Mathematics

Linear Equations in One Variable

Question:

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:

ncert-exemplar-problems-class-8-mathematics-linear-equations-in-one-variable-13

previuos
next

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.

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 4.

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 5.

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

Q 6.

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

Q 7.

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

Q 8.

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

Q 10.

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

Q 11.

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 12.

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

Q 13.

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

Q 14.

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 15.

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 16.

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

Q 17.

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 18.

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.

Q 19.

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

Q 20.

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 21.

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.

Q 22.

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 23.

If a and b are positive integers, then the solution of the equation ax = b has to be always
(a) positive (b) negative (c) one (d) zero

Q 24.

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

Q 25.

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

Q 26.

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

Q 27.

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

Q 28.

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

Q 29.

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 30.

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 31.

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

Q 32.

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

Q 33.

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

Q 34.

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

Q 35.

 frac { x }{ 5 } + 30 = 18 has the solution as——–.

Q 36.

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

Q 37.

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.

Q 38.

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.

Q 39.

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

Q 40.

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

Q 41.

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).

Q 42.

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

Q 43.

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

Q 44.

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

Q 45.

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

Q 46.

0.25(4x-5)=0.75x +8

Q 47.

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

Q 48.

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

Q 49.

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 50.

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