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Expert Member
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.
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Junior Member
Re: New Stations.
James could you give the answer for this with the method of achieving the solution.
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Expert Member
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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