Mathematics

Linear Equations in One Variable

Question:

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

Answer:

ncert-exemplar-problems-class-8-mathematics-linear-equations-in-one-variable-39

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Linear Equations in One Variable

Q 1.

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

Q 2.

For what value of x is the perimeter of shape 186 cm?
ncert-exemplar-problems-class-8-mathematics-linear-equations-in-one-variable-42

Q 3.

A lady went to a bank with Rs 100000. She asked the cashier to give her Rs 500 and Rs 1000 currency notes in return. She got 175 currency notes in all. Find the number of each kind of currency notes.

Q 4.

The value of x, for which the expressions 3x – 4 and 2x + 1 become equal, is
(a) -3 (b) 0
(c) 5 x (d) 1

Q 5.

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

Q 6.

The value of S in frac { 1 }{ 3 } + S = frac { 2 }{ 5 } is
(a)frac { 4 }{ 5 } (b)frac { 1 }{ 15 }
(c)10 (d)0

Q 7.

If –frac { 4 }{ 3 } y = –frac { 3 }{ 4 } then y is equal to
(a)-{ left[ frac { 3 }{ 4 } 
ight] }^{ 2 } (b)-{ left[ frac { 4 }{ 3 } 
ight] }^{ 2 }
(c){ left[ frac { 3 }{ 4 } 
ight] }^{ 2 } (d){ left[ frac { 4 }{ 3 } 
ight] }^{ 2 }

Q 8.

15 The sum of three consecutive multiples of 7 is 357. Find the smallest multiple.(a) 112 (b) 126 (c) 119 (d) 116

Q 9.

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

Q 10.

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

Q 11.

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.

Q 12.

 frac { 2y-3 }{ 4 } -frac { 3y-5 }{ 2 } =y+frac { 3 }{ 4 }

Q 13.

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

Q 14.

In a two-digit number, digit in unit’s place is twice the digit in ten’s place. If 27 is added to it, digits are reversed. Find the number.

Q 15.

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?

Q 16.

If  frac { 2 }{ 5 } x-2=5- frac { 3 }{ 5 } x,then x=——-.

Q 17.

ncert-exemplar-problems-class-8-mathematics-linear-equations-in-one-variable-1

Q 18.

frac { 8}{ x } =frac { 5 }{ x-1 }

Q 19.

 frac { 3x+2 }{ 2x-3 } =-frac { 3 }{ 4 }

Q 20.

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

Q 21.

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

Q 22.

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 100000, how much money did Anima have?

Q 23.

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

Q 24.

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?

Q 25.

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.

Q 26.

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

ncert-exemplar-problems-class-8-mathematics-linear-equations-in-one-variable-40

Q 27.

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, what is B’s share?

Q 28.

The solutoni of the equation ax + b = 0 is

ncert-exemplar-problems-class-8-mathematics-linear-equations-in-one-variable-3

Q 29.

The shifting of a number from one side of an equation to other is called
(a) transposition (b) distributivity
(c) commutativity (d) associativity .

Q 30.

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

Q 31.

ncert-exemplar-problems-class-8-mathematics-linear-equations-in-one-variable-3

Q 32.

If frac { x }{ 11 } , then x=frac { 11 }{ 15 } .

Q 33.

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

Q 34.

frac { 3x-8 }{ 2x } =1

Q 35.

frac { 5(1-x)+3(1+x) }{ 1-2x } =8

Q 36.

frac { 0.2x+5 }{ 3.5x-3 } =frac { 2 }{ 5 }

Q 37.

frac { x }{ 5 } =frac { x-1 }{ 6 }

Q 38.

5(x-1)-2(x+8)=0

Q 39.

1-(x-2)-[(x-3)-(x-1)]=0

Q 40.

 frac { 3t+5 }{ 4 } -1=frac { 4t-3 }{ 5 }

Q 41.

 m-frac { m-1 }{ 2 } =1-frac { m-2 }{ 3 }

Q 42.

0.16 (5x-2)=0.4x +7

Q 43.

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 volumes of water in each tank.

Q 44.

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

Q 45.

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

Q 46.

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?

Q 47.

A lady went to a bank with Rs 100000. She asked the cashier to give her Rs 500 and Rs 1000 currency notes in return. She got 175 currency notes in all. Find the number of each kind of currency notes.

Q 48.

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/h, then find the speed of the steamer in still water.

Q 49.

In questions 16 to 32, fill in the blanks to make each statement true.
Question. 16 In a linear equation, the——— power of the variable appearing in the equation is one.

Q 50.

9x – ……………….. = – 21 has the solution (- 2).