Question

A railway half ticket costs half the full fare and the reservation charge is the some on half ticket as on full ticket. One reserved first class ticket from Mumbai to Delhi costs ₹4150 while one full and one half reserved first class ticket cost ₹ 6255. What is the basic first class full fare and what is the reservation charge?

Answer 1

Let the basic first class full fare be Rs.x and the reservation charge be Rs.y.
Case 1: One reservation first class full ticket cost Rs.4, 150
x + y = 4150             ………(i)
Case 2: One full and one and half reserved first class tickets cost Rs.6,255
`(x + y) + (1/2𝑥+𝑦) = 6255`
⇒ 3x + 4y = 12510            ………(ii)
Substituting y = 4150 – x from (i) in (ii), we get
3x + 4(4150 – x) = 12510
⇒3x – 4x + 16600 = 12510
⇒x = 16600 – 12510 = 4090
Now, putting x = 4090 in (i), we have
4090 + y = 4150
⇒ y = 4150 – 4090 = 60
Hence, cost of basic first class full fare = Rs.4,090 and reservation charge = Rs.60.