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 and 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?

a.full fare = rs.210 reservation charge = rs.6
b.full fare = rs.144 reservation charge = rs.72
c.full fare = rs.180 reservation charge = rs.36
d.full fare = rs.200 reservation charge = rs.16

Answer 1

The basic first class full fare is Rs. 210, and the reservation charge is Rs. 6. We solve this by defining two variables, creating equations based on the given information, and then solving these equations simultaneously.

Step-by-step explanation:

We are given two scenarios in the question:

1. The cost of one reserved first class ticket from Mumbai to Ahmedabad is Rs. 216.
2. The combined cost of one full and one half reserved first class tickets is Rs. 327.

Let's define F as the full fare for a first-class ticket without the reservation charge, and R as the reservation charge. A half ticket would therefore cost F/2.

The full cost for a reserved first class ticket (scenario 1) can be expressed as:

F + R = 216

Similarly, the combined cost for one full and one half reserved first class ticket (scenario 2) is:

F + F/2 + 2R = 327

Simplifying by multiplying through by 2 to remove the fraction we get:

2F + F + 4R = 654
3F + 4R = 654

Now we have two equations with two unknowns which we can solve simultaneously:

1. F + R = 216
2. 3F + 4R = 654

By multiplying the first equation by 3 (3F + 3R = 648) and subtracting it from the second one (3F + 4R = 654), we can find R:

654 - 648 = 6
R = 6

Now that we know R, we can solve for F by substituting R back into the first equation:

F + 6 = 216
F = 216 - 6
F = 210

Therefore, the basic first class full fare is Rs. 210, and the reservation charge is Rs. 6, which corresponds to option (a).