Mathematics

Linear Equations in One Variable

Question:

Anima left one-half of her property to her daughter, one-third to her son and donated the rest to an educational institute. If the donation was worth Rs 100000, how much money did Anima have?

Answer:

ncert-exemplar-problems-class-8-mathematics-linear-equations-in-one-variable-18

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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.

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

Q 4.

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 5.

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

Q 6.

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

Q 7.

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 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.

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 10.

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

Q 11.

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

Q 12.

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

Q 13.

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

Q 14.

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 15.

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

Q 16.

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

Q 17.

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 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.

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

Q 20.

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 21.

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 22.

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 23.

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

Q 24.

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

Q 25.

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

Q 26.

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

Q 27.

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

Q 28.

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

Q 29.

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 30.

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 31.

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

Q 32.

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

Q 33.

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 34.

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

Q 35.

A carpenter charged Rs 2500 for making a bed. The cost of materials used is Rs 1100 and the labour charge is Rs 200 per hour. For how many hours did the carpenter work?

Q 36.

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 37.

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 38.

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

Q 39.

When 9 is subtracted from the product of p and 4, the result is 11. The value of p is—-.

Q 40.

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

Q 41.

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 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.

Two different equations can never have the same answer.

Q 44.

If frac { x }{ 11 } , then x=frac { 11 }{ 15 } .

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.

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 47.

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

Q 48.

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

Q 49.

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

Q 50.

frac { x }{ 2 } -frac { 1 }{ 4 } left( x-frac { 1 }{ 3 } 
ight) =frac { 1 }{ 6 } left( x+1 
ight) +frac { 1 }{ 12 }