Her father’s age is (23 + x) years
∴ x + x + 23 = 41
⇒ 2x = 41 – 23
⇒ 2x = 18
⇒ x = 9
Therefore the age of the daughter is 9 years and her father’s age is (23 + 9) = 32 years.
(15) Let the age of the son be x years.
His mother’s age is (x + 19) years.
∴ x + x + 19 = 37
⇒ 2x = 37 – 19
⇒ 2x = 18
⇒ x = 9
Therefore the age of the son is 9 years.
(16) Let the numbers be x and (x – 6)
∴ x + x – 6 = 36
⇒ 2x = 36 + 6 = 42
⇒ x = 21
The larger number is 21.
(17) Difference of two numbers = 15.
Let the smaller number be x.
∴ Second number = x + 15
Sum of the two numbers are 71.
(i) Expression for smaller number,
∴ x + x + 15 = 71
⇒ 2x = 71 – 15 = 56
⇒ x = 28
(ii) The larger number is (28 + 15) = 43.
(18) Difference of two numbers = 15.
Let the larger number be x.
∴ Second number = x – 23
Sum of the two numbers are 91
(i) Expression for smaller number = x – 23
(ii) x + x – 23 = 91
⇒ 2x = 91 + 23
⇒ 2x = 114
⇒ x = 57
Therefore the smaller number is (57 – 23) = 34.
(19) Let the numbers be x, (x + 1) and (x + 2).
∴ x + x + 1 + x + 2 = 78
⇒ 3x = 78 – 3
⇒ 3x = 75
⇒ x = 25
Therefore the numbers are 25, (25 + 1) = 26 and (25 + 2) = 27.
(20) Let the three numbers be (x – 1), x and (x + 1).
(i) The smallest number = (x – 1)
Ans the largest number = (x + 1)
(ii) x – 1 + x + x + 1 = 54
⇒ 3x = 54
⇒ x = 18
Therefore the numbers are (18 – 1) = 17, 18 and (18 + 1) = 19.