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?

Given:

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. 

To do:

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

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

One reserved first-class ticket from Mumbai to Ahmedabad costs Rs. 216.

This implies,

$x+y=216$

$x=216-y$.....(i)

One full and one half reserved first class tickets cost Rs. 327. 

$\frac{3}{2}x + 2y = 327$

$\frac{3x+2(2y)}{2} = 327$

$3x+4y=2(327)$     (On cross multiplication)

$3(216-y)+4y=654$     (From (i))

$648-3y+4y=654$

$y=654-648$

$y=6$

Substituting $y=6$ in equation (i), we get,

$x=216-6$

$x=210$

Therefore, the basic first-class full fare is Rs. 210 and the reservation charge is Rs. 6.

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Updated on: 10-Oct-2022

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