Question

A railway half ticket costs half the full fare and the reservation charges are the same on half ticket as on full ticket. One reserved first class ticket from station A to B costs Rs. 432 and one full and one half reserved first class ticket cost Rs. 654. What are the first class fare and from A to B reservation charges?

Answer 1

Answer:

Let the reservation charges be Rs. x and cost of full ticket of first class be Rs. y.

It is given that 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, therefore,

x+y=2530..........(1) and

since railway half ticket costs half the full fare, but the reservation charges are the same on a half ticket as on a full ticket so we get

(x+y)+(x+

2

y

)=3810

⇒4x+3y=7620.............(2)

Multiplying equation 1 by 3 we get,

3x+3y=7590..........(3)

Now subtracting equation 3 from equation 2, we get x=30.

Now substitute the value of x in equation 1 that is:

30+y=2530

implies y=2500

Hence, the full first class fare from station A to B is Rs. 2500.

Answer 2

let the Full fare=x

and Reservation charges=y

then,

A.T.Q

x+y−2530 ---(1)

Also,

x+x of 50%+2y=3810

x+

2

x

+2y=3810

2

3x

+2y=3810

3x+4y=7620−−−−(2)

from equation (1),

x+y=2530

y=2530−x put in (2)

3X+4(2530−X)=7620

3X+10120−4X=7620

3X−4X=7620−10120

−X=−2500

X=2500

put the value of x in equation (1)

x+y=2530

2500+y=2530

y=2530−2500

y=30

Hence, the Full pare=2500Rs

the reservation charges=30Rs