NCERT Solutions for Class 8 Chapter 2 Linear Equations in One Variable Maths

Page No: 23

Exercise 2.1

Solve the following equations.
(1) x – 2 = 7
(2) y + 3 = 10
(3) 6 = z + 2
(4) 3/7 + x = 17/7
(5) 6x = 12
(6) t/5 = 10
(7) 2x/3 = 18 
(8) 1.6 = y/1.5
(9) 7x – 9 = 16
(10) 14y – 8 = 13
(11) 17 + 6p = 9
(12) x/3 + 1 = 7/15

Answer

(1) x - 2 = 7
⇒ x = 7 + 2
⇒ x = 9

(2)  y + 3 = 10
⇒ y = 10 - 3
⇒ y = 7

(3) 6 = z + 2
⇒ z + 2 = 6
⇒ z = 6 - 2
⇒ z = 4

(4) 3/7 + x = 17/7
⇒ x = 17/7 - 3/7
⇒ x = (17 - 3)/7
⇒ x = 14/7
⇒ x = 2

(5) 6x = 12
⇒ x = 12/6
⇒ x = 2

(6) t/5 = 10
⇒ t = 10 × 5
⇒ t = 50

(7) 2x/3 = 18
⇒ 2x = 18 × 3
⇒ x = 54/2
⇒ x = 27

(8) 1.6 = y/1.5
⇒ y/1.5 = 1.6
⇒ y = 1.6 × 1.5
⇒ y = 2.4

(9) 7x – 9 = 16
⇒ 7x = 16 + 9
⇒ x = 25/7

(10) 14y – 8 = 13
⇒ 14y = 13 + 8
⇒ 14y = 21
⇒ y = 21/14
⇒ y = 3/2

(11) 17 + 6p = 9
⇒ 6p = 9 - 17
⇒ 6p = -8
⇒ p = -8/6
⇒ p = -4/3

(12) x/3 + 1 = 7/15
⇒ x/3 = 7/15 - 1
⇒ x/3 = 7/15 - 15/15
⇒ x/3 = (7-15)/15
⇒ x/3 = -8/15
⇒ x = -8/15 × 3
⇒ x = -8/5

Page No: 28

Exercise 2.2

1. If you subtract 1/2 from a number and multiply the result by 1/2, you get  1/8. What is the number?

Answer

Let the number be x.
A/q,
(x - 1/2) × 1/2 = 1/8
⇒ x/2 - 1/4 = 1/8
⇒ x/2 = 1/8 + 1/4
⇒ x/2 = 1/8 + 2/8
⇒ x/2 = (1+2)/8
⇒ x = 3/8 × 2
⇒ x = 6/8 = 3/4

2. The perimeter of a rectangular swimming pool is 154 m. Its length is 2 m more than twice its breadth. What are the length and the breadth of the pool?

Answer

Given,
Perimeter of rectangular swimming pool = 154 m
Let the breadth of rectangle be x.
A/q,
Length of the rectangle = 2x + 2
Perimeter = 2(length + breadth)
⇒ 2(2x + 2 + x) = 154 m
⇒ 2(3x + 2) = 154
⇒ 3x + 2 = 154/2
⇒ 3x = 77 - 2
⇒ x = 75/3
⇒ x = 25 m
Thus,
Breadth = x = 25 m
Length = 2x + 2 = 50 + 2 = 52 m

3. The base of an isosceles triangle is 4/3 cm. The perimeter of the triangle is 62/15 cm. What is the length of either of the remaining equal sides?

Answer

Base of isosceles triangle = 4/3 cm
Perimeter of triangle = 62/15 cm
Let the length of equal sides of triangle be x.
A/q,
4/3 + x + x = 62/15 cm
⇒ 2x = (62/15 - 4/3) cm
⇒ 2x = (62 - 20)/15 cm
⇒ 2x = 42/15 cm
⇒ x = 42/15 × 1/2
⇒ x = 42/30 cm
⇒ x =7/5 cm
The length of either of the remaining equal sides are 7/5 cm.

