Question & Answer
QUESTION

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 full first class ticket from station A to station B costs Rs. 2125. Also, one reserved a full first class ticket and a half first class ticket from A to B costs Rs. 3200. Find the full fare from station A to station B and also the reservation charges for a ticket.

ANSWER Verified Verified
Hint: Assume that the full fare of the ticket is Rs. $x$ and reservation charges on a ticket is Rs. $y$. Form two sets of linear equations in two variables with the help of provided conditions and solve them to get the answer.

Complete step-by-step answer:

Let us assume that the full fare of the ticket is Rs. $x$ and reservation charges on a ticket is Rs. $y$. It is given that, half-ticket costs half the full fare and the reservation charges are the same on a half-ticket as on a full ticket. Therefore,

Cost of a full ticket $=x+y$,

And, Cost of a half ticket $=\dfrac{x}{2}+y$.

Now, one reserved full first class ticket from station A to station B costs Rs. 2125. Therefore, mathematically,

$x+y=2125........................(i)$

Also, one reserved full first class ticket and a half first class ticket from A to B costs Rs. 3200. Therefore, mathematically,

$\begin{align}

  & x+y+\dfrac{x}{2}+y=3200 \\

 & \dfrac{3x}{2}+2y=3200...................(ii) \\

\end{align}$

Now, multiplying equation (i) by 2 and subtracting it from equation (ii) we get,

$\begin{align}

  & \dfrac{3x}{2}+2y-(2x+2y)=3200-2\times 2125 \\

 & \dfrac{3x}{2}-2x=3200-4250 \\

 & \dfrac{-x}{2}=-1050 \\

\end{align}$

Cancelling the minus sign and cross multiplying, we get,

$\begin{align}

  & x=2\times 1050 \\

 & x=2100 \\

\end{align}$

Substituting the value of $x$ in equation (i) we get,

$\begin{align}

  & y=2125-2100 \\

 & y=25 \\

\end{align}$

Hence, full fare and reservation charge for a ticket from station A to B are Rs. 2100 and Rs. 25 respectively.

Note: One may get confused in understanding such a long question. The main problem here is to form linear equations with the help of provided information. So, we have to go thoroughly through the question.