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Question

# Railway Half Ticket costs half the full fare but the reservation are same for half and full Ticket. one reserved first class ticket from station A to B costs 2350 rupees. Also one first class ticket and one reserved first class half ticket from A to B cost rupees 3810 . find the full first class fare from station a to b and also a reservation charge for a ticket.

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Solution

## Let the cost of full and half first class fare be Rs. x and Rs. 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 2350 ⇒ x + y = 2350 Case II The cost of one reserved first class ticket and one reserved first class half ticket from stations A to B = Rs. 3810 ⇒x+y+x2+y=3810 ⇒ 3x/2 + 2y = 3810 ⇒ 3x + 4y = 7620 Now, multiplying Eq. (i) by 4 and then subtracting from Eq. (ii), we get 3x + 4y = 7620 4x + 4y = 9400 - x = - 1780 ⇒ x = 1780 On putting the value of x in Eq. (i), we get 1780 + y = 2350 ⇒ y = 2350 – 1780 ⇒ y = 570 Hence, full first class fare from stations A to B is Rs. 1780 and the reservation for a ticket is Rs. 570.

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