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 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.

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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 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.

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Cost of full first-class fare is Rs3500 and reservation charges is Rs30

Cost of full first-class fare is Rs500 and reservation charges is Rs20

Cost of full first-class fare is Rs1000 and reservation charges is Rs50

Cost of full first-class fare is Rs2500 and reservation charges is Rs30

answer is D.

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Detailed Solution

Given that the charges of different tickets are one reserved first class ticket from the stations

A

B

costs Rs 2530. Also, one reserved first class ticket and one reserved first class half ticket from stations

A

B

costs Rs 3810.
Let the cost of full first-class fare be x Then, the cost of half first-class fare is

x 2

. Also, let reservation charges be y per ticket.
The cost of one reserved first-class ticket from the station's A to B

= 2530 ⇒ x + y = 2530 … (i)

The cost of one reserved first-class ticket and one reserved first-class half ticket from stations A to B =3810

⇒ x + y + x 2 + y = 3810 ⇒ 3 x 2 + 2 y = 3810 ⇒ 3 x + 4 y = 7620 … (i i)

Solving above equations, we get x=2500, y=30.
Therefore, the cost of full first-class fare is Rs2500 and reservation charges is Rs30.
Hence, option (4) is correct.

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