# NCERT solutions for Mathematics Exemplar Class 8 chapter 4 - Linear Equation In One Variable [Latest edition]

## Chapter 4: Linear Equation In One Variable

Exercise
Exercise [Pages 110 - 121]

### NCERT solutions for Mathematics Exemplar Class 8 Chapter 4 Linear Equation In One Variable Exercise [Pages 110 - 121]

#### Choose the correct alternative:

Exercise | Q 1 | Page 110

The solution of which of the following equations is neither a fraction nor an integer ______.

• 3x + 2 = 5x + 2

• 4x – 18 = 2

• 4x + 7 = x + 2

• 5x – 8 = x + 4

Exercise | Q 2 | Page 110

The solution of the equation ax + b = 0 is ______.

•  x = a/b

• x = -b

• x = (-b)/a

• x = b/a

Exercise | Q 3 | Page 111

If 8x – 3 = 25 + 17x, then x is ______.

• A fraction

• An integer

• A rational number

• Cannot be solved

Exercise | Q 4 | Page 111

The shifting of a number from one side of an equation to other is called ______.

• Transposition

• Distributivity

• Commutativity

• Associativity

Exercise | Q 5 | Page 111

If (5x)/3 - 4 = (2x)/5, then the numerical value of 2x – 7 is ______.

• 19/13

• - 13/19

• 0

• 13/19

Exercise | Q 6 | Page 111

The value of x for which the expressions 3x – 4 and 2x + 1 become equal is ______.

• –3

• 0

• 5

• 1

Exercise | Q 7 | Page 111

If a and b are positive integers, then the solution of the equation ax = b has to be always ______.

• Positive

• Negative

• One

• Zero

Exercise | Q 8 | Page 111

Linear equation in one variable has ______.

• Only one variable with any power

• Only one term with a variable

• Only one variable with power 1

• Only constant term

Exercise | Q 9 | Page 112

Which of the following is a linear expression?

• x2 + 1

• y + y2

• 4

• 1 + z

Exercise | Q 10 | Page 112

A linear equation in one variable has ______.

• Only one solution

• Two solutions

• More than two solutions

• No solution

Exercise | Q 11 | Page 112

Value of S in 1/3 + S = 2/5 is ______.

• 4/5

• 1/15

• 10

• 0

Exercise | Q 12 | Page 112

(-4)/3 y = - 3/4, then y = ______.

• -(3/4)^2

• -(4/3)^2

• (3/4)^2

• (4/3)^2

Exercise | Q 13 | Page 112

The digit in the tens place of a two-digit number is 3 more than the digit in the units place. Let the digit at units place be b. Then the number is ______.

• 11b + 30

• 10b + 30

• 11b + 3

• 10b + 3

Exercise | Q 14 | Page 112

Arpita’s present age is thrice of Shilpa. If Shilpa’s age three years ago was x. Then Arpita’s present age is ______.

• 3(x – 3)

• 3x + 3

• 3x – 9

• 3(x + 3)

Exercise | Q 15 | Page 113

The sum of three consecutive multiples of 7 is 357. Find the smallest multiple ______.

• 112

• 126

• 119

• 116

#### Fill in the blanks:

Exercise | Q 16 | Page 113

In a linear equation, the ______ power of the variable appearing in the equation is one.

Exercise | Q 17 | Page 113

The solution of the equation 3x – 4 = 1 – 2x is ______.

Exercise | Q 18 | Page 113

The solution of the equation 2y = 5y - 18/5 is ______.

Exercise | Q 19 | Page 113

Any value of the variable which makes both sides of an equation equal is known as a ______ of the equation.

Exercise | Q 20 | Page 113

9x – ______ = – 21 has the solution (– 2)

Exercise | Q 21 | Page 113

Three consecutive numbers whose sum is 12 are ______, ______ and ______.

Exercise | Q 22 | Page 113

The share of A when Rs 25 are divided between A and B so that A gets Rs. 8 more than B is ______.

Exercise | Q 23 | Page 113

A term of an equation can be transposed to the other side by changing its ______.

Exercise | Q 24 | Page 113

On subtracting 8 from x, the result is 2. The value of x is ______.

Exercise | Q 25 | Page 113

x/5 + 30 = 18 has the solution as ______.

Exercise | Q 26 | Page 113

When a number is divided by 8, the result is –3. The number is ______.

Exercise | Q 27 | Page 113

9 is subtracted from the product of p and 4, the result is 11. The value of p is ______.

Exercise | Q 28 | Page 113

If 2/5 x - 2 = 5 - 3/5 x, then x = ______.

