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Exercise - 2.6

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

Solution :-
  (8x - 3)/3x = 2
  8x - 3 = 2 x 3x
  8x = 3 + 6x
  8x - 6x = 3
       2x = 3
        x = 3/2
  Verification : 
  L.H.S = (8x - 3)/3x 
        = (8 x 3/2 - 3)/(3 x 3/2)
        = (12 - 3)/(9/2)
        = (9 x 2)/9
        = 2 = R.H.S
    

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

Solution :-
  9x/(7 - 6x) = 15
  9x = 15 x (7 - 6x)
  9x = 105 - 90x
  9x + 90x = 105
       99x = 105
         x = 105/99
         x = 35/33
  Verification : 
  L.H.S = 9x/(7 - 6x) 
        = [(9 x 35)/33] ÷ [7 - (6 x 35/33)]
        = (3 x 35/11) ÷ [7 - (2 x 35/11)]
        = (105/11) ÷ (7 - 70/11)
        = (105/11) ÷ [(77 - 70)/11]
        = 105/11 ÷ 7/11
        = 105/7
        = 15 = R.H.S
    

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

Solution :-
   z/(z + 15) = 4/9
   9z = 4 x (z + 15)
   9z = 4z + 60
   9z - 4z = 60
        5z = 60
         z = 60/5
         z = 12 
   Verification : 
   L.H.S = z/(z + 15)
         = 12/(12 + 15)
         = 12/27
         = 4/9 = R.H.S
    

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

Solution :-
  (3y + 4)/(2 - 6y) = -2/5
  5 x (3y + 4) = -2 x (2 - 6y)
  15y + 20 = -4 + 12y
  15y - 12y = -4 - 20
        3y = -24
         y = -24/3
         y = -8
  Verification : 
  L.H.S = (3y + 4)/(2 - 6y)
        = (-24 + 4)/(2 + 48)
        = -20/50
        = -2/5 = R.H.S
    

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

Solution :-
  (7y + 4)/(y + 2) = -4/3
  3 x (7y + 4) = -4 x (y + 2)
  21y + 12 = -4y - 8
  21y + 4y = -8 - 12
       25y = -20
         y = -20/25
         y = -4/5
  Verification :
  L.H.S = (7y + 4)/(y + 2)  
        = (-28/5 + 4) ÷ (-4/5 + 2)
        = [(-28 + 20)/5] ÷ [(-4 + 10)/5]
        = (-8/5) ÷ (6/5)
        = (-8 x 5)/(5 x 6)
        = -8/6
        = -4/3 = R.H.S
    

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.

Solution :-
   Let the age of Hari = 5x years
       the age of Harry = 7x years
   According to question : 
   (5x + 4)/(7x + 4) = 3/4
   4 (5x + 4) = 3 (7x + 4)
   20x + 16 = 21x + 12
   20x - 21x = 12 - 16
          -x = -4
           x = 4
   The age of Hari = 5x = 5 x 4 = 20 years
   The age of Harry = 7x = 7 x 4 = 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.

Solution :-
  Let the numerator of a rational number  = x
      the denominator = x + 8
      rational number = x/(x+8)
  According to question :
  (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
       -x = -13
        x = 13 
  The numerator of a rational number  = x = 13
  The denominator = x + 8 = 13 + 8 = 23
  Rational number = x/(x + 8) = 13/(13 + 8) = 13/21
    
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