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# RD Sharma solutions for Class 8 Mathematics chapter 9 - Linear Equation in One Variable

## Chapter 9: Linear Equation in One Variable

Ex. 9.10Ex. 9.20Ex. 9.30Ex. 9.40

#### Chapter 9: Linear Equation in One Variable Exercise 9.10 solutions [Page 5]

Ex. 9.10 | Q 1 | Page 5

Solve the following equation and also verify your solution:
$9\frac{1}{4} = y - 1\frac{1}{3}$

Ex. 9.10 | Q 2 | Page 5

Solve the following equation and also verify your solution:
$\frac{5x}{3} + \frac{2}{5} = 1$

Ex. 9.10 | Q 3 | Page 5

Solve the following equation and also verify your solution:
$\frac{x}{2} + \frac{x}{3} + \frac{x}{4} = 13$

Ex. 9.10 | Q 4 | Page 5

Solve the following equation and also verify your solution:

$\frac{x}{2} + \frac{x}{8} = \frac{1}{8}$
Ex. 9.10 | Q 5 | Page 5

Solve the following equation and also verify your solution:
$\frac{2x}{3} - \frac{3x}{8} = \frac{7}{12}$

Ex. 9.10 | Q 6 | Page 5

Solve the following equation and also verify your solution:
(x + 2)(x + 3) + (x − 3)(x − 2) − 2x(x + 1) = 0

Ex. 9.10 | Q 7 | Page 5

Solve the following equation and also verify your solution:

$\frac{x}{2} - \frac{4}{5} + \frac{x}{5} + \frac{3x}{10} = \frac{1}{5}$
Ex. 9.10 | Q 8 | Page 5

Solve the following equation and also verify your solution:
$\frac{7}{x} + 35 = \frac{1}{10}$

Ex. 9.10 | Q 9 | Page 5

Solve the following equation and also verify your solution:

$\frac{2x - 1}{3} - \frac{6x - 2}{5} = \frac{1}{3}$
Ex. 9.10 | Q 10 | Page 5

Solve the following equation and also verify your solution:
13(y − 4) − 3(y − 9) − 5(y + 4) = 0

Ex. 9.10 | Q 11 | Page 5

Solve the following equation and also verify your solution:
$\frac{2}{3}(x - 5) - \frac{1}{4}(x - 2) = \frac{9}{2}$

#### Chapter 9: Linear Equation in One Variable Exercise 9.20 solutions [Pages 11 - 12]

Ex. 9.20 | Q 1 | Page 11

Solve the following equation and also check your result:
$\frac{2x + 5}{3} = 3x - 10$

Ex. 9.20 | Q 2 | Page 11

Solve the following equation and also check your result:

$\frac{a - 8}{3} = \frac{a - 3}{2}$
Ex. 9.20 | Q 3 | Page 11

Solve the following equation and also check your result:
$\frac{7y + 2}{5} = \frac{6y - 5}{11}$

Ex. 9.20 | Q 4 | Page 11

Solve the following equation and also check your result:
$x - 2x + 2 - \frac{16}{3}x + 5 = 3 - \frac{7}{2}x$

Ex. 9.20 | Q 5 | Page 11

Solve the following equation and also check your result:
$\frac{1}{2}x + 7x - 6 = 7x + \frac{1}{4}$

Ex. 9.20 | Q 6 | Page 11

Solve the following equation and also check your result:

$\frac{3}{4}x + 4x = \frac{7}{8} + 6x - 6$
Ex. 9.20 | Q 7 | Page 11

Solve the following equation and also check your result:
$\frac{7}{2}x - \frac{5}{2}x = \frac{20}{3}x + 10$

Ex. 9.20 | Q 8 | Page 11

Solve the following equation and also check your result :
$\frac{6x + 1}{2} + 1 = \frac{7x - 3}{3}$

Ex. 9.20 | Q 9 | Page 11

Solve the following equation and also check your result:
$\frac{3a - 2}{3} + \frac{2a + 3}{2} = a + \frac{7}{6}$

Ex. 9.20 | Q 10 | Page 11

Solve the following equation and also check your result :

$x - \frac{(x - 1)}{2} = 1 - \frac{(x - 2)}{3}$
Ex. 9.20 | Q 11 | Page 11

Solve the following equation and also check your result:

$\frac{3x}{4} - \frac{(x - 1)}{2} = \frac{(x - 2)}{3}$

Ex. 9.20 | Q 12 | Page 11

Solve each of the following equation and also check your result in each case:
$\frac{5x}{3} - \frac{(x - 1)}{4} = \frac{(x - 3)}{5}$

Ex. 9.20 | Q 13 | Page 11

Solve the following equation and also check your result:
$\frac{(3x + 1)}{16} + \frac{(2x - 3)}{7} = \frac{(x + 3)}{8} + \frac{(3x - 1)}{14}$

Ex. 9.20 | Q 14 | Page 11

Solve each of the following equation and also check your result in each case:
$\frac{(1 - 2x)}{7} - \frac{(2 - 3x)}{8} = \frac{3}{2} + \frac{x}{4}$

Ex. 9.20 | Q 15 | Page 11

Solve the following equation and also check your result:

$\frac{9x + 7}{2} - \left( x - \frac{x - 2}{7} \right) = 36$
Ex. 9.20 | Q 16 | Page 11

Solve each of the following equation and also check your result in each case:
0.18(5x − 4) = 0.5x + 0.8

Ex. 9.20 | Q 17 | Page 11

Solve the following equation and also check your result:
$\frac{2}{3x} - \frac{3}{2x} = \frac{1}{12}$

Ex. 9.20 | Q 18 | Page 11

Solve the following equation and also check your result:
$\frac{4x}{9} + \frac{1}{3} + \frac{13}{108}x = \frac{8x + 19}{18}$

Ex. 9.20 | Q 19 | Page 12

Solve the following equation and also check your result:

$\frac{(45 - 2x)}{15} - \frac{(4x + 10)}{5} = \frac{(15 - 14x)}{9}$
Ex. 9.20 | Q 20 | Page 12

Solve the following equation and also check your result:
$5\left( \frac{7x + 5}{3} \right) - \frac{23}{3} = 13 - \frac{4x - 2}{3}$

Ex. 9.20 | Q 21 | Page 12

Solve the following equation and also check your result:

$\frac{7x - 1}{4} - \frac{1}{3}\left( 2x - \frac{1 - x}{2} \right) = \frac{10}{3}$
Ex. 9.20 | Q 22 | Page 12

Solve the following equation and also check your result:

$\frac{0 . 5(x - 0 . 4)}{0 . 35} - \frac{0 . 6(x - 2 . 71)}{0 . 42} = x + 6 . 1$
Ex. 9.20 | Q 23 | Page 12

Solve the following equation and also check your result:
$6 . 5x + \frac{19 . 5x - 32 . 5}{2} = 6 . 5x + 13 + \left( \frac{13x - 26}{2} \right)$

Ex. 9.20 | Q 24 | Page 12

Solve the following equation and also check your result:
(3x − 8)(3x + 2) − (4x − 11)(2x + 1) = (x − 3)(x + 7)

Ex. 9.20 | Q 25 | Page 12

Solve the following equation and also check your result:
[(2x + 3) + (x + 5)]2 + [(2x + 3) − (x + 5)]2 = 10x2 + 92

#### Chapter 9: Linear Equation in One Variable Exercise 9.30 solutions [Page 17]

Ex. 9.30 | Q 1 | Page 17

$\frac{2x - 3}{3x + 2} = - \frac{2}{3}$
Ex. 9.30 | Q 2 | Page 17

$\frac{2 - y}{y + 7} = \frac{3}{5}$
Ex. 9.30 | Q 3 | Page 17

$\frac{5x - 7}{3x} = 2$
Ex. 9.30 | Q 4 | Page 17

$\frac{3x + 5}{2x + 7} = 4$
Ex. 9.30 | Q 5 | Page 17

$\frac{2y + 5}{y + 4} = 1$
Ex. 9.30 | Q 6 | Page 17

$\frac{2x + 1}{3x - 2} = \frac{5}{9}$
Ex. 9.30 | Q 7 | Page 17

$\frac{1 - 9y}{19 - 3y} = \frac{5}{8}$
Ex. 9.30 | Q 8 | Page 17

$\frac{2x}{3x + 1} = - 3$
Ex. 9.30 | Q 9 | Page 17

$\frac{y - (7 - 8y)}{9y - (3 + 4y)} = \frac{2}{3}$
Ex. 9.30 | Q 10 | Page 17

$\frac{6}{2x - (3 - 4x)} = \frac{2}{3}$
Ex. 9.30 | Q 11 | Page 17

$\frac{2}{3x} - \frac{3}{2x} = \frac{1}{12}$
Ex. 9.30 | Q 12 | Page 17

$\frac{3x + 5}{4x + 2} = \frac{3x + 4}{4x + 7}$
Ex. 9.30 | Q 13 | Page 17

$\frac{7x - 2}{5x - 1} = \frac{7x + 3}{5x + 4}$
Ex. 9.30 | Q 14 | Page 17

$\left( \frac{x + 1}{x + 2} \right)^2 = \frac{x + 2}{x + 4}$
Ex. 9.30 | Q 15 | Page 17