4. Sum of two numbers is 95. If one exceeds the other by 15, find the numbers.

Answer

Let the one of the number be x.
Then, other number will be x + 15
A/q,
x + x + 15 = 95
⇒ 2x + 15 = 95
⇒ 2x = 80
⇒ x = 40
First number = x = 40
Other number = x + 15 = 40 + 15 = 55

5. Two numbers are in the ratio 5:3. If they differ by 18, what are the numbers?

Answer

Let the two numbers be 5x and 3x.
A/q,
5x - 3x = 18
⇒ 2x = 18
⇒ x = 9
Thus, the numbers are 5x = 45 and 3x = 27.

6. Three consecutive integers add up to 51. What are these integers?

Answer

Let the three consecutive integers are x, x+1 and x+2.
A/q,
x + (x+1) + (x+2) = 51
⇒ 3x + 3 = 51
⇒ 3x = 51 - 3
⇒ 3x = 48
⇒ x = 16
Thus, the integers are x = 16, x+1 = 17 and x+2 = 18

7. The sum of three consecutive multiples of 8 is 888. Find the multiples.

Answer

Let the three consecutive multiples of 8 are 8x, 8(x+1) and 8(x+2).
A/q,
8x + 8(x+1) + 8(x+2) = 888
⇒ 8 (x + x+1 + x+2) = 888    (Taking 8 as common)
⇒ 8 (3x + 3) = 888
⇒ 3x + 3 = 888/8
⇒ 3x + 3 = 111
⇒ 3x = 108
⇒ x = 36
Thus, the three consecutive multiples of 8 are 8x = 8 × 36 = 288,
8(x+1) = 8 × (36+1) = 8 × 37 = 296 and
8(x+2) = 8 × (36+2) = 8 × 38 = 304

8. Three consecutive integers are such that when they are taken in increasing order and multiplied by 2, 3 and 4 respectively, they add up to 74. Find these numbers.

Answer

Let the three consecutive integers are x, x+1 and x+2.
A/q,
2x + 3(x+1) + 4(x+2) = 74
⇒ 2x + 3x +3 + 4x + 8 = 74
⇒ 9x + 11 = 74
⇒ 9x = 74 - 11
⇒ x = 63/9
⇒ x = 7
Thus, the numbers are x = 7, x+1 = 8 and x+2 = 9

9. The ages of Rahul and Haroon are in the ratio 5:7. Four years later the sum of their ages will be 56 years. What are their present ages?

Answer

Let the ages of Rahul and Haroon be 5x and 7x.
Four years later their age will be (5x + 4) and (7x + 4) respectively.
A/q,
(5x + 4) + (7x + 4) = 56
⇒ 5x + 4 + 7x + 4 = 56
⇒ 12x + 8 = 56
⇒ 12x = 56 - 8
⇒ x = 48/12
⇒ x = 4
Present age of Rahul = 5x = 5×4 = 20
Present age of Haroon = 7x = 7×4 = 28

10. The number of boys and girls in a class are in the ratio 7:5. The number of boys is 8 more than the number of girls. What is the total class strength?

Answer

Let the number of boys be 7x and girls be 5x.
A/q,
7x = 5x + 8
⇒ 7x - 5x = 8
⇒ 2x = 8
⇒ x = 4
Number of boys = 7×4 = 28
Number of girls = 5×4 = 20

11. Baichung’s father is 26 years younger than Baichung’s grandfather and 29 years older than Baichung. The sum of the ages of all the three is 135 years. What is the age of each one of them?

Answer

Let the age of Baichung’s father be x.
Therefor, Age of Baichung’s grandfather = (x+26)
and, Age of Baichung = (x-29)
A/q,
x + (x+26) + (x-29) = 135
⇒ 3x + 26 - 29 = 135
⇒ 3x = 135 + 3
⇒ 3x = 138
⇒ x = 138/3
⇒ x = 46
Age of Baichung’s father = x = 46
Age of Baichung’s grandfather = (x+26) = 46 + 26 = 72
Age of Baichung = (x-29) = 46 - 29 = 17

12. Fifteen years from now Ravi’s age will be four times his present age. What is Ravi’s present age?

Answer

Let the present age of Ravi be x.
Fifteen years later, Ravi age will be x+15 years.
A/q,
x + 15 = 4x
⇒ 4x - x = 15
⇒ 3x = 15
⇒ x = 5
Present age of Ravi = 5 years.

