Question

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

Answer 1

Let the cost of full and half first class fare be Rs. X and `Rs. (x)/(2)`, respectively and reservation charges be Rs. Y per ticket.
Case I The cost of one reserved first class ticket from the stations A to B
=rs. 2530
`rAss " " 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 = Rs. 3810
`rArr " " x+y+(x)/(2)+y=3810`
`rArr " " (3x)/(2)+2y=3810`
`rArr " " 3x+4y=7620 " " ...(ii)`
Now, multiplying Eq. (i) by 4 and then subtracting from Eq. (ii), we get
`{:(3x+4y=7620),(ul(underset(-)4x+underset(-)4y=underset(-)(1)0120)),(" " -x=-2500):}`
`rArr " " x=2500`
On putting the value of x in Eq. (i), we get
2500+y=2530
`rArr " " y=30`
Hence, full first class fare from stations A to B is Rs. 2500 and the reservation for a ticket is Rs. 30.