Question

A railway half ticket costs half the full fare and the reservation charge is the same of 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 ticket 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 correct option is A Full Fare = Rs.210, Reservation Charge = Rs.6

Let cost of full fare ticket be Rs $x$ and reservation charge be Rs $y$.
As per the statement, "One reserved first class ticket from Mumbai to Ahmedabad costs Rs. $216$." $=>x+y=216$ --- (1)

And, "one full and one half reserved first class ticket cost Rs. $327"=>(x+y)+(\frac{x}{2}+y)=327=>\frac{3x}{2}+2y=327$ --- (2)

Multiplying equation $\left(1\right)$ with $2$ we get, $2x+2y=432$ ----- equation $\left(3\right)$

Subtracting equation $\left(2\right)$ from $\left(3\right)$, we get $\frac{x}{2}=105=>x=210$
Substituting $x=210$ in the equation $\left(1\right)$, we get $210+y=216=>y=6$

Hence, cost of full far ticket is Rs $210$ and reservation charge is Rs $6$