Question

A taxi ride in a city cost one rupee for the first $km$ and sixty paise for each additional $km$. The cost for each $km$ is incurred at the beginning the $km$ so that the rider pays for the whole $km$. What is the average cost for $2\frac{3}{4}km$ ?

Answer 1

Solution:-

Let $y$ be the total fare and $x$ be the total distance

Now according to the question:-

Fare for first kilometer $=Rs.1$

Fare for additional distance after first kilometer $=Rs.0.60\times (\text{total distance}-1)$

Total fare $=$ Fare for first kilometer $+$ fare for additional distance

$y=1+0.60(x-1)$

$y=1+0.6x-0.6$

$y=0.6x+0.4$

Now given that,

total distance travelled $\left(x\right)=2\frac{3}{4}=\frac{11}{4}=3(\because \text{cost for each km is incurred at the beginning of the km})$

$\therefore y=0.6\times 3+0.4=1.8+0.4=2.2$

$\therefore$ the average cost for $2\frac{3}{4}km=\frac{2.2}{\left(\frac{11}{4}\right)}=\frac{2.2\times 4}{11}=0.8$

Hence the average cost for $2\frac{3}{4}km$ is $Rs.0.8\text{per km}$.