Question

From Delhi station , if we buy $2$ tickets for station $A$ and $3$ tickets for station $B$ , the total cost is $Rs77$ but if we buy $3$ tickets for station $A$ and $5$ tickets for station $B$ , the total cost is $rs124$ What are the fares Delhi to station $A$ and to station $B$.

Answer 1

Let, the fare of ticket for station $A$ be Rs. $x$
and the fare of ticket for station $B$ be Rs.$y$
$2x+3y=\mathrm{77.....}\left(1\right)$
and$3x+5y=\mathrm{124.....}\left(2\right)$
Multiplying equation no. (1) by $3$ and (2) by $2$.
$6x+9y=\mathrm{231.....}\left(3\right)$
$6x+10y=\mathrm{248.....}\left(4\right)$.
$---$
______________
$-y=-17$
$y=17$
From $\left(1\right)2x+3\left(17\right)=77$
$2x=77-51$
$2x=36$
$x=13$
Thus, fare for station $A$=Rs. $13$
and, fare for station $B$=Rs. $17$.