Mathematics

Linear Equations in One Variable

Question:

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.

Answer:

True
Let the age of A be x yr.
Then, age of S = (90 – x) yr
Five years ago, the age of A = (x- 5) yr
The age of B= 90-x-5 = (85-x)yr
Hence, the ages of A and 8 five years back would be (x – 5) yr and (85 – x) yr, respectively.

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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.

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

Q 3.

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 4.

The solution of the equation 2y = 5y-frac { 18 }{ 5 } is————.

Q 5.

The sum of three consecutive numbers is 156. Find the number which is a multiple of 13 out of these numbers.

Q 6.

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

Q 7.

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 8.

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

Q 10.

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

Q 11.

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 12.

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 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.

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

Q 15.

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

Q 16.

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 17.

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 18.

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

Q 19.

frac { 5(1-x)+3(1+x) }{ 1-2x } =8

Q 20.

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

Q 21.

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 22.

The solutoni of the equation ax + b = 0 is

ncert-exemplar-problems-class-8-mathematics-linear-equations-in-one-variable-3

Q 23.

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

Q 24.

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 25.

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 26.

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

Q 27.

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

Q 28.

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.

Q 29.

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

Q 30.

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

Q 31.

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

Q 32.

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 33.

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 34.

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 35.

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 36.

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 37.

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 38.

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

Q 39.

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

Q 40.

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

Q 41.

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

Q 42.

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

Q 43.

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

Q 44.

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

Q 45.

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

Q 46.

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

Q 47.

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

Q 48.

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

Q 49.

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

Q 50.

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.