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

Let the basic first class full fare and reservation charge be Rs. x and Rs. y respectively.

According to question -

Full fare + reservation charge = Rs. 4150

x + y = 4150.....(1)

and,

[full fare + reservation charge] + [half fare + reservation charge] = Rs. 6255

x + y + (x/2) + y = 6255

(3x/2) + 2y = 6255.....(2)

Subtracting equation (2) from [2×equation (1)], we get -

x/2 = 2045

x = 4090

Substituting the value of x in the equation (1), we get -

y = 60

Thus, basic full fare = Rs. 4090

reservation charge = Rs. 60

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