B as a percentage of A is equal to A as a percentage of (A + B). Find B as a percentage of A

• From the question stem, we know
  B
  A
  =(
  A
  A+B
  ) --------------- (1)
  
  As B is a percent of A, let us assume B=Ax
  Then, equation (1) can be re-written as x=(
  1
  1+x
  )
  ⇒ x(1+x)=1
  
  solving, we get x2+x−1=0
  
  ⇒ x=(
  −1+√5
  2
  ) or x=(
  −1−√5
  2
  )
  So, x=(
  −1+√5
  2
  )=
  1.24
  2
  
  
  Or 0.62 = 62%
• 6 years agoHelpfull: Yes(0) No(0)
• From the question stem, we know
  B
  A
  =
  (
  A
  A
  +
  B
  )
  --------------- (1)
  
  As B is a percent of A, let us assume
  B
  =
  A
  x
  
  Then, equation (1) can be re-written as
  x
  =
  (
  1
  1
  +
  x
  )
  
  ⇒
  x
  (
  1
  +
  x
  )
  =
  1
  
  
  After this step, trial and error works best. The solution is 62%, answer choice (A) is the correct one.
  
  Alternatively, solving, we get
  x
  2
  +
  x
  −
  1
  =
  0
  
  ⇒
  x
  =
  (
  −
  1
  +
  5
  2
  )
  or
  x
  =
  (
  −
  1
  −
  5
  2
  )
  
  So,
  x
  =
  (
  −
  1
  +
  5
  2
  )
  =
  1.24
  2
  
  
  Or 0.62 = 62%
• 6 years agoHelpfull: Yes(0) No(0)