The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is Rs.105 and for a journey of 15 km, the charge paid is Rs.155. What are the fixed charges and the charge per km? How much does a person have to pay for travelling a distance of 25 km?

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 3. (iv) The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is Rs.105 and for a journey of 15 km, the charge paid is Rs.155. What are the fixed charges and the charge per km? How much does a person have to pay for travelling a distance of 25 km?

Solution:

Let be fixed charges = Rs.x

Let be per km charges = Rs.y

    X+10y=115--------(1)

    X+15y=155--------(2)

 By solving equation (1)

    X+10y=105

    10y=105-x

  Y=(105-x)/10--------(3)

 Now substitute y=105-x/10 in equation (2)

   X+15y=155

   x/1+15(105-x)/10=155

   10x+1575-15x/10=155

   1575-5x/10=155

   1575-5x=1550

   1575-1550=5x

   5x=25

   X=25/5=5

 X=5 substitute in equation (3)

  Y=105-x/10

  Y=105-5/10=100/10=10

   Y=10

 Fixed charges (x)=5

  Per km charges (y)=10

  25km charges 

Fixed charges+per km charges

  X+25y

  5+25(10)

  =5+250=255

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