Mathematics

Linear Equations in One Variable

Question:

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

Answer:

ncert-exemplar-problems-class-8-mathematics-linear-equations-in-one-variable-12

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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.

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 3.

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 9.

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

Q 10.

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

Q 11.

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

Q 12.

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 13.

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

Q 14.

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 15.

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 16.

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 17.

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 18.

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

Q 19.

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 20.

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

Q 21.

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

Q 22.

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 23.

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 24.

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 25.

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

Q 26.

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

Q 27.

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

Q 28.

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

Q 29.

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

Q 30.

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

Q 31.

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

Q 32.

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

Q 33.

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 34.

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 35.

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

Q 36.

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

Q 37.

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

Q 38.

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

Q 39.

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

Q 40.

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.

Q 41.

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 42.

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 43.

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 44.

Two different equations can never have the same answer.

Q 45.

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

Q 46.

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

Q 47.

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 48.

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

Q 49.

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

Q 50.

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