Question

The taxi charges in Hyderabad are fixed, along with the charge for the distance covered. For a distance of 10 km, the charge paid is Rs. 220. For a journey of 15 km, the charge paid is Rs. 310
1) What are the fixed charges and charges per km?
2) How much does a person have to pay for travelling a distance of 25 km?

Answer 1

Hint:
Let $x$ be the fixed charge and let $y$ be the charge per km. then we need to form the equations bases on the given conditions. Solve the equations simultaneously using elimination or substitution to find the value of $x$ and $y$.

Complete step by step solution:
First of all, let $x$ be the fixed charge and let $y$ be the charge per km.
Then we will form equations based on the above conditions.
The fixed charge will be added to the product of the distance travelled and the charge per km.
Thus, the equations are formed as,
$
  x + 10y = 220 \\
  x + 15y = 310 \\
$
Now, we will solve the equations using the elimination method.
Subtract both the equations and solve for the value of $y$.
$ {\text{ }}x + 10y = 220 \\
  \underline { - x - 15y = - 310} \\
  {\text{ }} - 5y{\text{ }} = - 90 \\
  {\text{5}}y{\text{ = 90}} \\
\Rightarrow y = 18 \\
$
Substitute the value of $y$in any of the formed equations to find the value of $x$.
$
  x + 10\left( {18} \right) = 220 \\
  \Rightarrow x + 180 = 220 \\
  \Rightarrow x = 40 \\
$
In the second part of the question, we have to find the total amount paid after travelling a distance of 25 km.
The total amount of distance travelled is the fixed charge and then added to the product of the distance travelled and the charge per km.
$40 + 25\left( {18} \right) = 490$

Hence, a person will pay Rs. 490 to travel a distance of 25 km.

Note:
The equations can be solved by any method such as elimination or substitution. Many students make mistakes while formulating equations. Also, do not forget to add a fixed charge while calculating the total amount paid on distance travelled.