Mathematics

Linear Equations in One Variable

Question:

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:

ncert-exemplar-problems-class-8-mathematics-linear-equations-in-one-variable-32

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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.

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 14.

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

Q 15.

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 16.

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 17.

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

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

Q 22.

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 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.

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

Q 26.

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

Q 27.

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

Q 28.

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

Q 29.

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 30.

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 31.

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 32.

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 33.

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

Q 34.

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

Q 35.

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

Q 36.

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

Q 37.

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 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.

Two different equations can never have the same answer.

Q 40.

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

Q 41.

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

Q 42.

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

Q 43.

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

Q 44.

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

Q 45.

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 46.

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?

Q 47.

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 48.

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 49.

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 50.

An employee works in a company on a contract of 30 days on the condition that he will receive Rs 120 for each day he works and he will be fined Rs 10 for each day he is absent. If he receives Rs 2300 in all, for how many days did he remain absent?