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Chapter 2 Linear Equations in One Variable Ex 2.6 Solutions

Question - 1 : -
Solve the equation.
 9x/(7 – 6x) = 15

Answer - 1 : -

9x/(7 – 6x) = 15
⇒ 9x = 15(7 – 6x)
⇒ 9x = 105 – 90x
⇒ 9x + 90x = 105
⇒ 99x = 105
⇒ x = 105/99 = 35/33

Question - 2 : -
Solve the equation.
 z/(z + 15) = 4/9

Answer - 2 : -

z/(z + 15) = 4/9
⇒ z = 4/9 (z + 15)
⇒ 9z = 4(z + 15)
⇒ 9z = 4z + 60
⇒ 9z – 4z = 60
⇒ 5z = 60
⇒ z = 12

Question - 3 : -
Solve the equation.
 (3y + 4)/(2 – 6y) = -2/5

Answer - 3 : -

(3y + 4)/(2 – 6y) = -2/5
⇒ 3y + 4 = -2/5 (2 – 6y)
⇒ 5(3y + 4) = -2(2 – 6y)
⇒ 15y + 20 = -4 + 12y
⇒ 15y – 12y = -4 – 20
⇒ 3y = -24
⇒ y = -8

Question - 4 : -
Solve the equation.
 (7y + 4)/(y + 2) = -4/3

Answer - 4 : -

(7y + 4)/(y + 2) = -4/3
⇒ 7y + 4 = -4/3 (y + 2)
⇒ 3(7y + 4) = -4(y + 2)
⇒ 21y + 12 = -4y – 8
⇒ 21y + 4y = -8 – 12
⇒ 25y = -20
⇒ y = -20/25 = -4/5

Question - 5 : - 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 - 5 : -

Let the age of Hari be 5x and Harry be 7x. 4 years later,
Age of Hari = 5x + 4 Age of Harry = 7x + 4
According to the question,
(5x + 4)/(7x + 4) = ¾
⇒ 4(5x + 4) = 3(7x + 4)
⇒ 20x + 16 = 21x + 12
⇒ 21x – 20x = 16 – 12
⇒ x = 4
Hari age = 5x = 5 × 4 = 20 years
Harry age = 7x = 7 × 4 = 28 years

Question - 6 : - 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 - 6 : -

Let the numerator be x then denominator will be (x + 8)
According to the question,
(x + 17)/(x + 8 – 1) = 3/2
⇒ (x + 17)/(x + 7) = 3/2
⇒ 2(x + 17) = 3(x + 7)
⇒ 2x + 34 = 3x + 21
⇒ 34 – 21 = 3x – 2x
⇒ 13 = x
The rational number is x/(x + 8) = 13/21

Question - 7 : -
Solve the equation.
 (8x – 3)/3x = 2

Answer - 7 : -

(8x – 3)/3x = 2
⇒ 8x/3x – 3/3x = 2
⇒ 8/3 – 1/x = 2
⇒ 8/3 – 2 = 1/x
⇒ (8 – 6)/3 = 1/x
⇒ 2/3 = 1/x
⇒ x = 3/2

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