Mathematics

Linear Equations in One Variable

Question:

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

Answer:

ncert-exemplar-problems-class-8-mathematics-linear-equations-in-one-variable-25

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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.

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

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.

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 6.

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

Q 7.

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

Q 8.

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

Q 10.

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

Q 11.

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

Q 12.

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 13.

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 14.

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

Q 15.

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 16.

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 17.

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 18.

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 19.

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

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.

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

Q 22.

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

Q 23.

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

Q 24.

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

Q 25.

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

Q 26.

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

Q 27.

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 28.

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

Q 29.

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

Q 30.

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

Q 31.

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 32.

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 33.

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 34.

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 35.

If frac { x }{ 11 } , then x=frac { 11 }{ 15 } .

Q 36.

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

Q 37.

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

Q 38.

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

Q 39.

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

Q 40.

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

Q 41.

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

Q 42.

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

Q 43.

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

Q 44.

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

Q 45.

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

Q 46.

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

Q 47.

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

Q 48.

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

Q 49.

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 50.

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.