# Linear Equations in One Variable

## Exercise 2.2 (NCERT) Part - 1

Question – 1 – If you subtract from a number and multiply the result by , you get . What is the number?

Solution:

Let the number is m.

Question -2 - The perimeter of a rectangular swimming pool is 154 m. Its length is 2 m more than twice its breadth. What are the length and the breadth of the pool?

Solution:

Given, perimeter of the rectangular swimming pool = 154 m

Length is 2 m more than the breadth.

Let the breadth of the swimming pool = a metre

Therefore, as per question, length of the swimming pool = (2a + 2) metre

We know that, perimeter of rectangle = 2 (length + breadth)

Therefore, 154 m = 2 [ (2a + 2) + a]

⇒ 154 m = 2(2a + 2 + a )

⇒ 154 m = 2 (3a + 2)

⇒ 154 m = 6a + 4

By subtracting 4 from both sides, we get

154 m – 4 = 6a + 4 – 4

⇒ 150 m = 6a

After dividing both sides by 6, we get

⇒ 25 m = a

⇒ a = 25 m

Since, length = (2a + 2) m

Therefore, by substituting the value of breadth (a), we get

(2 x 25 + 2) m= (50 + 2) m = 52 m

Thus, length of the given pool = 52 m

And breadth = 25 m

Question – 3 - The base of an isosceles triangle is The perimeter of the triangle is .What is the length of either of the remaining equal sides?

Solution:

Isosceles triangles have two sides equal.

We know that perimeter of an isosceles triangle = Sum of two equal sides + third side

Let the length of equal sides of the given isosceles triangle = a

And length of unequal side = b

Therefore, perimeter = 2a + b

After dividing both sides by 2, we get

Question – 4 - Sum of two numbers is 95. If one exceeds the other by 15, find the numbers.

Solution:

Let one number is ‘a’.

Therefore, according to question second number = a + 15

Now, as given, sum of two numbers = 95

Therefore,

a + a + 15 = 95

⇒ 2a + 15 = 95

By subtracting 15 from both sides, we get

2a + 15 – 15 = 95 – 15

⇒ 2a = 95 – 15

⇒ 2a = 80

After dividing both sides by 2, we get

Now, since second number = a + 15

Therefore, by substituting the value of ‘a’, we get

The second number = 40 + 15 = 55

Thus, first number = 40 and second number = 55

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

Solution:

Given, two numbers are in the ratio of 5:3

Their difference = 18

After dividing both sides by 2, we get

Linear Equations in One Variable - Exercise - 2.2 - Part - 2

Linear Equations in One Variable - Exercise - 2.2 - Part - 3