# . What is the basic first class full fare and what is the reservation charge

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 Ahmadabad costs. Rs.216 while 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?

The basic first class full fare is = Rs 210 and reservation charge is =Rs 6.

Explanation:

Let the basic first class half fare be =x and reservation charge be =y

Since the half fare is half of the full fare then basic first class full fare =2x

Firstly, One reserved first class ticket from Mumbai to Ahmedabad costs Rs 216 while one full.

2x + y = 216......(1)

Secondly, same reservation ticket while it is one full and one half costs Rs 327

2x + y + x + y = 327 ⟹ 3x + 2y = 327......(2), Since the reservation charge is half and full.

(1) × 2 - (2) ⟹

2 (2x + y) - (3x + 2y) = 2 × 216 - 327

⟹ 4x + 2y - 3x - 2y = 432 - 327

⟹ x = 105

Substituting x = 105 in (1) we get,

2 × 105 + y = 216

⟹ 210 + y = 216

⟹y = 216 - 210

⟹ y = 6

Hence, full first class fair is = 2 x = 2 × 105 = Rs 210

Reservation charge = Rs 6