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 kilometer? How much does a person have to pay for traveling a distance of 25 km?

• A. Fixed charge is Rs.$5$ and the charge per kilometer is Rs.$10$ For $25$ km person have to pay Rs.$255$.
• B. Fixed charge is Rs.$10$. and the charge per kilometer is Rs.$5$. For $25$ km person have to pay Rs$135$.
• C. Fixed charge is Rs. $15$ and the charge per kilometer is Rs. $5$. For $25$ km person have to pay Rs.$140$.
• D. Fixed charge is Rs.$50$. and the charge per kilometer is Rs$20$. For $25$ km person have to pay Rs$50$

Answer 1

The correct option is A Fixed charge is Rs.$5$ and the charge per kilometer is Rs.$10$ For $25$ km person have to pay Rs.$255$.

Let fixed charge be Rs x and charge per km be Rs y.
$\Rightarrow x+10y=105...\left(1\right)$
$\Rightarrow x+15y=155..\left(2\right)$.

Now From eq 2
$\Rightarrow 15y=155-x$

$\Rightarrow y=\frac{155-x}{15}...\left(3\right)$

Substituting y from eq3 in eq1

$\Rightarrow x+\frac{10(155-x)}{15}=105$

$\Rightarrow 15x+1550-10x=1575$
$\Rightarrow 5x=1575-1550$
$\Rightarrow 5x=25$
$\Rightarrow x=5$

Substituting x in eq2
$\Rightarrow 5+15y=155$
$\Rightarrow 15y=155-5$
$\Rightarrow 15y=150$
$\Rightarrow y=10$

Hence $x=5$ and $y=10$

Fixed charge is Rs.55 and the charge per kilometer is Rs.1010

For 2525 km person have to pay = $5+10\times 25=255Rs.$