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.

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

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.