The taxi charges in a city consist of a fixed charge together with the charge for thedistance covered. For a distance of 10 km, the charge paid is ` 105 and for ajourney of 15 km, the charge paid is ` 155. What are the fixed charges and thecharge per km? How much does a person have to pay for travelling a distance of25 km?

To find the fixed charges and the charge per km, we can set up a system of equations using the given information.

Let's denote the fixed charge as "F" and the charge per km as "C".

From the first piece of information, we know that for a distance of 10 km, the charge paid is `105. This can be written as:

10C + F = 105 (Equation 1)

From the second piece of information, we know that for a journey of 15 km, the charge paid is `155. This can be written as:

15C + F = 155 (Equation 2)

Now, we can solve this system of equations to find the values of F and C.

Subtracting Equation 1 from Equation 2, we get:

(15C + F) - (10C + F) = 155 - 105

Simplifying, we have:

5C = 50

Dividing both sides by 5, we find:

C = 10

Now, we can substitute the value of C back into either Equation 1 or Equation 2 to find the value of F. Let's use Equation 1:

10(10) + F = 105

Simplifying, we have:

100 + F = 105

Subtracting 100 from both sides, we find:

F = 5

Therefore, the fixed charges are 5 and the charge per km is 10.

To find how much a person has to pay for traveling a distance of 25 km, we can use the charge per km value we found. Let's denote the total charge as "T".

We can use the formula:

T = 25C + F

Substituting the values we found, we have:

T = 25(10) + 5

Simplifying, we find:

T = 250 + 5

T = 255

Therefore, a person would have to pay `255 for traveling a distance of 25 km.