Question

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?

Answer 1

Let the cost of fare be Rs.${}^{\prime }{x}^{\prime }$ and the reservation charge be Rs.${}^{\prime }{y}^{\prime }$.

By condition $I:x+y=216$ ....$\left(i\right)$

By condition $II:$

one full and one half ticket $=1+\frac{1}{2}=\frac{3}{2}$

cost of half railway ticket is $=\frac{x}{2}$

$\therefore ,x+y+\frac{x}{2}+y=327$

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

$\Rightarrow 3x+4y=654$ ....$\left(ii\right)$(after multiplying by $2$ )

By solving $\left(i\right)$ and $\left(ii\right)$ we will get

$3x+4y-4x-4y=654-864$

$\therefore x=210$ and put $x=210$ in $\left(i\right)$ we get $y=216-x=216-210=6$

$\therefore y=6$

Hence, basic fare for one ticket is Rs.$210$ and reservation fare is Rs.$6$