Mathematics

Linear Equations in One Variable

Question:

 m-frac { m-1 }{ 2 } =1-frac { m-2 }{ 3 }

Answer:

Given  m-frac { m-1 }{ 2 } =1-frac { m-2 }{ 3 }
ncert-exemplar-problems-class-8-mathematics-linear-equations-in-one-variable-37

 

previuos
next

Linear Equations in One Variable

Q 1.

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 2.

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 3.

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

Q 5.

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

Q 6.

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 9.

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

Q 10.

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 11.

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

Q 12.

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

Q 13.

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 14.

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

Q 15.

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 16.

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 17.

The solution of the equation 3x – 4 = 1 – 2x is————- .

Q 18.

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

Q 19.

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

Q 20.

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

Q 21.

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

Q 22.

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

Q 23.

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 24.

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 25.

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 26.

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 27.

Three consecutive numbers whose sum is 12 are——–,————-and———.

Q 28.

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

Q 29.

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

Q 30.

In the equation 3x – 3 = 9, transposing – 3 to RHS, we get 3x = 9.

Q 31.

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

Q 32.

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

Q 33.

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 34.

0.4(3x-1)=0.5x +1

Q 35.

4t-3-(3t+1)=5t-4

Q 36.

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

Q 37.

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

Q 38.

 frac { 3t+5 }{ 4 } -1=frac { 4t-3 }{ 5 }

Q 39.

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

Q 40.

0.16 (5x-2)=0.4x +7

Q 41.

Rs 13500 are to be distributed among Salma, Kiran and Jenifer in such a way that Salma gets Rs 1000 more than Kiran and Jenifer gets Rs 500 more than Kiran. Find the money received by Jenifer.

Q 42.

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

Q 43.

Divide 54 into two parts, such that one part is 2/7 of the other.

Q 44.

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

Q 45.

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 46.

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 47.

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 48.

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 49.

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

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 }