A naughty student breaks a pencil in such a way that the ratio of two broken parts is same as that of the original length of the pencil to one of the larger part of the pencil. the ratio of the other part to the original length of pencil is?

• Let the pencil be broken in ratio 1:k where k being a greater fraction.
  
  According to the condition:
  1/k=k/(k+1)
  k^2 - k - 1 =0
  k=[1+(5)^(1/2)]/2
  
  Ans.1/(k+1)= 2/(3+sqroot5)
• 8 years agoHelpfull: Yes(6) No(1)
• Length of pencil be 10
  two parts: x, 10-x
  let us assume x part is larger part
  x/(10-x) = 10/ x
  or x= 5 * ( sqrt5 -1 ) = 6.18
  other part= 5*(3- sqrt5) = 3.82
  
  ratio of other part to original = 3.82 / 10 = 0 .382
• 8 years agoHelpfull: Yes(0) No(3)