MathematicsFrom 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?

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?


  1. A
    A=Rs.12, B=Rs.17
  2. B
    A=Rs.13, B=Rs.17
  3. C
    A=Rs.18, B=Rs.17
  4. D
    A=Rs.19, B=Rs.17  

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    Solution:

    Let the price of ticket for station A.
    be Rs. x and for station B be Rs. y.
    According to the given condition,
    2x+3y=77 … (1)
    3x+5y=124 …(2)
    Multiplying equation (1) by 3,
    6x+9y=231……….(3)
    Multiplying equation (2) by 2,
    6x + 10y  = 248…(4)
    Subtracting equation (3) from equation (4), we get,
    ⇒ y = 248 −231
    ⇒ y = 17
    Substituting value of y in equation (1),
    2x +3(17) = 77
    ⇒2x + 51=77 ⇒ 2x = 26
    Therefore, x =13.
    Hence, the correct option is 2.
     
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