In a fraction, if 1 is added to both the numerator at the denominator, the fraction becomes 1/2. If numerator is subtracted from the denominator, the fraction becomes 3/4. Find the fraction.

• Let fraction be a/b, where a and b are integers.
  
  "If 1 is added to both the numerator and denominator, the fraction becomes 1/2"
  (a+1)/(b+1) = 1/2
  2(a+1) = b+1
  2a + 2 = b + 1
  2a - b = -1
  
  "If numerator is subtracted from the denominator, the fraction becomes 3/4"
  a/(b-a) = 3/4
  4a = 3(b-a)
  4a = 3b - 3a
  4a + 3a - 3b = 0
  7a - 3b = 0
  
  Now we just need to solve system of linear equations:
  2a - b = -1 . . . [1]
  7a - 3b = 0 . . . [2]
  
  From [1], we get:
  b = 2a + 1
  
  Substituting in this value of b into [2], we get
  7a - 3(2a+1) = 0
  7a - 6a - 3 = 0
  a - 3 = 0
  a = 3
  
  b = 2(3)+1
  b = 7
  
  So original fraction is a/b = 3/7
  
• 13 years agoHelpfull: Yes(21) No(3)
• 4/1.
  x-1/y-1=1/2 and x-y/y=3/4
• 13 years agoHelpfull: Yes(1) No(6)
• a+1/b+1=1/2
  a-b/b=3/4
  solving we get a=-7/10
  b=-2/5
  fraction is 7/4
• 10 years agoHelpfull: Yes(1) No(2)
• answer is 0.5/2
  1.(x+1)/(y+1)=1/2
  
  
  (y-x)/y=3/4
  4y -4x=3y
  2.>y=4x
  (x+1)/4x+1=1/2
  2x+2=4x+1
  2x=1
  x=1/2
  x=0.5
  
  
• 8 years agoHelpfull: Yes(0) No(0)
• (x+1)/(y+1)=1/2; ---------(1)
  (y-x)/y=3/4; ---------(2)
  Solving the (2) eqn
  4y-4x=3y
  4y-3y=4x
  so, y=4x;---------(3)
  Eqn (1) becomes,
  2x+2=y+1
  y-2x=1
  apply (3) in (1)
  4x-2x=1
  2x=1
  x=1/2;
  then y=4*1/2=2
  thn, x/y=(1/2)/2
• 7 years agoHelpfull: Yes(0) No(0)