$\left( \frac{x + 1}{x - 4} \right)^2 = \frac{x + 8}{x - 2}$

Ex. 9.30 | Q 16 | Page 17

$\frac{9x - 7}{3x + 5} = \frac{3x - 4}{x + 6}$
Ex. 9.30 | Q 17 | Page 17

$\frac{x + 2}{x + 5} = \frac{x}{x + 6}$
Ex. 9.30 | Q 18 | Page 17

$\frac{2x - (7 - 5x)}{9x - (3 + 4x)} = \frac{7}{6}$
Ex. 9.30 | Q 19 | Page 17

$\frac{15(2 - x) - 5(x + 6)}{1 - 3x} = 10$
Ex. 9.30 | Q 20 | Page 17

$\frac{x + 3}{x - 3} + \frac{x + 2}{x - 2} = 2$
Ex. 9.30 | Q 21 | Page 17

$\frac{(x + 2)(2x - 3) - 2 x^2 + 6}{x - 5} = 2$
Ex. 9.30 | Q 22 | Page 17

$\frac{x^2 - (x + 1)(x + 2)}{5x + 1} = 6$
Ex. 9.30 | Q 23 | Page 17

$\frac{(2x + 3) - (5x - 7)}{6x + 11} = - \frac{8}{3}$
Ex. 9.30 | Q 24.1 | Page 17

Find a positive value of x for which the given equation is satisfied:

$\frac{x^2 - 9}{5 + x^2} = - \frac{5}{9}$
Ex. 9.30 | Q 24.2 | Page 17

Find a positive value of x for which the given equation is satisfied:

$\frac{y^2 + 4}{3 y^2 + 7} = \frac{1}{2}$

#### Chapter 9: Linear Equation in One Variable Exercise 9.40 solutions [Pages 29 - 31]

Ex. 9.40 | Q 1 | Page 29

Four-fifth of a number is more than three-fourth of the number by 4. Find the number.

Ex. 9.40 | Q 2 | Page 29

The difference between the squares of two consecutive numbers is 31. Find the numbers.

Ex. 9.40 | Q 3 | Page 29

Find a number whose double is 45 greater than its half.

Ex. 9.40 | Q 4 | Page 29

Find a number such that when 5 is subtracted from 5 times the number, the result is 4 more than twice the number.

Ex. 9.40 | Q 5 | Page 29

A number whose fifth part increased by 5 is equal to its fourth part diminished by 5. Find the number.

Ex. 9.40 | Q 6 | Page 29

A number consists of two digits whose sum is 9. If 27 is subtracted from the number, its digits are reversed. Find the number.

Ex. 9.40 | Q 7 | Page 29

Divide 184 into two parts such that one-third of one part may exceed one-seventh of another part by 8.

Ex. 9.40 | Q 8 | Page 29

The numerator of a fraction is 6 less than the denominator. If 3 is added to the numerator, the fraction is equal to $\frac{2}{3}$. What is the original fraction equal to?

Ex. 9.40 | Q 9 | Page 29

A sum of Rs 800 is in the form of denominations of Rs 10 and Rs 20. If the total number of notes be 50, find the number of notes of each type.

Ex. 9.40 | Q 10 | Page 29

Seeta Devi has Rs 9 in fifty-paise and twenty five-paise coins. She has twice as many twenty-five paise coins as she has fifty-paise coins. How many coins of each kind does she have?

Ex. 9.40 | Q 11 | Page 30

Sunita is twice as old as Ashima. If six years is subtracted from Ashima's age and four years added to Sunita's age, then Sunita will be four times Ashima's age. How old were they two years ago?

Ex. 9.40 | Q 12 | Page 30

The ages of sonu and Monu are in the ratio 7 : 5. Ten years hence, the ratio of their ages will be 9 : 7. Find their present ages.

