Question

The car hire charges in a city comprise fixed charges together with the charge for the distance covered. For a journey of 12 km, the charges paid is Rs. 89 and for a journey of 20 km the charge paid is Rs. 145. What will a person have to pay for travelling a distance of 30km?

Answer 1

Hint: The total amount a person has to pay would be the sum of the fixed charges and the cost (per km) in accordance to the total distance he has travelled.

Complete Step-by-Step solution:
Let us consider,
The total charge =$y$
The fixed charge = $c$
Charge per Km = $x$
If a person travels $zkm$, the charge is
$ \Rightarrow y = c + zx$
Since we know that,
Charge = fixed charge $ + $ Charge per $Km$ $ \times $ No. of $Km $ travelled

Given that
For $12Km$ charge = $Rs.89$
Let us apply the formula of charge then we get
$89 = c + 12z \to (1)$
For $20Km$ charge = $Rs.145$
 On applying the formula of charge we get
$145 = c + 20z \to (2)$
On solving equation $(1) \& (2)$ we get
$  z = Rs.7/km $
$  c = Rs.5  $
By using charge formula
Charge for $30Km$ will be $y = Rs(5 + 7x)$
Where $x$ is no. of kilometres travelled and here $x = 30$
$\therefore $Charge for $30Km$=$Rs.(5 + 7 \times 30) = Rs.215$

Note: When solving problems like these, make sure to add the fixed charge too and do not just calculate the cost per km in accordance to the kilometres travelled and leave the answer.