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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.
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Solution
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.
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