Selina Concise Class 7 Math Chapter 12 Simple Linear Equations Exercise 12D Solution
EXERCISE 12D
(1) Let the number be x.
∴ x/5 = 5
⇒ x = 5 × 5
⇒ x = 25
Hence, the number is 25.
(2) Let the number be x.
∴ 6x = 72
⇒ x = 72/6
⇒ x = 12
Hence, the number is 12.
(3) Let the number be x.
∴ x + 15 = 69
⇒ x = 69 – 15
⇒ x = 54
Hence, the number is 54.
(4) Let the number be 2x.
∴ 2x + 4 = 80
⇒ 2x = 80 – 4
⇒ x = 76/2
⇒ x = 38
Hence, the number is 38.
(7) Let the number be x.
∴ x – 35 = 53 – x
⇒ x + x = 53 + 35
⇒ 2x = 88
⇒ x = 88/2
⇒ x = 44
(8) Let the numbers are x and 2x.
∴ x + 2x = 18
⇒ 3x = 18
⇒ x = 18/3
⇒ x = 6
Hence, the numbers are 6 and (2 × 6) = 12.
(9) Let the numbers are x and (x + 15).
∴ x + x + 15 = 195
⇒ 2x = 195 – 15
⇒ 2x = 180
⇒ x = 180/2
⇒ x = 90
Hence, the numbers are 90 and (90 + 15) = 105.
(10) Let the numbers are x, (x + 1) and (x + 2).
∴ x + x + 1 + x + 2 = 54
⇒ 3x + 3 = 54
⇒ 3x = 54 – 3 = 51
⇒ x = 51/3
⇒ x = 17
Hence, the numbers are 17, (17+1) = 18 and (17 + 2) = 19.
(11) Let the three numbers are x, (x + 2) and (x + 4).
∴ x + x + 2 + x + 4 = 63
⇒ 3x + 6 = 63
⇒ 3x = 63 – 6
⇒ x = 57/3
⇒ x = 19
Hence, the numbers are 19, (19 + 2) = 21 and (19 + 4) = 23.
(12) Given, 2x = 86
⇒ x = 86/2
⇒ x = 43
The man sped = Rs 6
Hence, the total money = Rs (43 + 6) = Rs 49.
(13) Let the age of the son be x years and his father’s age is 4x years.
After 20 years son’s age = (x + 20) years
And father’s age = 4x + 20
But given after 20 years father’s age will be 2(x + 20) years.
Then, 4x + 20 = 2(x + 20)
⇒ 4x + 20 = 2x + 40
⇒ 4x – 2x = 40 – 20
⇒ 2x = 20
⇒ x = 20/2 = 10
Hence, the son’s age is 10 years and father’s age is (4 × 10) = 40 years.
(14) Let the number be x.
∴ 3x – 5 = 16
⇒ 3x = 16 + 5 = 21
⇒ x = 21/3
⇒ x = 7
(15) Let the three numbers are x, (x + 1) and (x + 2).
∴ x + x + 1 = 15 + x + 2
⇒ 2x + 1 = x + 17
⇒ 2x – x = 17 – 1
⇒ x = 16
Hence, the numbers are 16, (16 + 1) = 17 and (16 + 2) = 18.
(16) Let the smallest number be x and the larger be x + 7.
∴ 6x + 7 + x = 77
⇒ 7x = 77 – 7
⇒ x = 70/7
⇒ x = 10
Hence, the numbers are (10 +7) = 17 and 10.
(17) Let the breadth be x and length = (x + 5) m.
∴ 2 (x + x + 5) = 142
⇒ 2(2x + 5) = 142
⇒ 4x + 10 = 142
⇒ 4x = 142 – 10
⇒ x = 132/4
⇒ x = 33
Hence, the breadth is 33 m and length (33 + 50 = 38 m.
(19) Let the age of the son be x years and his father’s age be 3x years.
After 12 years son’s age is = (x + 12) years.
And his father’s age is = (3x + 12) years.
But given, after 12 years his father’s age will be = 2(x + 12) years.
∴ 3x + 12 = 2x + 24
⇒ 3x – 2x = 24 – 12
⇒ x = 12
Hence, the present age of the son is 12 years and his father’s age is (3 × 12) = 36 years.
(20) Let the number of Rs 5 notes = x and Number Rs 10 = 10(90 – x)
∴ 5x + 10(90 – x) = 500
⇒ 5x + 900 – 10x = 500
⇒ – 5x = 500 – 900 = – 400
⇒ x = 400/5
⇒ x = 80
Hence, the number of Rs 5 notes is 80 and Rs 10 notes = (90 – 80) = 10.
Done in simple and understandable method.Excellent
Gud
thank u made homework easy