13. A rational number is such that when you multiply it by 5/2 and add 2/3 to the product, you get -7/12. What is the number?

Answer

Let the rational be x.
A/q,
x × (5/2) + 2/3 = -7/12
⇒ 5x/2 + 2/3 = -7/12
⇒ 5x/2 = -7/12 - 2/3
⇒ 5x/2 = (-7 - 8)/12
⇒ 5x/2 = -15/12
⇒ 5x/2 = -5/4
⇒ x = (-5/4) × 2/5
⇒ x = -10/20
⇒ x = -1/2
Thus, the rational number is -1/2

14. Lakshmi is a cashier in a bank. She has currency notes of denominations ₹100, ₹50 and ₹10, respectively. The ratio of the number of these notes is 2:3:5. The total cash with Lakshmi is ₹4,00,000. How many notes of each denomination does she have?

Answer

Let the numbers of notes of  ₹100, ₹50 and ₹10 be 2x, 3x and 5x respectively.
Value of ₹100 = 2x × 100 = 200x
Value of ₹50 = 3x × 50 = 150x
Value of ₹10 = 5x × 10 = 50x
A/q,
200x + 150x + 50x = 4,00,000
⇒ 400x = 4,00,000
⇒ x = 4,00,000/400
⇒ x = 1000
Numbers of ₹100 notes = 2x = 2000
Numbers of ₹50 notes = 3x = 3000
Numbers of ₹10 notes = 5x = 5000

15. I have a total of ₹300 in coins of denomination ₹1, ₹2 and ₹5. The number of ₹2 coins is 3 times the number of ₹5 coins. The total number of coins is 160. How many coins of each denomination are with me?

Answer

Let the number of ₹5 coins be x.
Therefor, number ₹2 coins = 3x
and, number of ₹1 coins = (160 - 4x)
Now,
Value of ₹5 coins = x × 5 = 5x
Value of ₹2 coins = 3x × 2 = 6x
Value of ₹1 coins = (160 - 4x) × 1 = (160 - 4x)
A/q,
5x + 6x + (160 - 4x) = 300
⇒ 11x + 160 - 4x = 300
⇒ 7x = 140
⇒ x = 140/7
⇒ x = 20
Number of ₹5 coins = x = 20
Number of ₹2 coins = 3x = 60
Number of ₹1 coins = (160 - 4x) = 160 - 80 = 80

16. The organisers of an essay competition decide that a winner in the competition gets a prize of ₹100 and a participant who does not win gets a prize of ₹25. The total prize money distributed is ₹3,000. Find the number of winners, if the total number of participants is 63.

Answer

Let the numbers of winner be x.
Therefor, number of participant didn't win = 63 - x
Total money given to the winner = x × 100 = 100x
Total money given to participant didn't win = 25×(63-x)
A/q,
100x + 25×(63-x) = 3,000
⇒ 100x + 1575 - 25x = 3,000
⇒ 75x = 3,000 - 1575
⇒ 75x = 1425
⇒ x = 1425/75
⇒ x = 19
Thus, the numbers of winners are 19.

Page No: 30

Exercise 2.3

Solve the following equations and check your results.
(1) 3x = 2x + 18
(2) 5t – 3 = 3t – 5
(3) 5x + 9 = 5 + 3x
(4) 4z + 3 = 6 + 2z 
(5) 2x – 1 = 14 – x
(6) 8x + 4 = 3 (x – 1) + 7
(7) x = 4/5(x + 10)
(8) 2x/3 + 1 = 7x/15 + 3
(9) 2y + 5/3 = 26/3 - y
(10)  3m = 5 m – 8/5

Answer

(1) 3x = 2x + 18
⇒ 3x - 2x = 18
⇒ x = 18
Putting the value of x in RHS and LHS we get,
3 × 18 = (2 × 18)+18
⇒ 54 = 54
⇒ LHS = RHS

