A railway half the ticket cost …

Let the costs of the full fare be Rs x and that of the reservation charge be Rs. y. Then,
{tex}x + y = 216{/tex} ...(i) [given]
And, {tex}(x + y) + \left( {\frac{1}{2}x + y} \right) = 327{/tex} [given]
{tex}x + y + \frac{1}{2}x + y = 327{/tex}
{tex}\Rightarrow x + \frac{1}{2}x + 2y = 327{/tex}
{tex}\Rightarrow \frac{{3x}}{2} + 2y = 327{/tex}
{tex}\Rightarrow{/tex} {tex}3x + 4y = 654{/tex} ...(ii)
Multiplying equation (i) by 4, we get
{tex}4x + 4y = 864{/tex} ....(iii)
Subtracting equation (ii) from equation (iii), we get
{tex}4x - 3x = 864 - 654{/tex}
{tex}\Rightarrow{/tex} {tex}x = 210{/tex}
Putting {tex}x = 210{/tex} in equation (i), we get
{tex}210 + y = 216{/tex}
{tex}\Rightarrow{/tex} {tex}y = 216 - 210 = 6{/tex}
Hence, the cost of the full fare ={tex} Rs. 210{/tex} and, the cost of the reservation charge = {tex}Rs. 6{/tex}.