Mathematics

Linear Equations in One Variable

Question:

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

Answer:

ncert-exemplar-problems-class-8-mathematics-linear-equations-in-one-variable-36

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Linear Equations in One Variable

Q 1.

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

Q 2.

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 4.

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

Q 5.

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

Q 6.

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

Q 7.

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?

Q 8.

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 9.

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

Q 10.

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

Q 11.

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

Q 12.

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 13.

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 14.

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 15.

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

Q 16.

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

Q 17.

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

Q 18.

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 19.

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 20.

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 21.

In questions 16 to 32, fill in the blanks to make each statement true.
Question. 16 In a linear equation, the——— power of the variable appearing in the equation is one.

Q 22.

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

Q 23.

frac { 2x-3 }{ 4x+5 } =frac { 1 }{ 3 }

Q 24.

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

Q 25.

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

Q 26.

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

Q 27.

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 28.

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 29.

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

Q 30.

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

Q 31.

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 32.

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 33.

Two different equations can never have the same answer.

Q 34.

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

Q 35.

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

Q 36.

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

Q 37.

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

Q 38.

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 39.

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

Q 40.

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

Q 41.

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

Q 42.

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

Q 43.

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

Q 44.

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

Q 45.

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

Q 46.

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 47.

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 48.

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 49.

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 50.

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