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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