Question

a railway half tickect costs half the full fare and the reservation charges is the same on half ticket as on full ticket. one reserved first class ticket from Mumbai to Ahmadabad costs rs 216 and one full and one half reserved first class tickets costs rs 327. what is the basic first class full fare and what is the reservation charges
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Answer 1

Let the cost of ticket be = x
Let the reservation charge be = y

1st case
x+y = 216 (1)

2nd case
1.5x+2y = 327. (2)

Eliminating (1) and (2)
x+y = 216 x 2

2x + 2y = 432
1.5x+ 2y = 327
0.5x = 105
X = 210

Substituting x in (1)
x+y = 216
210+ y = 216
y = 216-210
y = 6

Answer
Cost of ticket = 216
Reservation charge = 6

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