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.

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