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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 Delhi to station $$ A $$ and to station $$ B $$.


Solution

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

Mathematics

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