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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 station A to B costs Rs 2530. Also, one reserved first class ticket and one reserved fi

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 station A to B costs Rs 2530. Also, one reserved first class ticket and one reserved first class half ticket from A to B costs Rs 3810. Find the full first class fare from station A to B, and also the reservation charges for a ticket.

Answers (1)

Solution:
Let the full ticket cost = y Rs.
Let reservation charge = x Rs.
According to questions
x + y = 2530                            … (1)

(x + y) + (x + y/2) = 3810       …(2)

Here x + y is for full ticket and x + y/2 is for half.
Solve equation (1) and (2)
x + y + x + \frac{y}{2} = 3810

2x + y + \frac{y}{2} = 3810
4x + 2y + y = 3810 × 2
4x + 3y = 7620                        … (3)
Multiply equation (1) by 3
3x + 3y = 7590
4x + 3y = 7620
–      –        –
–x = – 30
Put x = 30 in eq. (1)
30 + y = 2530
y = 2500
Hence Reservation charge  = 30Rs.
Full First class charge = 2500 Rs.

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