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Thread: New Stations.

  1. #1
    Expert Member
    Join Date
    Jun 2006
    Answers
    410

    New Stations.

    There N stations on a railroad. After adding X stations on the rail route 46 additional tickets have to be printed.

    Find N and X.

    -- James.


  2. #2
    Junior Member
    Join Date
    Sep 2006
    Answers
    23

    Re: New Stations.

    James could you give the answer for this with the method of achieving the solution.


  3. #3
    Expert Member
    Join Date
    Jun 2006
    Answers
    410

    Re: New Stations.

    It is given that X stations are added. Therefore each existing stations requires tickets for each new stations.
    This requires N *x new tickets.

    Each new stations needs to have N + x -1 tickets.
    This requires x(N +x-1) new tickets.

    => N *x + x(N +x-1) =46
    => (2N -1 +x)x =46

    Both x and N are positve integers. Therefore value of x can be either 1,2 or 23.

    if x =1 then 2n =46 => N=23.
    if x =2 then (2N +1)2=46
    => 2N+1 =23
    => N =11

    if x=23 then (2N+22)23=46
    => N = -11 (which is not possible)

    Hence values of N and X are either 23 and 1 or 11 and 2.

    -- James.


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