(2) 5t – 3 = 3t – 5
⇒ 5t - 3t = -5 + 3
⇒ 2t = -2
⇒ t = -1
Putting the value of t in RHS and LHS we get,
5×(-1) - 3 = 3×(-1) - 5
⇒ -5 - 3 = -3 - 5
⇒ -8 = -8
⇒ LHS = RHS

(3) 5x + 9 = 5 + 3x
⇒ 5x - 3x = 5 - 9
⇒ 2x = -4
⇒ x = -2
Putting the value of x in RHS and LHS we get,
5×(-2) + 9 = 5 + 3×(-2)
⇒ -10 + 9 = 5 + (-6)
⇒ -1 = -1
⇒ LHS = RHS

(4) 4z + 3 = 6 + 2z
⇒ 4z - 2z = 6 - 3
⇒ 2z = 3
⇒ z = 3/2
Putting the value of z in RHS and LHS we get,
(4 × 3/2) + 3 = 6 + (2 × 3/2)
⇒ 6 + 3 = 6 + 3
⇒ 9 = 9
⇒ LHS = RHS

(5) 2x – 1 = 14 – x
⇒ 2x + x = 14 + 1
⇒ 3x = 15
⇒ x = 5
Putting the value of x in RHS and LHS we get,
(2×5) - 1 = 14 - 5
⇒ 10 - 1 = 9
⇒ 9 = 9
⇒ LHS = RHS

(6) 8x + 4 = 3 (x – 1) + 7
⇒ 8x + 4 = 3x – 3 + 7
⇒ 8x + 4 = 3x + 4
⇒ 8x - 3x = 4 - 4
⇒ 5x = 0
⇒ x = 0
Putting the value of x in RHS and LHS we get,
(8×0) + 4 = 3 (0 – 1) + 7
⇒ 0 + 4 = 0 - 3 + 7
⇒ 4 = 4
⇒ LHS = RHS

(7) x = 4/5(x + 10)
⇒ x = 4x/5 + 40/5
⇒ x - 4x/5 = 8
⇒ (5x - 4x)/5 = 8
⇒ x = 8 × 5
⇒ x = 40
Putting the value of x in RHS and LHS we get,
40 = 4/5(40 + 10)
⇒ 40 = 4/5 × 50
⇒ 40 = 200/5
⇒ 40 = 40
⇒ LHS = RHS

(8) 2x/3 + 1 = 7x/15 + 3
2x/3 - 7x/15 = 3 - 1
⇒ (10x - 7x)/15 = 2
⇒ 3x = 2 × 15
⇒ 3x = 30
⇒ x = 10
Putting the value of x in RHS and LHS we get,
(2×10)/3 + 1 = (7×10)/15 + 3
⇒ 20/3 + 1 = 70/15 + 3
⇒ (20 + 3)/3 = (70 + 45)/15
⇒ 23/3 = 115/15
⇒ 23/3 = 23/3
⇒ LHS = RHS

(10) 3m = 5 m – 8/5
⇒ 3m - 5m = -8/5
⇒ -2m = -8/5

⇒-2m × 5 = -8
⇒ -10m = -8
⇒ m = -8/-10
⇒ m = 4/5
Putting the value of m in RHS and LHS we get,
3 × 4/5 = (5 × 4/5) – 8/5
⇒ 12/5 = 4 - 8/5
⇒ 12/5 = (20 - 8)/5
⇒ 12/5 = 12/5
⇒ LHS = RHS

Page No: 31

Exercise 2.4

1. Amina thinks of a number and subtracts 5/2 from it. She multiplies the result by 8. The result now obtained is 3 times the same number she thought of. What is the number?

Answer

Let the number be x.
A/q,
(x - 5/2) × 8 = 3x
⇒ 8x - 40/2 = 3x
⇒ 8x - 3x = 40/2
⇒ 5x = 20
⇒ x = 4
Thus, the number is 4.

2. A positive number is 5 times another number. If 21 is added to both the numbers, then one of the new numbers becomes twice the other new number. What are the numbers?

Answer

Let one of the positive number be x then other number will be 5x.
A/q,
5x + 21 = 2(x + 21)
⇒ 5x + 21 = 2x + 42
⇒ 5x - 2x = 42 - 21
⇒ 3x = 21
⇒ x = 7
One number = x = 7
Other number = 5x = 5×7 = 35
The two numbers are 5 and 35.

