A railway half ticket cost half the full fare but the reservation charges are the same on a half ticket as on a full ticket. One reserved first class ticket from the station A to B costs ₹ 2530. Also, one reserved first class ticket and one reserved first class half ticket from stations A to B costs ₹ 3810. Find the full first class fare from stations A to B and also the reservation charges for a ticket.
Let the cost of full and half first class fare be ₹ x and ₹ x/2 respectively and reservation charges be ₹ y per ticket.
Case I The cost of one reserved first class ticket from the stations A to B
= ₹ 2530
…(i)
Case II The cost of one reserved first class ticket and one reserved first class half ticket from stations A to B = ₹ 3810
3x + 4y = 7620 ..(ii)
Now, multiplying Eq. (i) by 4 and then subtracting from Eq. (ii), we get
On putting the value of x in Eq. (i), we get
Hence, full first class fare from stations A to B is ₹ 2500 and the reservation for a ticket is ₹ 30.