# 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 ahmedabad costs Rs. 216 and one full and one half reserved first class tickets cost Rs. 327. what is the basic first class full fare and what is the reservation charge.

Let x be the cost of full first class ticket from Mumbai to Ahmedabad.

Let y be the cost of reservation.

Since a reserved first class ticket costs Rs.216,

....(1)

Since one full and one half first class reserved ticket costs Rs.327,

....(2)

Thus, equations (1) and (2) form the system of equations.

Multiply equation (2) by 2 and rewrite the equation (2) as

....(3)

Let us solve the system of equations (3) and (1).

Multiply equation (1) by 3 to get

....(4)

Subtract equation (4) from equation (3) to get

Substitute the value of y in equation (1) to get the value of x

Thus, the first class ticket from Mumbai to Ahmedabad is Rs.210 and the reservation cost is Rs.6

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