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 Ahmedabad 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

Hint: In this question, we have to assume the cost of fare and reservation charge and then make two equations by using the given mention in the question. So, after eliminating the variables we will get the required answer.

Complete Step-by-Step solution:
Let the cost of basic first class fare be Rs. x and the reservation charge be Rs. y.
Now, one reserved first class ticket from Mumbai to Ahmedabad costs. Rs.216
$ \Rightarrow x + y = 216.................\left( 1 \right)$
Now, one full and one half reserved first class tickets cost Rs.327.
(One full ticket and their reservation charge) + (One half ticket and their reservation charge) = Rs. 327
$
   \Rightarrow \left( {x + y} \right) + \left( {\dfrac{x}{2} + y} \right) = 327 \\
   \Rightarrow x + \dfrac{x}{2} + y + y = 327 \\
   \Rightarrow \dfrac{{3x}}{2} + 2y = 327 \\
$
Multiply by 2 in above equation,
$ \Rightarrow 3x + 4y = 654................\left( 2 \right)$
Now, we have to solve both equations by eliminating variables.
Multiply by 4 in (1) equation,
$ \Rightarrow 4x + 4y = 864.................\left( 3 \right)$
Now, subtract (2) equation from (3) equation.
$
   \Rightarrow 4x + 4y - 3x - 4y = 864 - 654 \\
   \Rightarrow x = Rs.210 \\
 $
Put value of x in (1) equation,
\[
   \Rightarrow 210 + y = 216 \\
   \Rightarrow y = 216 - 210 \\
   \Rightarrow y = Rs.6 \\
\]
So, the cost of basic first class fare is Rs.210 and the reservation charge is Rs.6.

Note: In such types of problems we should always remember one thing that reservation charges always be fixed even if we buy a full ticket or half ticket. In this question we solve the two equations by eliminating method but we are free to use substitution method or any other method to solve the equations.