Question

Scooter charges consist of fixed charges and the remaining depending upon the distance traveled in kilometers. If a person travels $12km,$ he pays Rs. 45 and for travelling 20 $km,$ he pays Rs. $73.$ Express the above statements in the form of simultaneous equations and hence, find the fixed charges and the rate per km.

Answer 1

Let fixed charge $=Rs.x$ and charge per kilometer $=Rs.y$
According to the question, $x+12y=45\dots \left(i\right)$
and $x+20y=73\dots$ (ii)
On subtracting Eq. (i) from Eq. (ii), we get
$x+20y-x-12y=73-45$
$\Rightarrow 8y=28$
$\Rightarrow y=\frac{28}{8}=3.5$
On putting the value of $y=3.5$ in Eq. (i), we get
$x+12(3\cdot 5)=45$$\Rightarrow x+42=45$
$\Rightarrow x=45-42=3$
Hence, monthly fixed charges is Rs. $3$ and charge per kilometer is Rs. $3\cdot 5$