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# NCERT solutions for Class 8 Mathematics chapter 2 - Linear Equations in One Variable

## Chapter 2: Linear Equations in One Variable

Ex. 2.10Ex. 2.20Ex. 2.30Ex. 2.40Ex. 2.50Ex. 2.60

#### Chapter 2: Linear Equations in One Variable Exercise 2.10 solutions [Pages 23 - 24]

Ex. 2.10 | Q 1 | Page 23

Solve : x - 2 = 7

Ex. 2.10 | Q 2 | Page 23

Solve: y + 3 = 10

Ex. 2.10 | Q 3 | Page 23

Solve: 6 = z + 2

Ex. 2.10 | Q 4 | Page 23

Solve: 3/7 + x = 17/7

Ex. 2.10 | Q 5 | Page 23

Solve: 6x = 12

Ex. 2.10 | Q 6 | Page 23

Solve: t/5 = 10

Ex. 2.10 | Q 7 | Page 23

Solve: (2x)/3 = 18

Ex. 2.10 | Q 8 | Page 23

Solve: 1.6 = y/1.5

Ex. 2.10 | Q 9 | Page 23

Solve: 7x – 9 = 16

Ex. 2.10 | Q 10 | Page 24

Solve: 14y – 8 = 13

Ex. 2.10 | Q 11 | Page 24

Solve: 17 + 6p = 9

Ex. 2.10 | Q 12 | Page 24

Solve: x/3 + 1 = 7/15

#### Chapter 2: Linear Equations in One Variable Exercise 2.20 solutions [Page 28]

Ex. 2.20 | Q 1 | Page 28

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

Ex. 2.20 | Q 2 | Page 28

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?

Ex. 2.20 | Q 3 | Page 28

The base of an isosceles triangle is 4/3 cm. The perimeter of the triangle is 4 2/15 cm. What is the length of either of the remaining equal sides?

Ex. 2.20 | Q 4 | Page 28

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

Ex. 2.20 | Q 5 | Page 28

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

Ex. 2.20 | Q 6 | Page 28

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

Ex. 2.20 | Q 7 | Page 28

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

Ex. 2.20 | Q 8 | Page 28

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.

Ex. 2.20 | Q 9 | Page 28

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?

Ex. 2.20 | Q 10 | Page 28

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?

Ex. 2.20 | Q 11 | Page 28

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?

Ex. 2.20 | Q 12 | Page 28

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

Ex. 2.20 | Q 13 | Page 28

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

Ex. 2.20 | Q 14 | Page 28

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

Ex. 2.20 | Q 15 | Page 28

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

Ex. 2.20 | Q 16 | Page 28

The organizers of an essay competition decide that a winner in the competition gets a prize of Rs 100 and a participant who does not win gets a prize of Rs 25. The total prize money distributed is Rs 3000. Find the number of winners, if the total number of participants is 63.

#### Chapter 2: Linear Equations in One Variable Exercise 2.30 solutions [Page 30]

Ex. 2.30 | Q 1 | Page 30

Solve and check result: 3x = 2x + 18

Ex. 2.30 | Q 2 | Page 30

Solve and check result: 5t − 3 = 3t − 5

Ex. 2.30 | Q 3 | Page 30

Solve and check result: 5x + 9 = 5 + 3x

Ex. 2.30 | Q 4 | Page 30

Solve and check result: 4z + 3 = 6 + 2z

Ex. 2.30 | Q 5 | Page 30

Solve and check result: 2x − 1 = 14 − x

Ex. 2.30 | Q 6 | Page 30

Solve and check result: 8x + 4 = 3(x − 1) + 7

Ex. 2.30 | Q 7 | Page 30

Solve and check result: x = 4/5 (x + 10)

Ex. 2.30 | Q 8 | Page 30

Solve and check result: (2x)/3 + 1 = (7x)/15 + 3

Ex. 2.30 | Q 9 | Page 30

Solve and check result: 2y + 5/3 = 26/3 - y

Ex. 2.30 | Q 10 | Page 30

Solve and check result: 3m = 5m - 8/5

#### Chapter 2: Linear Equations in One Variable Exercise 2.40 solutions [Pages 31 - 32]

Ex. 2.40 | Q 1 | Page 31

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?

Ex. 2.40 | Q 2 | Page 31

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?

Ex. 2.40 | Q 3 | Page 31

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?

