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 ?

Answer 1

Let, the fare of ticket for station A be Rs. x and the fare of ticket for station B be Rs. y
According, to the question
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)

Subtracting equation (4) from (3)
    6x + 9y = 231
-  6x + 10y = 248 
   -     -         -       
         - y = - 17
            y = 17
From (1) 
2x + 3 (17) = 77
2x = 77 - 51
2x = 26
x = 13
Thus, fare for station A = Rs. 13 and, fare for station B = Rs. 17.