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 $₹\ 105$ and for a journey of $15\ km$, the charge paid is $₹\ 155$. What are the fixed charges and the charge per $km$? How much does a person have to pay for travelling a distance of $25\ km$.

Given: For a distance of $10\ km$, the charge paid is $₹\ 105$ and for a distance of $15\ km$, the charge paid is $₹\ 155$.          

To do: To find the fix charges and also to find the charge paid by a person to travel $25\ km/h$.

Solution:

Let the fixed charge for taxi $=₹\ x$                  

And variable cost per km$=₹\ y$                  

Total cost $=$ fixed charge$+$variable charge                  

According to the Question,              

$x + 10y = 105$ ..... $( i)$                  

$x=105-10y$                

$x + 15y = 155$               

Putting the value of $x$ we get                  

$105-10y+15y=155$                  

$\Rightarrow 5y=155-105$                  

$\Rightarrow 5y=50$                  

$\Rightarrow y=\frac{50}{5}=10$              

Putting this value in equation $( i)$ we get                  

$x=105-10\times10$                  

$\Rightarrow x = 5$           

Cost for traveling a distance of $25\ km$                  

$=x+25y$                  

$=5+25\times10$                  

$=5+250$                  

$=₹\ 255$

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Updated on: 10-Oct-2022

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