## Class 8 - Mathematics

#### Linear Equations in One Variable

Q&A
Question:

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

Linear Equations in One Variable - Questions
1.

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

2.

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

3.

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

4.

The solutoni of the equation ax + b = 0 is

5.

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.

6.

The sum of two consecutive multiples of 10 is 210. The smaller multiple is——-.

7.

Radha takes some flowers in a basket and visits three temples one-by-one. At each temple, she offers one half of the flowers from the basket. If she is left with 3 flowers at the end, then find the number of flowers she had in the beginning.

8.

Kaustubh had 60 flowers. He offered some flowers in temple and found that the ratio of the number of remaining flowers to that of flowers in the beginning is 3 : 5. Find the number of flowers offered by him in the temple.

9.

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

10.

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

11.

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.

12.

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

13.

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

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.

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.

16.

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?

17.

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.

18.

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.

19.

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?

20.

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

21.

The solution of which of the following equations is neither a fraction nor an integer?
(a) -3x + 2=5x + 2 (b)4x-18=2 (c)4x + 7 = x + 2 (d)5x-8 = x +4

22.

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

23.

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)${ left[ frac { 4 }{ 3 } ight] }^{ 2 }$

24.

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

25.

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

26.

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

27.

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

28.

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

29.

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

30.

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

31.

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.

32.

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.

33.

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.

34.

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.

35.

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

37.

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

38.

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

39.

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

40.

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

41.

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

42.

10x-5-7x=5x+15-8

43.

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

44.

$frac { 1 }{ 2 } left( x+1 ight) +frac { 1 }{ 3 } left( x-1 ight) =frac { 5 }{ 12 } left( x-2 ight)$

45.

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

46.

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

47.

$frac { 9-3y }{ 1-9y } =frac { 8 }{ 5 }$

48.

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

49.

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

50.

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

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