Mathematics

Linear Equations in One Variable

Question:

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.

Answer:

False
Given, Shikha's present age = pyr
Then, Reemu's present age = 4 x (Shikha’s present age) = 4pyr After 5 yr, Reemu's age = (4p+5)yr

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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.

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 6.

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

Q 7.

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

Q 8.

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 9.

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

Q 10.

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

Q 11.

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 12.

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

Q 13.

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

Q 14.

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

Q 15.

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 16.

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

Q 17.

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

Q 18.

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

Q 19.

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

Q 20.

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 21.

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

Q 22.

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 23.

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 24.

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

Q 25.

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

Q 26.

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

Q 27.

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

Q 28.

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 29.

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 30.

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

Q 31.

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

Q 32.

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

Q 33.

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

Q 34.

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

Q 35.

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

Q 36.

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 37.

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

Q 38.

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

Q 39.

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

Q 40.

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

Q 41.

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 42.

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

Q 43.

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

Q 44.

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

Q 45.

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

Q 46.

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

Q 47.

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

Q 48.

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 49.

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 50.

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.