Question

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 $B$.

• A. Rs. $1280$
• B. Rs. $2500$
• C. Rs. $3570$
• D. Rs. $2250$

Answer 1

The correct option is B Rs. $2500$

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,

$x+y=2530..........\left(1\right)$ 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

$(x+y)+(x+\frac{y}{2})=3810\Rightarrow 4x+3y=\mathrm{7620.............}\left(2\right)$

Multiplying equation 1 by $3$ we get,

$3x+3y=7590..........\left(3\right)$

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. $2500$.