Every station in N railroad issues every other station ticket. Some stations are added. Now they have to issue 46 more tickets. Give the No. of stations after and before added.

• Let newly added one be x.
  
  the earlier stations are n. , then
  
  total number of tickets issued earlier = n(n-1)
  
  n(n-1) + 46 = (n+x)(n+x-1)
  
  n^2 - n + 46 = n^2 + x^2 + 2nx -n-x, thus
  x^2 + 2nx -x = 46, since x,n are integers, and 46 is expressed as, 2*23 or 1*46
  
  considering x(x+2n-1) ,
  if x = 2, n =11
  if x=1, n = 23
  hence no of stations before and after are
  {11,13}
  No of tickets earlier = 11*10=110
  No of tickets later = 13*12= 156
  or
  {23,24}
  No of tickets earlier = 23*22=506
  no of tickets later = 24*23= 552
  
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