#### Question

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 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 + 10y = 105 … (i)

x = 105 – 10y

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

x + 15y = 155

Putting the value of x we get

105 – 10y + 15y = 155

5y = 155 – 105

5y = 50

Dividing by 5, we get

y = 50/5 = 10

Putting this value in equation (i) we get

x = 105 – 10 × 10

x = 5

People have to pay for traveling a distance of 25 km

= x + 25y

= 5 + 25 × 10

= 5 + 250

=255

A person have to pay Rs 255 for 25 Km.