Question

From Delhi station, if we buy $2$ tickets for station $A$ and $3$ tickets for station $B$, the total cost is Rs $77$. But if we buy $3$ tickets for station $A$ and $5$ tickets for station $B$, the total cost is Rs $124$. What are the fares from Delhi to station $A$ and to station $B$?

• A. $A=$ Rs $21$ and $B=$ Rs $19$
• B. $A=$ Rs $13$ and $B=$ Rs $17$
• C. $A=$ Rs $18$ and $B=$ Rs $12$
• D. $A=$ Rs $16$ and $B=$ Rs $19$

Answer 1

The correct option is B $A=$ Rs $13$ and $B=$ Rs $17$

From the given information, we can write

$2A+3B=77$ ...(1)

$3A+5B=124$ ...(2)

Subtracting (1) and (2), we get

$A+2B=47$

$\Rightarrow A=47-2B$

Sub that in (1)

$2(47-2B)+3B=77$

$\Rightarrow 94-B=77$

$B=$ Rs $17$

$A=47-2\left(17\right)=$ Rs $13$