Exercise | Q 29 | Page 113

After 18 years, Swarnim will be 4 times as old as he is now. His present age is ______.

Exercise | Q 30 | Page 113

Convert the statement Adding 15 to 4 times x is 39 into an equation ______.

Exercise | Q 31 | Page 115

The denominator of a rational number is greater than the numerator by 10. If the numerator is increased by 1 the and denominator is decreased by 1, then expression for new denominator is ______.

Exercise | Q 32 | Page 115

The sum of two consecutive multiples of 10 is 210. The smaller multiple is ______.

#### State whether the following statement is True or False:

Exercise | Q 33 | Page 115

3 years ago, the age of a boy was y years. His age 2 years ago was (y – 2) years.

• True

• False

Exercise | Q 34 | Page 115

Shikha’s present age is p years. Reemu’s present age is 4 times the present age of Shikha. After 5 years Reemu’s age will be 15p years.

• True

• False

Exercise | Q 35 | Page 115

In a 2 digit number, the units place digit is x. If the sum of digits be 9, then the number is (10x – 9).

• True

• False

Exercise | Q 36 | Page 115

Sum of the ages of Anju and her mother is 65 years. If Anju’s present age is y years then her mother’s age before 5 years is (60 – y) years.

• True

• False

Exercise | Q 37 | Page 115

The number of boys and girls in a class are in the ratio 5:4. If the number of boys is 9 more than the number of girls, then number of boys is 9.

• True

• False

Exercise | Q 38 | Page 115

A and B are together 90 years old. Five years ago A was thrice as old as B was. Hence, the ages of A and B five years back would be (x – 5) years and (85 – x) years respectively.

• True

• False

Exercise | Q 39 | Page 115

Two different equations can never have the same answer.

• True

• False

Exercise | Q 40 | Page 115

In the equation 3x – 3 = 9, transposing –3 to RHS, we get 3x = 9.

• True

• False

Exercise | Q 41 | Page 115

In the equation 2x = 4 – x, transposing – x to LHS, we get x = 4.

• True

• False

Exercise | Q 42 | Page 115

If 15/8 - 7x = 9, then – 7x = 9 + 15/8

• True

• False

Exercise | Q 43 | Page 115

If x/3 + 1 = 7/15, then x/3 = 6/15

• True

• False

Exercise | Q 44 | Page 115

If 6x = 18, then 18x = 54

• True

• False

Exercise | Q 45 | Page 115

If x/11 = 15, then x = 11/15

• True

• False

Exercise | Q 46 | Page 115

If x is an even number, then the next even number is 2(x + 1).

• True

• False

Exercise | Q 47 | Page 116

If the sum of two consecutive numbers is 93 and one of them is x, then the other number is 93 – x.

• True

• False

Exercise | Q 48 | Page 116

Two numbers differ by 40, when each number is increased by 8, the bigger becomes thrice the lesser number. If one number is x, then the other number is (40 – x).

• True

• False

#### Solve the following:

Exercise | Q 49 | Page 116

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

Exercise | Q 50 | Page 116

(5x)/(2x - 1) = 2

Exercise | Q 51 | Page 116

(2x - 3)/(4x + 5) = 1/3

Exercise | Q 52 | Page 116

8/x = 5/(x - 1)

Exercise | Q 53 | Page 116

(5(1 - x) + 3(1 + x))/(1 - 2x) = 8

Exercise | Q 54 | Page 116

(0.2x + 5)/(3.5x - 3) = 2/5

Exercise | Q 55 | Page 116

(y - (4 - 3y))/(2y - (3 + 4y)) = 1/5

Exercise | Q 56 | Page 116

x/5 = (x - 1)/6

Exercise | Q 57 | Page 116

0.4(3x – 1) = 0.5x + 1

Exercise | Q 58 | Page 116

8x – 7 – 3x = 6x – 2x – 3

Exercise | Q 59 | Page 116

10x – 5 – 7x = 5x + 15 – 8

Exercise | Q 60 | Page 116

4t – 3 – (3t + 1) = 5t – 4

Exercise | Q 61 | Page 116

5(x – 1) – 2(x + 8) = 0

Exercise | Q 62 | Page 116

x/2 - 1/4(x - 1/3) = 1/6(x + 1) + 1/12

Exercise | Q 63 | Page 117

1/2(x + 1) + 1/3(x - 1) = 5/12(x - 2)