3. Sum of the digits of a two-digit number is 9. When we interchange the digits, it is found that the resulting new number is greater than the original number by 27. What is the two-digit number?

Answer

Let the digit at tens place be x then digit at ones place will be (9-x).
Original two digit number = 10x + (9-x)
After interchanging the digits, the new number = 10(9-x) + x
A/q,
10x + (9-x) + 27 = 10(9-x) + x
⇒ 10x + 9 - x + 27 = 90 - 10x + x
⇒ 9x + 36 = 90 - 9x
⇒ 9x + 9x = 90 - 36
⇒ 18x = 54
⇒ x = 3
Original number = 10x + (9-x) = (10×3) + (9-3) = 30 + 6 = 36
Thus, the number is 36.

4. One of the two digits of a two digit number is three times the other digit. If you interchange the digits of this two-digit number and add the resulting number to the original number, you get 88. What is the original number?

Answer

Let the digit at tens place be x then digit at ones place will be 3x.
Original two digit number = 10x + 3x
After interchanging the digits, the new number = 30x + x
A/q,
(30x + x) + (10x + 3x) = 88
⇒ 31x + 13x = 88
⇒ 44x = 88
⇒ x = 2
Original number = 10x + 3x = 13x = 13×2 = 26

5. Shobo’s mother’s present age is six times Shobo’s present age. Shobo’s age five years from now will be one third of his mother’s present age. What are their present ages?

Answer

Let the present age of Shobo be x then age of her mother will be 6x.
Shobo's age after 5 years = x + 5
A/q,
(x + 5) = 1/3 × 6x
⇒ x + 5 = 2x
⇒ 2x - x = 5
⇒ x = 5
Present age of Shobo = x = 5 years
Present age of Shobo's mother = 6x = 30 years

6. There is a narrow rectangular plot, reserved for a school, in Mahuli village. The length and breadth of the plot are in the ratio 11:4. At the rate ₹100 per metre it will cost the village panchayat ₹75000 to fence the plot. What are the dimensions of the plot?

Answer

Let the length of the rectangular plot be 11x and breadth be 4x.
Rate of fencing per metre = ₹100
Total cost of fencing = ₹75000
Perimeter of the plot = 2(l+b) = 2(11x + 4x) = 2×15x = 30x
Total amount of fencing = (30x × 100)
A/q,
(30x × 100) = 75000
⇒ 3000x = 75000
⇒ x = 75000/3000
⇒ x = 25
Length of the plot = 11x = 11×25 = 275
Breadth of the plot = 4x = 4×25 = 100

7. Hasan buys two kinds of cloth materials for school uniforms, shirt material that costs him ₹50 per metre and trouser material that costs him ₹90 per metre. For every 3 meters of the shirt material he buys 2 metres of the trouser material. He sells the materials at 12% and 10% profit respectively. His total sale is ₹36,600. How much trouser material did he buy?

Answer

Let 2x m of trouser material and 3x m of shirt material be bought by him.
Selling price of shirt material per metre = ₹ 50 + 50×(12/100) = ₹ 56
Selling price of trouser material per metre = ₹ 90 + 90×(10/100) = ₹99
Total amount of sale = ₹36,600
A/q,
(2x × 99) + (3x × 56) = 36600
⇒ 198x + 168x = 36600
⇒ 366x = 36600
⇒ x = 36600/366
⇒ x =100
Total trouser material he bought = 2x = 2×100 = 200 m.

Page No: 32

8. Half of a herd of deer are grazing in the field and three fourths of the remaining are playing nearby. The rest 9 are drinking water from the pond. Find the number of deer in the herd.

