Question

A railway half ticket costs 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 Rs 2530. Also, one reserved first class ticket and one reserved first class half ticket from A to B costs Rs 3810. Find the full first class fare from station A to B, and also the reservation charges for a ticket.

Answer 1

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

⇒ x + y = 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

⇒ `x + y + x/2 + y` = 3810

⇒ `(3x)/2 + 2y` = 3810

⇒ 3x + 4y = 7620  .....(ii)

Now, multiplying equation (i) by 4 and then subtracting from equation (ii), we get

(3x + 4y) – (4x + 4y) = 7620 – 10120

⇒ –x = –2500

⇒ x = 2500

On putting the value of x in equation (i), we get

2500 + y = 2530

⇒ y = 2530 – 2500

⇒ y = 30

Hence, full first class fare from stations A to B is ₹ 2500 and the reservation charge for the ticket is ₹ 30.