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# A railway half ticket costs half the full fare, but the reservation charges are the same on a half ticket as on a full ticket. One reserved first class ticket from the station A to B costs Rs 2530 . Also, one reserved first class ticket and one reserved first class half ticket from A to B costs Rs 3810 . Find the full first class fare from station $ \mathrm{A} $ to $ \mathrm{B} $, and also the reservation charges for a ticket.

Given:

A railway half ticket costs half the full fare, but the reservation charges are the same on a half ticket as on a full ticket. One reserved first class ticket from the station A to B costs Rs 2530 . Also, one reserved first class ticket and one reserved first class half ticket from A to B costs Rs 3810.

To do:

We have to find the basic first class full fare and the reservation charge.

Solution:Let the rate of the full ticket and the rate of reservation be $x$ and $y$ respectively.

One reserved first-class ticket from A to B costs Rs. 2530.

This implies,

$x+y=2530$

$x=2530-y$.....(i)

One full and one half reserved first class tickets cost Rs. 3810.

$\frac{3}{2}x + 2y = 3810$

$\frac{3x+2(2y)}{2} = 3810$

$3x+4y=2(3810)$ (On cross multiplication)

$3(2530-y)+4y=7620$ (From (i))

$7590-3y+4y=7620$

$y=7620-7590$

$y=30$

Substituting $y=30$ in equation (i), we get,

$x=2530-30$

$x=2500$

Therefore, the basic first-class full fare is Rs. 2500 and the reservation charge is Rs. 30.

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