Exercise | Q 64 | Page 117

(x + 1)/4 = (x - 2)/3

Exercise | Q 65 | Page 117

(2x - 1)/5 = (3x + 1)/3

Exercise | Q 66 | Page 117

1 –(x – 2) – [(x – 3) – (x – 1)] = 0

Exercise | Q 67 | Page 117

3x - (x - 2)/3 = 4 - (x - 1)/4

Exercise | Q 68 | Page 117

(3t + 5)/4 - 1 = (4t - 3)/5

Exercise | Q 69 | Page 117

(2y - 3)/4 - (3y - 5)/2 = y + 3/4

Exercise | Q 70 | Page 117

0.25 (4x – 5) = 0.75x + 8

Exercise | Q 71 | Page 117

(9 - 3y)/(1 - 9y) = 8/5

Exercise | Q 72 | Page 117

(3x + 2)/(2x - 3) = - 3/4

Exercise | Q 73 | Page 117

(5x + 1)/(2x) = - 1/3

Exercise | Q 74 | Page 117

(3t - 2)/3 + (2t + 3)/2 = t + 7/6

Exercise | Q 75 | Page 117

m - (m - 1)/2 = 1 - (m - 2)/3

Exercise | Q 76 | Page 117

4(3p + 2) – 5(6p –1) = 2(p – 8) – 6(7p – 4)

Exercise | Q 77 | Page 117

3(5x – 7) + 2(9x – 11) = 4(8x – 7) – 111

Exercise | Q 78 | Page 117

0.16(5x – 2) = 0.4x + 7

Exercise | Q 79 | Page 117

Radha takes some flowers in a basket and visits three temples one by one. At each temple, she offers one-half of the flowers from the basket. If she is left with 3 flowers at the end, find the number of flowers she had in the beginning.

Exercise | Q 80 | Page 118

Rs. 13500 are to be distributed among Salma, Kiran and Jenifer in such a way that Salma gets Rs. 1000 more than Kiran and Jenifer gets Rs. 500 more than Kiran. Find the money received by Jenifer.

Exercise | Q 81 | Page 118

The volume of water in a tank is twice of that in the other. If we draw out 25 litres from the first and add it to the other, the volumes of the water in each tank will be the same. Find the volume of water in each tank.

Exercise | Q 82 | Page 118

Anushka and Aarushi are friends. They have equal amount of money in their pockets. Anushka gave 1/3 of her money to Aarushi as her birthday gift. Then Aarushi gave a party at a restaurant and cleared the bill by paying half of the total money with her. If the remaining money in Aarushi’s pocket is Rs.1600, find the sum gifted by Anushka.

Exercise | Q 83 | Page 118

Kaustubh had 60 flowers. He offered some flowers in a temple and found that the ratio of the number of remaining flowers to that of flowers in the beginning is 3:5. Find the number of flowers offered by him in the temple.

Exercise | Q 84 | Page 118

The sum of three consecutive even natural numbers is 48. Find the greatest of these numbers.

Exercise | Q 85 | Page 118

The sum of three consecutive odd natural numbers is 69. Find the prime number out of these numbers.

Exercise | Q 86 | Page 118

The sum of three consecutive numbers is 156. Find the number which is a multiple of 13 out of these numbers.

Exercise | Q 87 | Page 118

Find a number whose fifth part increased by 30 is equal to its fourth part decreased by 30.

Exercise | Q 88 | Page 118

Divide 54 into two parts such that one part is 2/7 of the other.

Exercise | Q 89 | Page 118

Sum of the digits of a two-digit number is 11. The given number is less than the number obtained by interchanging the digits by 9. Find the number.

Exercise | Q 90 | Page 118

Two equal sides of a triangle are each 4m less than three times the third side. Find the dimensions of the triangle, if its perimeter is 55m.

Exercise | Q 91 | Page 119

After 12 years, Kanwar shall be 3 times as old as he was 4 years ago. Find his present age.

Exercise | Q 92 | Page 119

Anima left one-half of her property to her daughter, one-third to her son and donated the rest to an educational institute. If the donation was worth Rs. 1,00,000, how much money did Anima have?

Exercise | Q 93 | Page 119

If 1/2 is subtracted from a number and the difference is multiplied by 4, the result is 5. What is the number?

Exercise | Q 94 | Page 119

The sum of four consecutive integers is 266. What are the integers?

Exercise | Q 95 | Page 119

Hamid has three boxes of different fruits. Box A weighs 2 1/2 kg more than Box B and Box C weighs 10 1/4 kg more than Box B. The total weight of the three boxes is 48 3/4 kg. How many kilograms (kg) does Box A weigh?

