Form the pair of linear equations for the following problem and find their solution by 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?

Let ₹x be the fixed charge and ₹y be the charge for every distance covered.

Given,

For a distance of 10 km, the charge paid is ₹105.

x + 10y = 105 ……(1)

For a distance of 15 km, the charge paid is ₹ 155.

x + 15y = 155 …….(2)

Subtracting equation (1) from (2), we get :

⇒ x + 15y - (x + 10y) = 155 - 105

⇒ x - x + 15y - 10y = 50

⇒ 5y = 50

⇒ y = $\dfrac{50}{5}$ = 10.

Substituting value of y in equation (1), we get :

⇒ x + 10 × 10 = 105

⇒ x + 100 = 105

⇒ x = 5.

For 25 km charge, will be :

⇒ x + 25y = 5 + 25 × 10 = 5 + 250 = ₹255.

Hence, pair of linear equations are x + 10y = 105 and x + 15y = 155, where x is the fixed charge (in ₹) and y is the charge (in ₹ per km); x = 5, y = 10; and charge for 25 km = ₹255.