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?

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?

Let        the fixed charge  for taxi    = Rs x

And      variable cost per Km          = Rs y

Total cost      = fixed charge + variable charge

Given that for a distance of 10 km, the charge paid is Rs 105

x + 10 y         = 105                          … (1)

                                                x          = 105 – 10 y

Given that for a journey of 15 km, the charge paid is Rs 155

x + 15 y          = 155

Plug the value of x we get

105 – 10 y + 15 y      = 155

5y        = 155 – 105

5y        = 50

Divide by 5  we get

                                                y    = 50 / 5           = 10

Plug this value in equation (1) we get

                                    x          = 105 – 10 * 10

                                    x          = 5

People have to pay for traveling a distance of 25 km

                                                = x + 25 y

                                                 = 5 + 25*10

                                                 = 5 + 250

                                                =255

              Answer pay for 25 Km is Rs 255