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.

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 4.

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.

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

Q 12.

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 13.

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 14.

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

Q 15.

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

Q 16.

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 17.

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 18.

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

Q 19.

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 20.

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 21.

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 22.

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

Q 23.

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

Q 24.

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

Q 25.

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

Q 26.

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 27.

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 28.

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 29.

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

Q 30.

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

Q 31.

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

Q 32.

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

Q 33.

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 34.

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

Q 35.

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

Q 36.

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 37.

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

Q 38.

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

Q 39.

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

Q 40.

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

Q 41.

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 42.

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 43.

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 44.

Distance between two places A and B is 210 km. Two cars start simultaneously from A and B in opposite directions and distance between them after 3 hours is 54 km. If speed of one car is less than that of other by 8 km/h, then find the speed of each.

Q 45.

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 46.

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

Q 47.

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

Q 48.

The value of S in frac { 1 }{ 3 } + S = frac { 2 }{ 5 } is
(a)frac { 4 }{ 5 } (b)frac { 1 }{ 15 }
(c)10 (d)0

Q 49.

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 50.

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