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**CBSE Mathematics Solutions Class VIII **

### Ncert Solutions of 8th Maths Exercise 2.2

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__Linear Equations in One Variable__

__Linear Equations in One Variable__

*(page 28)*

Q 1: If you subtract 1/2 from a number and multiply the result by 1/2, you get 1/8. What is the number?

Solution:

Let the number be

*x*. Then by subtracting 1/2 from*x*and multiplying the result by 1/2 we get,Q 2: The perimeter of a rectangular swimming pool is 154 m. Its length is 2m more than twice its breadth. What are the length and breadth of the pool?

Solution:

Let the breadth of the swimming pool be

*x*.
Therefore, its length = 2

*x*+ 2
Given the perimeter of the pool = 154 m.

or, 2(2

*x*+ 2 +*x*) = 154
or, 6

*x*+ 4 = 154
or,

*x*= 25m
Hence, Breadth = 25m and

Length = 2 x 25 + 2 = 52m

Q 3: The base of an isosceles triangle is 4/3 cm. The perimeter of the triangle is 4

^{2/15}cm. What is the length of either of the remaining equal sides?
Solution:

Let the length of one equal side of the isosceles triangle be

*x*.
Base of the isosceles triangle = 4/3cm (given)

Q 4: Sum of two numbers is 95. If one exceeds the other by 15, find the numbers.

Solution:

Let one number be

*x*and so, the other number is (*x*+ 15).
or,

*x*+*x*+ 15 = 95 (sum of the numbers given).
or,

*x*= 40 (and the other number is 40 + 15 = 55)
So, the numbers are 40 and 55 respectively.

Q 5: Two numbers are in the ratio 5 : 3. If they differ by 18, what are the numbers?

Solution:

Let the numbers are

*x*and y
Under the given conditions:

Q 6: Three consecutive integers add up to 51. What are these integers?

Solution:

Let the three consecutive integers be

*x,*(*x*+ 1) and (*x*+ 2).
According to the given condition,

*x*+

*(*

*x*+ 1) + (

*x*+ 2) = 51

or,

*x*= 16
Therefore the three consecutive integers are 16, 17 and 18 respectively.

Q 7: The sum of three consecutive multiples of 8 is 888. Find the multiples.

Solution:

Let the first multiple of 8 be 8

*x*.
Second multiple be 8

*x*+ 8.
Third multiple be 8

*x*+ 8 + 8 = 8*x*+ 16.
According to the given condition,

8

*x*+ 8*x*+ 8 + 8*x*+ 16 = 888
or, 24

*x*= 864
or,

*x*= 36.
Hence, 8

*x*= 8 x 36 = 288,
8

*x*+ 8 = 296,
8

*x*+ 16 = 304.
So, the numbers will be 288, 296 and 304.

Q 8: Three consecutive integers are such that when they are taken in increasing order and multiplied by 2, 3, and 4 respectively, they add up to 74. Find these numbers.

Solution: (Taking hint from Q7 solution do it yourself.)

**View solutions of remaining questions visit:**

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