In this page we have *NCERT book Solutions for Class 8th Maths:Linear equations* for
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If you subtract ½ from a number and multiply the result by 1/2, you get 1/8. What is the number?

Let x be the number then as per the question

The LCM of denominator is 8, so multiplying by 8 on both sides

4x-2=1

Transposing 2 to R.H.S, we obtain

4x=3

Dividing 4 on both the sides

x=3/4

Let the breadth be

Then as per question the length will be (2

Perimeter of swimming pool = 2(

2(2

2(3

Dividing both sides by 2

3

Transposing 2 to R.H.S, we obtain

3

3

Dividing 3 on both the sides

So

Breath is 25 m

Length =2

Hence, the breadth and length of the pool are 25 m and 52 m respectively.

The base of an isosceles triangle is 4/3 cm. The perimeter of the triangle is cm. What is the length of either of the remaining equal sides?

Let the length of equal sides be

Perimeter =

Substituting the values, we get

The LCM of the denominator is 15, so multiplying both the sides by 15

30x+ 20=62

Transposing 20 to R.H.S, we obtain

30x=42

Dividing by 30 on both the sides

x=42/30=7/5

Therefore, the length of equal sides is 7/5 cm.

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

Let one number be

According to the question,

2

Transposing 15 to R.H.S, we obtain

2

2

Dividing both sides by 2, we obtain

So the other number will be

Hence, the numbers are 40 and 55.

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

Let the common ratio between these numbers be

Difference between these numbers = 18

5

2

Dividing both sides by 2,

First number = 5

Second number = 3

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

Let three consecutive integers be

Then as per question

Sum of these numbers

3

Transposing 3 to R.H.S, we obtain

3

3

Dividing both sides by 3

Hence, the consecutive integers are 16, 17, and 18.

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

Let the three consecutive multiples of 8 be 8

As per questions,

Sum of these numbers

8(

8(3

Dividing both sides by 8

3

Transposing 3 to R.H.S, we obtain

3

3

Dividing both sides by 3, we obtain

First multiple = 8

Second multiple = 8(

Third multiple = 8(

Hence, the required numbers are 288, 296, and 304.

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.

Let three consecutive integers be

According to the question,

2

2

9

Transposing 11 to R.H.S, we obtain

9

9

Dividing both sides by 9, we obtain

Hence, the numbers are 7, 8, and 9.

The ages of Rahul and Haroon are in the ratio 5:7. Four years later the sum of their ages will be 56 years. What are their present ages?

Let common ratio between Rahul’s age and Haroon’s age be

Then

Age of Rahul =5

Age of haroon = 7

So After 4 years, the age of Rahul and Haroon will be (5

According to the given question, after 4 years, the sum of the ages of Rahul and Haroon is 56 years.

(5

12

Transposing 8 to R.H.S, we obtain

12

12

Dividing both sides by 12

Rahul’s age = 5

Haroon’s age = 7

The number of boys and girls in a class are in the ratio 7:5. The number of boys is 8 more than the number of girls. What is the total class strength?

Let the common ratio between the number of boys and numbers of girls be

Number of boys = 7y

Number of girls = 5

As per the question,

Number of boys = Number of girls + 8

7

Transposing 5

7

2

Dividing both sides by 2

So the strength of boys and girls are

Number of boys = 7

Number of girls = 5

Hence, total class strength = 28 + 20 = 48 students

Baichung's father is 26 years younger than Baichung's grandfather and 29 years older than Baichung. The sum of the ages of all the three is 135 years. What is the age of each one of them?

Let us assume Baichung’s father’s age be

Therefore, Baichung’s age and Baichung’s grandfather’s age will be (

As per the question,

The sum of the ages of these 3 people is 135 years.

So

3

Transposing 3 to R.H.S, we obtain

3

3

Dividing both sides by 3

Baichung’s father’s age =

Baichung’s age = (

Baichung’s grandfather’s age = (

Fifteen years from now Ravi’s age will be four times his present age. What is Ravi’s present age?

Let Ravi’s present age be

Fifteen years later, Ravi’s age = 4 × His present age

Transposing

15 = 4

15 = 3

Dividing both sides by 3, we obtain

5 =

Hence, Ravi’s present age = 5 years

A rational number is such that when you multiply it by 5/2 and add 2/3 to the product, you get What is the number?

Let x be the rational number ,then

The LCM of 2,3 and 12 is 12,so multiplying by 12

30x+8=-7

Transposing 8 to R.H.S, we obtain

30x=-15

Dividing by 30 on both the sides

x=-1/2

Lakshmi is a cashier in a bank. She has currency notes of denominations Rs 100, Rs 50 and Rs 10, respectively. The ratio of the number of these notes is 2:3:5. The total cash with Lakshmi is Rs 4, 00,000. How many notes of each denomination does she have

Let the common ratio between the numbers of notes of different denominations be

Amount of Rs 100 notes = Rs (100 × 2y) = Rs 200

Amount of Rs 50 notes = Rs (50 × 3

Amount of Rs 10 notes = Rs (10 × 5

As per question the total amount is Rs 400000.

200

400

Dividing both sides by 400, we obtain

Number of Rs 100 notes = 2

Number of Rs 50 notes = 3

Number of Rs 10 notes = 5

I have a total of Rs 300 in coins of denomination Re 1, Rs 2 and Rs 5. The number of Rs 2 coins is 3 times the number of Rs 5 coins. The total number of coins is 160. How many coins of each denomination are with me?

Let the number of Rs 5 coins be

Then Number of Rs 2 coins = 3

Number of Re 1 coins = 160 − (Number of coins of Rs 5 and of Rs 2)

= 160 − (3

Amount of Re 1 coins = Rs [1 × (160 − 4

Amount of Rs 2 coins = Rs (2 × 3

Amount of Rs 5 coins = Rs (5 ×

As per question total amount is Rs 300.

160 − 4

160 + 7

Transposing 160 to R.H.S, we obtain

7

7

Dividing both sides by 7, we obtain

Number of Re 1 coins = 160 − 4

Number of Rs 2 coins = 3

Number of Rs 5 coins =

The organizers of an essay competition decide that a winner in the competition gets a prize of Rs 100 and a participant who does not win gets a prize of Rs 25. The total prize money distributed is Rs 3000. Find the number of winners, if the total number of participants is 63.

Let the number of winners be

Therefore, the number of participants who did not win will be 63 −

Amount given to the winners = Rs (100 ×

Amount given to the participants who did not win = Rs [25(63 −

= Rs (1575 − 25

As per the question,

100

Transposing 1575 to R.H.S, we obtain

75

75

Dividing both sides by 75, we obtain

Hence, number of winners = 19

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