Exercise | Q 96 | Page 119

The perimeter of a rectangle is 240 cm. If its length is increased by 10% and its breadth is decreased by 20%, we get the same perimeter. Find the length and breadth of the rectangle.

Exercise | Q 97 | Page 119

The age of A is five years more than that of B. 5 years ago, the ratio of their ages was 3:2. Find their present ages.

Exercise | Q 98 | Page 119

If numerator is 2 less than denominator of a rational number and when 1 is subtracted from numerator and denominator both, the rational number in its simplest form is 1/2. What is the rational number?

Exercise | Q 99 | Page 119

In a two-digit number, digit in units place is twice the digit in tens place. If 27 is added to it, digits are reversed. Find the number

Exercise | Q 100 | Page 119

A man was engaged as typist for the month of February in 2009. He was paid Rs. 500 per day but Rs. 100 per day were deducted for the days he remained absent. He received Rs. 9,100 as salary for the month. For how many days did he work?

Exercise | Q 101 | Page 119

A steamer goes downstream and covers the distance between two ports in 3 hours. It covers the same distance in 5 hours when it goes upstream. If the stream flows at 3 km/hr, then find what is the speed of the steamer upstream?

Exercise | Q 102 | Page 120

A lady went to a bank with Rs. 1,00,000. She asked the cashier to give her Rs. 500 and Rs. 1,000 currency notes in return. She got 175 currency notes in all. Find the number of each kind of currency notes.

Exercise | Q 103 | Page 120

There are 40 passengers in a bus, some with Rs. 3 tickets and remaining with Rs.10 tickets. The total collection from these passengers is Rs. 295. Find how many passengers have tickets worth Rs. 3?

Exercise | Q 104 | Page 120

Denominator of a number is 4 less than its numerator. If 6 is added to the numerator it becomes thrice the denominator. Find the fraction.

Exercise | Q 105 | Page 120

An employee works in a company on a contract of 30 days on the condition that he will receive Rs. 120 for each day he works and he will be fined Rs. 10 for each day he is absent. If he receives Rs. 2300 in all, for how many days did he remain absent?

Exercise | Q 106 | Page 120

Kusum buys some chocolates at the rate of Rs. 10 per chocolate. She also buys an equal number of candies at the rate of Rs. 5 per candy. She makes a 20% profit on chocolates and 8% profit on candies. At the end of the day, all chocolates and candies are sold out and her profit is Rs. 240. Find the number of chocolates purchased.

Exercise | Q 107 | Page 120

A steamer goes downstream and covers the distance between two ports in 5 hours while it covers the same distance upstream in 6 hours. If the speed of the stream is 1 km/hr, find the speed of the steamer in still water.

Exercise | Q 108 | Page 120

Distance between two places A and B is 210 km. Two cars start simultaneously from A and B in opposite direction and distance between them after 3 hours is 54 km. If speed of one car is less than that of other by 8 km/hr, find the speed of each.

Exercise | Q 109 | Page 120

A carpenter charged Rs. 2500 for making a bed. The cost of materials used is Rs. 1100 and the labour charges are Rs. 200/hr. For how many hours did the carpenter work?

Exercise | Q 110 | Page 120

For what value of x is the perimeter of shape 77 cm?

Exercise | Q 111 | Page 121

For what value of x is the perimeter of shape 186 cm?

Exercise | Q 112 | Page 121

On dividing Rs. 200 between A and B such that twice of A’s share is less than 3 times B’s share by 200, B’s share is?

Exercise | Q 113 | Page 121

Madhulika thought of a number, doubled it and added 20 to it. On dividing the resulting number by 25, she gets 4. What is the number?

Exercise

## NCERT solutions for Mathematics Exemplar Class 8 chapter 4 - Linear Equation In One Variable

NCERT solutions for Mathematics Exemplar Class 8 chapter 4 (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 Exemplar Class 8 solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Mathematics Exemplar Class 8 chapter 4 Linear Equation In One Variable are Reducing Equations to Simpler Form, Equations Reducible to the Linear Form, Linear Equation in One Variable, Solving Equations Which Have Linear Expressions on One Side and Numbers on the Other Side, Some Applications Solving Equations Which Have Linear Expressions on One Side and Numbers on the Other Side, Solving Equations Having the Variable on Both Sides, Some More Applications on the Basis of Solving Equations Having the Variable on Both Sides, The Idea of a Variable, Expressions with Variables, Concept of Equation, Balancing an Equation, The Solution of an Equation.

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