Mathematics

Linear Equations in One Variable

Question:

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

Answer:

ncert-exemplar-problems-class-8-mathematics-linear-equations-in-one-variable-21

ncert-exemplar-problems-class-8-mathematics-linear-equations-in-one-variable-22

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Linear Equations in One Variable

Q 1.

8x-7-3x=6x-2x-3

Q 2.

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

Q 4.

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

Q 6.

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 7.

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 8.

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

Q 9.

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

Q 10.

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

Q 11.

10x-5-7x=5x+15-8

Q 12.

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 13.

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

Q 14.

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

Q 15.

frac { x+1 }{ 4 } =frac { x-2 }{ 3 }

Q 16.

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

Q 17.

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

Q 18.

0.4(3x-1)=0.5x +1

Q 19.

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

Q 20.

frac { 2x-1 }{ 5 } =frac { 3x+1 }{ 3 }

Q 21.

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

Q 22.

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 23.

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 24.

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 25.

Which of the following is a linear expression?
(a) { x }^{ 2 } +1 (b) y + { y }^{ 2 }
(c) 4 (d) 1 + z

Q 26.

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

Q 27.

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

Q 28.

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

Q 29.

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

Q 30.

If 8x – 3 = 25 + 17x, then x is
(a) a fraction (b) an integer
(c) a rational number (d) Cannot be solved

Q 31.

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

Q 32.

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 33.

The solution of the equation 2y = 5y-frac { 18 }{ 5 } is————.

Q 34.

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

Q 35.

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

Q 36.

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

Q 37.

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 38.

Two different equations can never have the same answer.

Q 39.

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

Q 40.

If 6x = 18, then 18x = 54.

Q 41.

frac { 5x }{ 2x-1 } =2

Q 42.

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

Q 43.

 frac { y-(4-3y) }{ 2y-(3y+4y) } =frac { 1 }{ 5 }

Q 44.

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

Q 45.

frac { x }{ 2 } -frac { 1 }{ 4 } left( x-frac { 1 }{ 3 } 
ight) =frac { 1 }{ 6 } left( x+1 
ight) +frac { 1 }{ 12 }

Q 46.

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

Q 47.

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

Q 48.

frac { 3t-2 }{ 3 } +frac { 2t+3 }{ 2 } =t+frac { 7 }{ 6 }

Q 49.

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

Q 50.

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.