Chapter 2 Linear Equations in One Variable Exercise 2.6

Solve the following equations.
Question 1: (8x - 3)/3x = 2

= 8x - 3 = 2 × 3x
= 8x - 3 = 6x
= 8x - 6x = 3
= 2x = 3
= x = 3/2

Question 2: 9x/(7 - 6x) = 15

= 9x/7 - 6x = 15/1
= 9x = 105 - 90x
= 99x = 105
= x = 105/99
= x = 35/33

Question 3: z/(z + 15) = 4/9

= 9z = 4z + 60
= 9z - 4z = 60
= 5z = 60
= z = 60/5
= z = 12

Question 4: (3y + 4)/(2 - 6y) = -2/5

= 15y + 20 = -4 - (12y)
= 15y - 12ty = -4 - 20
= 3y = -24
= y = -24/3
= y = -8

Question 5: (7y + 4)/(y + 2) = -4/3

= -4(y + 2) = 3(7y + 4)
= -4y - 8 = 21y + 12
= -4y - 21y = 12 + 8
= -25y = 20
= y = 20/-25
= y = -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.

Let the present age of Hari and Harry be 5x and 7x.
After 4 years, Hari’s age = (5x + 4) years
After 4 years, Harry’s age = (7x + 4) years
= 5x + 4/7x + 4
= 5x + 4/7x + 4 = 3/4
= 4(5x + 4) = 3(7x + 4)
= 20x + 16 = 21x + 12
= 20x - 21x = 12 - 16
= -1x = -4
= 1x = 4
= x = 4
Hari's age = 5x = 5 × 4 = 20
Harry's age = 7x = 7 × 4 = 28
Therefore, the present age of Hari is 20 years, while the present age of Harry is 28 years.

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.

Let the numerator be x, denominator be x + 8.
Given
= x + 17/x + 8 - 1 = 3/2
= x + 17/x + 7 = 3/2
= 2(x + 17) = 3(x + 7)
= 2x + 34 = 3x + 21
= 2x - 3x = 21 - 34
= -1x = -13
= 1x = 13
= x = 13
Rational number
= x/x + 8
= 13/13 + 8
= 13/21
Therefore, the rational number is 13/21.