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Chapter 2 Linear Equations in One Variable Ex 2.6 Solutions

Question - 1 : -
Solve the equation.
┬а9x/(7 тАУ 6x) = 15

Answer - 1 : -

9x/(7 тАУ 6x) = 15
тЗТ 9x = 15(7 тАУ 6x)
тЗТ 9x = 105 тАУ 90x
тЗТ 9x + 90x = 105
тЗТ 99x = 105
тЗТ x = 105/99 = 35/33

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

Answer - 2 : -

z/(z + 15) = 4/9
тЗТ z = 4/9 (z + 15)
тЗТ 9z = 4(z + 15)
тЗТ 9z = 4z + 60
тЗТ 9z тАУ 4z = 60
тЗТ 5z = 60
тЗТ z = 12

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

Answer - 3 : -

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

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

Answer - 4 : -

(7y + 4)/(y + 2) = -4/3
тЗТ 7y + 4 = -4/3 (y + 2)
тЗТ 3(7y + 4) = -4(y + 2)
тЗТ 21y + 12 = -4y тАУ 8
тЗТ 21y + 4y = -8 тАУ 12
тЗТ 25y = -20
тЗТ 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) = ┬╛
тЗТ 4(5x + 4) = 3(7x + 4)
тЗТ 20x + 16 = 21x + 12
тЗТ 21x тАУ 20x = 16 тАУ 12
тЗТ x = 4
Hari age = 5x = 5 ├Ч 4 = 20 years
Harry age = 7x = 7 ├Ч 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 тАУ 1) = 3/2
тЗТ (x + 17)/(x + 7) = 3/2
тЗТ 2(x + 17) = 3(x + 7)
тЗТ 2x + 34 = 3x + 21
тЗТ 34 тАУ 21 = 3x тАУ 2x
тЗТ 13 = x
The rational number is x/(x + 8) = 13/21

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

Answer - 7 : -

(8x тАУ 3)/3x = 2
тЗТ 8x/3x тАУ 3/3x = 2
тЗТ 8/3 тАУ 1/x = 2
тЗТ 8/3 тАУ 2 = 1/x
тЗТ (8 тАУ 6)/3 = 1/x
тЗТ 2/3 = 1/x
тЗТ x = 3/2

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