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?
Let the cost of ticket to station A be Rs x and to station B be Rs y.
Given that, "if we buy 2 tickets for station A and 3 tickets for station B, the total cost is Rs. 77."
⇒2x+3y=77 --- (1)
Also, "if we buy 3 tickets for station A and 5 tickets for station B, the total cost is Rs. 124."
⇒3x+5y=124 --- (2)
Multiplying equation (1) by 3, we get,
6x+9y=231 ----- equation (3)
Multiplying equation (2) by 2, we get,
6x+10y=248 ----- equation (4)
Subtracting equation (3) from (4), we get:
(6x+10y)−(6x+9y)=248−231
⇒y=17
Substituting y=17 in the equation (1), we get:
2x+3(17)=77
⇒x=13
Hence, the fare from Delhi to station A is Rs. 13 and to station B is Rs. 17.