Form the pair of linear equations for the following problem and find their solution by the substitution method.
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 ₹ $105$ and for a journey of $15 \, km$,the charge paid is ₹ $155$. What are the fixed charges and the charge per $km$? How much does a person have to pay for travelling a distance of $25 \, km$?

(D) Let the fixed charge be ₹ $x$ and the charge per $km$ be ₹ $y$.
According to the given information:
$x + 10y = 105$ $(1)$
$x + 15y = 155$ $(2)$
From equation $(1)$,we obtain:
$x = 105 - 10y$ $(3)$
Substituting the value of $x$ from equation $(3)$ into equation $(2)$:
$(105 - 10y) + 15y = 155$
$105 + 5y = 155$
$5y = 155 - 105$
$5y = 50$
$y = 10$
Substituting $y = 10$ in equation $(3)$:
$x = 105 - 10(10)$
$x = 105 - 100$
$x = 5$
Thus,the fixed charge is ₹ $5$ and the charge per $km$ is ₹ $10$.
For a distance of $25 \, km$,the total charge is:
$x + 25y = 5 + 25(10) = 5 + 250 = ₹ 255$.