Mathematics

Linear Equations in One Variable

Question:

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.

Answer:

ncert-exemplar-problems-class-8-mathematics-linear-equations-in-one-variable-23

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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 4.

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

Q 5.

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

Q 6.

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 7.

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

Q 8.

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 9.

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

Q 10.

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

Q 11.

frac { 0.2x+5 }{ 3.5x-3 } =frac { 2 }{ 5 }

Q 12.

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 13.

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 14.

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

Q 15.

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 16.

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 17.

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 18.

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

Q 19.

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

Q 20.

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

Q 21.

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

Q 22.

Sum of the ages of Anju and her mother is 65 years. If Anju’s present age is y years, then her mother’s age before 5 years is (60 – y) years.

Q 23.

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

Q 24.

5(x-1)-2(x+8)=0

Q 25.

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

Q 26.

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

Q 27.

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.

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.

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

Q 30.

frac { 5x }{ 2x-1 } =2

Q 31.

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

Q 32.

frac { 5(1-x)+3(1+x) }{ 1-2x } =8

Q 33.

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

Q 34.

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

Q 35.

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

Q 36.

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 37.

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 38.

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 39.

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

Q 40.

9x – ……………….. = – 21 has the solution (- 2).

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——.

Q 42.

In a 2-digit number, the unit’s place digit is x. If the sum of digits be 9, then the number is (10x – 9).

Q 43.

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

Q 44.

ncert-exemplar-problems-class-8-mathematics-linear-equations-in-one-variable-1

Q 45.

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

Q 46.

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

Q 47.

The sum of three consecutive numbers is 156. Find the number which is a multiple of 13 out of these numbers.

Q 48.

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

Q 49.

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 50.

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.