Mathematics

Linear Equations in One Variable

Question:

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.

Answer:

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

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Linear Equations in One Variable

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.

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

Q 5.

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

Q 6.

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

Q 7.

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 8.

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 9.

The volume of water in a tank is twice of that in the other. If we draw out 25 litres from the first and add it to the other, the volumes of the water in each tank will be the same. Find the volumes of water in each tank.

Q 10.

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

Q 11.

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

Q 12.

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

Q 13.

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

Q 14.

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 15.

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

Q 16.

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

Q 17.

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 18.

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 19.

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

Q 20.

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 21.

Two different equations can never have the same answer.

Q 22.

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

Q 23.

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

Q 24.

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

Q 25.

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

Q 26.

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

Q 27.

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

Q 28.

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

Q 29.

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 30.

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 31.

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

Q 32.

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

Q 33.

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

Q 34.

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 35.

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

Q 36.

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

Q 37.

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

Q 38.

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

Q 39.

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

Q 40.

4t-3-(3t+1)=5t-4

Q 41.

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

Q 42.

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

Q 43.

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

Q 44.

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 45.

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 46.

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

Q 47.

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 48.

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.

Q 49.

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 50.

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.