Mathematics

Linear Equations in One Variable

Question:

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

Answer:

(b) Given, frac { 1 }{ 3 } + S = frac { 2 }{ 5 }
ncert-exemplar-problems-class-8-mathematics-linear-equations-in-one-variable-8

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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.

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

Q 7.

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

Q 8.

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

Q 9.

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

Q 10.

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

Q 11.

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 12.

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

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.

For what value of x is the perimeter of shape 77 cm?

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Q 15.

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

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.

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

Q 18.

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

Q 19.

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

Q 20.

frac { 3t-2 }{ 3 } +frac { 2t+3 }{ 2 } =t+frac { 7 }{ 6 }

Q 21.

The volume of water in a tank is twice of that in the other. If we draw out 25 litres from the first and add it to the other, the volumes of the water in each tank will be the same. Find the volumes of water in each tank.

Q 22.

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

Q 23.

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 24.

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 25.

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?

Q 26.

A steamer goes downstream and covers the distance between two ports in 5 hours, while it covers the same distance upstream in 6 hours. If the speed of the stream is 1 km/h, then find the speed of the steamer in still water.

Q 27.

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 28.

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

Q 29.

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

Q 30.

 frac { x }{ 5 } + 30 = 18 has the solution as——–.

Q 31.

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 32.

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 33.

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

Q 34.

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 35.

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

Q 36.

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

Q 37.

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

Q 38.

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

Q 39.

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

Q 40.

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

Q 41.

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 42.

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 43.

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

Q 44.

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 45.

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 46.

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 47.

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 48.

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 49.

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

Q 50.

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 }