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Ncert Solutions for Linear equations Class 8 CBSE Part 6


In this page we have NCERT book Solutions for Class 8th Maths:Linear equations for EXERCISE 6 . Hope you like them and do not forget to like , social share and comment at the end of the page.

Question 1

Solve: 

Answer

On multiplying both sides by 3x, we obtain

8x − 3 = 6x

Transposing 6x to LHS and 3 to RHS

8x − 6x = 3

2x = 3

Dividing 2 on both the sides

x=3/2

 

Question 2

 Solve: 

Answer

On multiplying both sides by 7 − 6x, we obtain

9x = 15(7 − 6x)

9x = 105 − 90x

Transposing 90x on LHS

9x + 90x = 105

99x = 105

Dividing 99 on both the sides

x=105/99

Question 3  

Solve: 

Answer

On multiplying both sides by 9(z + 15), we obtain

9= 4(z + 15)

9= 4z + 60

Transposing 4z on LHS

9− 4z = 60

5z = 60

Dividing 5 on both the sides

z = 12

 

Question 4  

Solve

Answer

On multiplying both sides by 5(2 − 6y), we obtain

5(3y + 4) = −2(2 − 6y)

15y + 20 = − 4 + 12y

Transposing 12y to LHS and 20 to RHS

15y − 12y = − 4 – 20

 3y = −24

Dividing by 3 on both  the sides

 y = −8

 

Question 5

 Solve: 

Answer

On multiplying both sides by 3(+ 2), we obtain

3(7y + 4) = −4(y + 2)

21y + 12 = − 4y – 8

Transposing 4y to LHS and 12 to RHS

21y + 4y = − 8 − 12

 25y = −20

Dividing by 25 on both the sides

y=-20/25=-4/5

 

Question 6- The ages of Hari and Harry are in the ratio 5:7. Four years from now the ratio of their ages will be 3:4. Find their present ages.

 

Answer

 Let the common ratio between their ages be x. Therefore, Hari’s age and Harry’s age will be 5x years and 7x years respectively and four years later, their ages will be (5x + 4) years and (7x + 4) years respectively.

According to the situation given in the question,

Multiplying both the sides by 4(7x+4)

4(5x+4)=3(7x+4)

20x+16=21x+12

Transposing 20x to RHS and 12 to LHS

4=x

x=4

Hari’s age = 5x years = (5 × 4) years = 20 years

Harry’s age = 7x years = (7 × 4) years = 28 years

Therefore, Hari’s age and Harry’s age are 20 years and 28 years respectively.

 

Question 7- The denominator of a rational number is greater than its numerator by 8. If the numerator is increased by 17 and the denominator is decreased by 1, the number obtained is 3/2 .  Find the rational number.

Answer - Let the numerator of the rational number be x. Therefore, its denominator will

be x + 8.

The rational number will be  x/(x+8) According to the question

 

 2(x + 17) = 3(x + 7)

 2x + 34 = 3x + 21

 34 − 21 = 3x − 2x

13 = x

Numerator of the rational number = x = 13

Denominator of the rational number = x + 8 = 13 + 8 = 21

 


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