Answer

Let the total number of deer be x.
Deer grazing in the field = x/2
Deer playing nearby = 3/4(x - x/2) = 3/4×x/2 = 3x/8
Deer drinking water = 9
A/q,
x/2 + 3x/8 + 9 = x
⇒ (4x + 3x)/8 + 9 = x
⇒ 7x/8 + 9 = x
⇒ x - 7x/8 = 9
⇒ (8x - 7x)/8 = 9
⇒ x = 9×8
⇒ x = 72

9. A grandfather is ten times older than his granddaughter. He is also 54 years older than her. Find their present ages.

Answer

Let the age of granddaughter be x and grandfather be 10x.
Also, he is 54 years older than her.
A/q,
10x = x + 54
⇒ 10x - x = 54
⇒ 9x = 54
⇒ x = 6
Age of grandfather = 10x = 10×6 = 60 years.
Age of granddaughter = x = 6 years.

10. Aman’s age is three times his son’s age. Ten years ago he was five times his son’s age. Find their present ages.

Answer

Let the age of Aman's son be x then age of Aman will be 3x.
A/q,
5(x - 10) = 3x - 10
⇒ 5x - 50 = 3x - 10
⇒ 5x - 3x = -10 + 50
⇒ 2x = 40
⇒ x = 20
Aman's son age = x = 20 years
Aman age = 3x = 3×20 = 60 years

Page No: 33

Exercise 2.5

Solve the following linear equations.
(1) x/2 - 1/5 = x/3 + 1/4
(2) n/2 - 3n/4 + 5n/6 = 21
(3) x + 7 - 8x/3 = 17/6 - 5x/2
(4) (x - 5)/3 = (x - 3)/5
(5) (3t - 2)/4 - (2t + 3)/3 = 2/3 - t
(6) m - (m - 1)/2 = 1 - (m - 2)/3

Answer

(1) x/2 - 1/5 = x/3 + 1/4
⇒ x/2 - x/3 = 1/4 + 1/5
⇒ (3x - 2x)/6 = (5 + 4)/20
⇒ 3x - 2x = 9/20 × 6
⇒ x = 54/20
⇒ x = 27/10

(2) n/2 - 3n/4 + 5n/6 = 21
⇒ (6n - 9n + 10n)/12 = 21
⇒ 7n/12 = 21
⇒ 7n = 21×12
⇒ n = 252/7
⇒ n = 36

(3) x + 7 - 8x/3 = 17/6 - 5x/2
⇒ x - 8x/3 + 5x/2 = 17/6 - 7
⇒ (6x - 16x + 15x)/6 = (17 - 42)/6
⇒ 5x/6 = -25/6
⇒ 5x = -25
⇒ x = -5

(4) (x - 5)/3 = (x - 3)/5
⇒ x/3 - 15 = x/5 - 15
⇒ x/3 - x/5 = -15 + 15
⇒ (5x - 3x)/15 = 0
⇒ 2x/15 = 0
⇒ x = 0

(5) (3t - 2)/4 - (2t + 3)/3 = 2/3 - t
⇒ 3t/4 - 1/2 - (2t/3 + 1) = 2/3 - t
⇒ 3t/4 - 1/2 - 2t/3 - 1 = 2/3 - t
⇒ 3t/4 - 2t/3 + t = 2/3 + 1 + 1/2
⇒ (9t - 8t + 12t)/12 = 2/3 + 3/2
⇒ 13t/12 = (4 + 9)/6
⇒ 13t/12 = 13/6
⇒ t = 13/6 × 12/13
⇒ t = 12/6 = 2

(6) m - (m - 1)/2 = 1 - (m - 2)/3
⇒ m - (m/2 - 1/2) = 1 - (m/3 - 2/3)
⇒ m - m/2 + 1/2 = 1 - m/3 + 2/3
⇒ m - m/2 + m/3 = 1 + 2/3 - 1/2
⇒ m/2 + m/3 = 1/2 + 2/3
⇒ (3m + 2m)/6 = (3 + 4)/6
⇒ 5m/6 = 7/6
⇒ m = 7/6 × 6/5
⇒ m = 7/5

Page No: 34

Simplify and solve the following linear equations.
(7) 3(t – 3) = 5(2t + 1)
(8) 15(y – 4) –2(y – 9) + 5(y + 6) = 0
(9) 3(5z – 7) – 2(9z – 11) = 4(8z – 13) – 17
(10) 0.25(4f – 3) = 0.05(10f – 9)

