NCERT Solutions for Linear equations Class 8 Chapter 2 Exercise 2.6

NCERT Solutions for Linear equations Class 8 Maths Chapter 2 Exercise 2.6

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
9z= 4(z+ 15)
9z= 4z+ 60
Transposing 4z on LHS
9z 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(y+ 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 bex. Therefore, Hari’s age and Harry’s age will be 5xyears and 7xyears 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 = 5xyears = (5 × 4) years = 20 years
Harry’s age = 7xyears = (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 bex. Therefore, its denominator will
bex+ 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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