Question

The taxi charges in a city consist of a fixed $2M$ charge together with the charge for the distance covered. For a distance of $10km$, the charge paid is $Rs105$ & for a journey of $15km$ the charge paid is $Rs155$. What is the fixed charges and the charge per $km$? How much does a person have to pay for travelling a distance of $25km$?

Answer 1

Given:

Fixed charge $=2M$

Let, charge per $km$ be $k$.

Case 1:

For a distance of $10km$ charge paid is $Rs.105$.

$\Rightarrow 2M+10k=105$ ---(1)

Case 2:

For a distance of $15km$ charge paid is $Rs.155$.

$\Rightarrow 2M+15k=155$ ---(2)

Lets do (1)-(2)

$2M+10k-2M-15k=105-155$

$\Rightarrow -5k=-50$

$\Rightarrow k=10$

i.e., Charge per $km$ is $Rs.10$.---(i)

Substitute $k=10$ in $2M+10k=105$

$\Rightarrow 2M+10\left(10\right)=105$

$\Rightarrow 2M+100=105$

$\Rightarrow 2M=105-100$

$\Rightarrow 2M=5$

i.e., Fixed chare is $Rs.5$.---(ii)

Now, Charge per $25km$ is,

$2M+25\times 10$

$=5+25\times 10$

$=5+250$

$=255$

Therefore, Charge per $25km$ is $Rs.255$.---(iii)