Answer

(7) 3(t – 3) = 5(2t + 1)
⇒ 3t - 9 = 10t + 5
⇒ 3t - 10t = 5 + 9
⇒ -7t = 14
⇒ t = 14/-7
⇒ t = -2

(8) 15(y – 4) –2(y – 9) + 5(y + 6) = 0
⇒ 15y - 60 -2y + 18 + 5y + 30 = 0
⇒ 15y - 2y + 5y = 60 - 18 - 30
⇒ 18y = 12
⇒ y = 12/18
⇒ y = 2/3

(9) 3(5z – 7) – 2(9z – 11) = 4(8z – 13) – 17
⇒ 15z - 21 - 18z + 22 = 32z - 52 - 17
⇒ 15z - 18z - 32z = -52 - 17 + 21 - 22
⇒ -35z = -70
⇒ z = -70/-35
⇒ z = 2

(10) 0.25(4f – 3) = 0.05(10f – 9)
⇒ f - 0.75 = 0.5f - 0.45
⇒ f - 0.5f = -0.45 + 0.75
⇒ 0.5f = 0.30
⇒ f = 0.30/0.5
⇒ f = 30/5 = 6

Page No: 35

Exercise 2.6

Solve the following equations.
(1) (8x - 3)/3x = 2
(2) 9x/(7 - 6x) = 15
(3) z/(z + 15) = 4/9
(4) (3y + 4)/(2 - 6y) = -2/5
(5) (7y + 4)/(y + 2) = -4/3

Answer

(1) (8x - 3)/3x = 2
⇒ 8x/3x - 3/3x = 2
⇒ 8/3 - 1/x = 2
⇒ 8/3 - 2 = 1/x
⇒ (8 - 6)/3 = 1/x
⇒ 2/3 = 1/x
⇒ x = 3/2

(2) 9x/(7 - 6x) = 15
⇒ 9x = 15(7 - 6x)
⇒ 9x = 105 - 90x
⇒ 9x + 90x = 105
⇒ 99x = 105
⇒ x = 105/99 = 35/33

(3) z/(z + 15) = 4/9
⇒ z = 4/9(z + 15)
⇒ 9z = 4(z + 15)
⇒ 9z = 4z + 60
⇒ 9z - 4z = 60
⇒ 5z = 60
⇒ z = 12

(4) (3y + 4)/(2 - 6y) = -2/5
⇒ 3y + 4 = -2/5(2 - 6y)
⇒ 5(3y + 4) = -2(2 - 6y)
⇒ 15y + 20 = -4 + 12y
⇒ 15y - 12y = -4 - 20
⇒ 3y = -24
⇒ y = -8

(5) (7y + 4)/(y + 2) = -4/3
⇒ 7y + 4 = -4/3(y + 2)
⇒ 3(7y + 4) = -4(y + 2)
⇒ 21y + 12 = -4y - 8
⇒ 21y + 4y = -8 - 12
⇒ 25y = -20
⇒ y = 20/25 = 4/5

6. The ages of Hari and Harry are in the ratio 5:7. Four years from now the ratio of their ages will be 3:4. Find their present ages.

Answer

Let the age of Hari be 5x and Hari be 7x.
After 4years,
Age of Hari = 5x + 4
Age of Harry = 7x + 4
A/q,
(5x + 4)/(7x + 4) = 3/4
⇒ 4(5x + 4) = 3(7x + 4)
⇒ 20x + 16 = 21x + 12
⇒ 21x - 20x = 16 - 12
⇒ x = 4
Hari age = 5x = 5×4 = 20 years
Harry age = 7x = 7×4 = 28 years

7. The denominator of a rational number is greater than its numerator by 8. If the numerator is increased by 17 and the denominator is decreased by 1, the number obtained is 3/2. Find the rational number.

Answer

Let the numerator be x then denominator will be (x + 8).
A/q,
(x + 17)/(x + 8 - 1) = 3/2
⇒ (x + 17)/(x + 7) = 3/2
⇒ 2(x + 17) = 3(x + 7)
⇒ 2x + 34 = 3x + 21
⇒ 34 - 21 = 3x - 2x
⇒ 13 = x
The rational number is x/(x + 8) = 13/21

NCERT Solutions for Class 8 Maths
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