Ex. 9.40 | Q 13 | Page 30

Five years ago a man was seven times as old as his son. Five years hence, the father will be three times as old as his son. Find their present ages.

Ex. 9.40 | Q 14 | Page 30

I am currently 5 times as old as my son. In 6 years time I will be three times as old as he will be then. What are our ages now?

Ex. 9.40 | Q 15 | Page 30

I have Rs 1000 in ten and five rupee notes. If the number of ten rupee notes that I have is ten more than the number of five rupee notes, how many notes do I have in each denomination?

Ex. 9.40 | Q 16 | Page 30

At a party, colas, squash and fruit juice were offered to guests. A fourth of the guests drank colas, a third drank squash, two fifths drank fruit juice and just three did not drink any thing. How many guests were in all?

Ex. 9.40 | Q 17 | Page 30

There are 180 multiple choice questions in a test. If a candidate gets 4 marks for every correct answer and for every unattempted or wrongly answered question one mark is deducted from the total score of correct answers. If a candidate scored 450 marks in the test, how many questions did he answer correctly?

Ex. 9.40 | Q 18 | Page 30

A labourer is engaged for 20 days on the condition that he will receive Rs 60 for each day, he works and he will be fined Rs 5 for each day, he is absent. If he receives Rs 745 in all, for how many days he remained absent?

Ex. 9.40 | Q 19 | Page 30

Ravish has three boxes whose total weight is $60\frac{1}{2}$  kg. Box B weighs $3\frac{1}{2}$ kg more than box A and box C weighs $5\frac{1}{3}$ kg more than box B. Find the weight of box A.

Ex. 9.40 | Q 20 | Page 30

The numerator of a rational number is 3 less than the denominator. If the denominator is increased by 5 and the numerator by 2, we get the rational number 1/2.  Find the rational number.

Ex. 9.40 | Q 21 | Page 30

In a rational number, twice the numerator is 2 more than the denominator. If 3 is added to each, the numerator and the denominator, the new fraction is 2/3. Find the original number.

Ex. 9.40 | Q 22 | Page 30

The distance between two stations is 340 km. Two trains start simultaneously from these stations on parallel tracks to cross each other. The speed of one of them is greater than that of the other by 5 km/hr. If the distance between the two trains after 2 hours of their start is 30 km, find the speed of each train.

Ex. 9.40 | Q 23 | Page 30

A steamer goes downstream from one point to another in 9 hours. It covers the same distance upstream in 10 hours. If the speed of the stream be 1 km/hr, find the speed of the steamer in still water and the distance between the ports.

Ex. 9.40 | Q 24 | Page 30

Bhagwanti inherited Rs 12000.00. She invested part of it as 10% and the rest at 12%. Her annual income from these investments is Rs 1280.00. How much did she invest at each rate?

Ex. 9.40 | Q 25 | Page 30

The length of a rectangle exceeds its breadth by 9 cm. If length and breadth are each increased by 3 cm, the area of the new rectangle will be 84 cm2 more than that of the given rectangle. Find the length and breath of the given rectangle.

Ex. 9.40 | Q 26 | Page 31

The sum of the ages of Anup and his father is 100. When Anup is as old as his father now, he will be five times as old as his son Anuj is now. Anuj will be eight years older than Anup is now, when Anup is as old as his father. What are their ages now?

Ex. 9.40 | Q 27 | Page 31

A lady went shopping and spent half of what she had on buying hankies and gave a rupee to a beggar waiting outside the shop. She spent half of what was left on a lunch and followed that up with a two rupee tip. She spent half of the remaining amount on a book and three rupees on bus fare. When she reached home, she found that she had exactly one rupee left. How much money did she start with?

## Chapter 9: Linear Equation in One Variable

Ex. 9.10Ex. 9.20Ex. 9.30Ex. 9.40

## RD Sharma solutions for Class 8 Mathematics chapter 9 - Linear Equation in One Variable

RD Sharma solutions for Class 8 Maths chapter 9 (Linear Equation 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 for Class 8 by R D Sharma (2019-2020 Session) solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Class 8 Mathematics chapter 9 Linear Equation in One Variable are Reducing Equations to Simpler Form, Equations Reducible to the Linear Form, Introduction of Linear Equation, Solving Equations Which Have Linear Expressions on One Side and Numbers on the Other Side, Some Applications, Solving Equations Having the Variable on Both Sides, Some More Applications.

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