Mathematics

Linear Equations in One Variable

Question:

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

Answer:

ncert-exemplar-problems-class-8-mathematics-linear-equations-in-one-variable-11

Questions and Answers

Linear Equations in One Variable

Q 1.

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

Answer

Q 2.

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) ${ left[ frac { 4 }{ 3 } ight] }^{ 2 }$

Answer

Q 3.

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

Answer

Q 4.

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

Answer

Q 5.

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

Answer

Q 6.

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.

Answer

Q 7.

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.

Answer

Q 8.

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

Answer

Q 9.

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.

Answer

Q 10.

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

Answer

Q 11.

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.

Answer

Q 12.

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

Answer

Q 13.

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

Answer

Q 14.

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

Q 15.

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

Answer

Q 16.

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

Answer

Q 17.

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

Answer

Q 18.

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

Answer

Q 19.

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

Answer

Q 20.

Convert the statement ‘adding 15 to 4 times x is 39’ into an equation.

Answer

Q 21.

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.

Answer

Q 22.

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

Answer

Q 23.

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

Answer

Q 24.

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.

Answer

Q 25.

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

Answer

Q 26.

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

Answer

Q 27.

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

Answer

Q 28.

Three consecutive numbers whose sum is 12 are——–,————-and———.

Answer

Q 29.

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

Answer

Q 30.

Two different equations can never have the same answer.

Answer

Q 31.

$frac { 2x-3 }{ 4x+5 } =frac { 1 }{ 3 }$

Answer

Q 32.

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

Answer

Q 33.

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.

Answer

Q 34.

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.

Answer

Q 35.

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

Answer

Q 36.

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?

Answer

Q 37.

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

Answer

Q 38.

If $frac { 5x }{ 3 }$ -4 = $frac { 2x }{ 5 }$ , then the numerical value of 2x – 7 is
(a) $frac { 19 }{ 13 }$ (b) $frac { -13 }{ 19 }$
(c)0 (d) $frac { 13 }{ 19 }$

Answer

Q 39.

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.

Answer

Q 40.

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

Answer

Q 41.

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——.

Answer