Ex. 2.40 | Q 4 | Page 31

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

Ex. 2.40 | Q 5 | Page 31

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 this mother’s present age. What are their present ages?

Ex. 2.40 | Q 6 | Page 31

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 Rs 100 per metre it will cost the village panchayat Rs 75, 000 to fence the plot. What are the dimensions of the plot?

Ex. 2.40 | Q 7 | Page 31

Hasan buys two kinds of cloth materials for school uniforms, shirt material that costs him Rs 50 per metre and trouser material that costs him Rs 90 per metre. For every 2 meters of the trouser material he buys 3 metres of the shirt material. He sells the materials at 12% and 10% profit respectively. His total sale is Rs 36660. How much trouser material did he buy?

Ex. 2.40 | Q 8 | Page 32

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.

Ex. 2.40 | Q 9 | Page 32

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

Ex. 2.40 | Q 10 | Page 32

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.

#### Chapter 2: Linear Equations in One Variable Exercise 2.50 solutions [Pages 33 - 34]

Ex. 2.50 | Q 1 | Page 33

Solve the linear equation x/2 - 1/5 = x/3 + 1/4

Ex. 2.50 | Q 2 | Page 33

Solve the linear equation n/2 - (3n)/4 + (5n)/6 = 21

Ex. 2.50 | Q 3 | Page 33

Solve the linear equation x + 7 -  (8x)/3 = 17/6 - (5x)/2

Ex. 2.50 | Q 4 | Page 34

Solve the linear equation (x - 5)/3 = (x - 3)/5

Ex. 2.50 | Q 5 | Page 34

Solve the linear equation (3t - 2)/4 - (2t + 3)/3 = 2/3 - t

Ex. 2.50 | Q 6 | Page 34

Solve the linear equation m - (m -1)/2 = 1 - (m - 2)/3

Ex. 2.50 | Q 7 | Page 34

Simplify and solve the linear equation 3(t - 3) = 5(2t + 1)

Ex. 2.50 | Q 8 | Page 34

Simplify and solve the linear equation  15(y - 4) - 2(y - 9) + 5(y + 6) = 0

Ex. 2.50 | Q 9 | Page 34

Simplify and solve the linear equation 3(5z – 7) – 2(9z – 11) = 4(8z – 13) – 17

Ex. 2.50 | Q 10 | Page 34

Simplify and solve the linear equation  0.25(4f – 3) = 0.05(10f – 9)

#### Chapter 2: Linear Equations in One Variable Exercise 2.60 solutions [Page 35]

Ex. 2.60 | Q 1 | Page 35

Solve: (8x - 3)/(3x) = 2

Ex. 2.60 | Q 2 | Page 35

Solve: (9x)/(7 - 6x) = 15

Ex. 2.60 | Q 3 | Page 35

Solve:  z/(z + 15) = 4/9

Ex. 2.60 | Q 4 | Page 35

Solve: (3y + 4)/(2 - 6y) = (-2)/5

Ex. 2.60 | Q 5 | Page 35

Solve: (7y + y)/(y + 2) = (-4)/3

Ex. 2.60 | Q 6 | Page 35

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.

Ex. 2.60 | Q 7 | Page 35

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.

## Chapter 2: Linear Equations in One Variable

Ex. 2.10Ex. 2.20Ex. 2.30Ex. 2.40Ex. 2.50Ex. 2.60

## NCERT solutions for Class 8 Mathematics chapter 2 - Linear Equations in One Variable

NCERT solutions for Class 8 Maths chapter 2 (Linear Equations in One Variable) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Mathematics Textbook for Class 8 solutions in a manner that help students grasp basic concepts better and faster.

Further, we at shaalaa.com are providing such solutions so that students can prepare for written exams. NCERT textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Class 8 Mathematics chapter 2 Linear Equations in One Variable are Some More Applications, Solving Equations Having the Variable on Both Sides, Equations Reducible to the Linear Form, Reducing Equations to Simpler Form, Some Applications, Solving Equations Which Have Linear Expressions on One Side and Numbers on the Other Side, Introduction of Linear Equation.

Using NCERT Class 8 solutions Linear Equations in One Variable exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in NCERT Solutions are important questions that can be asked in the final exam. Maximum students of CBSE Class 8 prefer NCERT Textbook Solutions to score more in exam.

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