Question

Question 10
A railway half ticket cost half the full fare bu the reservation charges are the same on a half ticket as on a full ticket. One reserved first class ticket from the stations A to B costs Rs. 2530. Also, one reserved first class ticket and one reserved first class half ticket from stations A to B costs Rs. 3810. Find the full first class fare from stations A to B and also the reservation charges for a ticket.

Answer 1

Let the cost of full and half first class fare be Rs. x and Rs. $\frac{x}{2}$ respectively and reservation I charges be Rs. Y per ticket.
Case I The cost of one reserved first class ticket from the stations A to B
= Rs 2530

$\Rightarrow$ x + y = 2530

Case II The cost of one reserved first class ticket and one reserved first class half ticket from stations A to B = Rs. 3810
$\Rightarrow x+y+\frac{x}{2},+y=3810$

$\Rightarrow$ + 2y = 3810

$\Rightarrow$ 3x + y = 7620

Now, multiplying Eq. (i) by 4 and then subtracting from Eq. (ii), we get

3x + 4y = 7620

4x + 4y = 10120

- x = - 2500

$\Rightarrow$ x = 2500

On putting the value of x in Eq. (i), we get

2500 + y = 2530

$\Rightarrow$ y = 2530 – 2500

$\Rightarrow$ y = 30
Hence, full first class fare from stations A to B is Rs. 2500 and the reservation for a ticket is Rs. 30.