Mathematics

Linear Equations in One Variable

Question:

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

Answer:

4x+ 15=39
To convert the given statement into an equation, first x is multiplied by 4 and then 15 is added to get the result 39.  i.e. 4x + 15=39

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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.

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 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.

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

Q 5.

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 6.

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

Q 8.

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

Q 9.

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

Q 10.

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

Q 11.

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

Q 12.

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

Q 13.

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

Q 14.

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 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.

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 17.

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

Q 18.

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 19.

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

Q 20.

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

Q 21.

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 22.

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

Q 23.

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

Q 24.

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

Q 25.

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 26.

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

Q 27.

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

Q 28.

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

Q 29.

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 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.

If frac { 5x }{ 3 }-4 =frac { 2x }{ 5 } , then the numerical value of 2x – 7 is
(a)frac { 19 }{ 13 } (b)frac { -13 }{ 19 }
(c)0 (d)frac { 13 }{ 19 }

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 3x – 4 = 1 – 2x is————- .

Q 34.

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

Q 35.

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

Q 36.

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

Q 37.

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

Q 38.

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

Q 39.

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

Q 40.

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

Q 41.

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 42.

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 43.

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 44.

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 45.

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

Q 46.

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

Q 47.

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

Q 48.

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

Q 49.

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 50.

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