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 2 + ) = 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.